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A Glossary for IWGS (Auto-Generated)

Michael Kohlhase , FAU Erlangen-Nürnberg https://kwarc.info/kohlhase July 1, 2021

Preface

This document contains an English glossary for the course Informatische Werkzeuge in den Geistes- und Sozialwissenschaften at FAU Erlangen-Nürnberg (IWGS). It is automatically generated from the sources of the IWGS course notes and should be up-to-date with the course progress. The glossary contains definitions for all technical terms used in the course, both theones defined in the course, as well as the ones presupposed. The latter should be relatively few,since IWGS is intended as a beginner’s course.

1 1 Glossary for IWGS

Given a description logic , a D-ontology consists of D-ontology–a terminology (or TBox): concepts and roles and a of concept axioms that describe them, and – assertions (or ABox): a set of individuals and statements about concept membership and role relationships for them.

To make the role of arguments extremely clear, we write functions in λ-notation. For f = {(x, E) | x ∈ X}, where E is an expression, we write λx ∈ X.E.

n n-dim Cartesianλ-notation space n-dim Cartesian space: A := {⟨a1, . . . , an⟩ | 1≤i≤n ⇒ ai ∈ A}, call ⟨a1, . . . , an⟩ a vector n-dimensional Cartesian space An n-dimensional Cartesian A1 × ... × An is called a n-dimensional Cartesian space n n over A (and denoted A ) iff Ai = A for some set A for all i. We call ⟨a1, . . . , an⟩ ∈ A a vector. n-fold Let A := {Ai | 1≤i≤n} be a collection of sets, then the n-fold Cartesian product A1 × ... × An is {⟨a1, . . . , an⟩ | ai ∈ Ai for all 1≤i≤n}, we call ⟨a1, . . . , an⟩ ∈ A1 × ... × An an n-. n is called the dimension of A1 × ... × An. n-fold Cartesian product n-fold Cartesian product: A1 × ... × An := {⟨a1, . . . , an⟩ | ∀ i 1≤i≤n ⇒ ai ∈ Ai}, call ⟨a1, . . . , an⟩ an n-tuple

n-fold composition We write the n-fold composition of the relation as Rn and define it by R1 := R and Ri + 1 := {S ◦ R | S ∈ Ri}

n-tuple Defined along with n-fold Cartesian product n-tuple Defined along with n-fold Cartesian product

p-closure Let p be a properties and R ⊆ A × B a relation, then we call the smallest (in terms of the ⊆) relation R′ ⊇ R that has property p the p-closure of R.

p-closure Let p be one of the properties above and R be a relation, then we call the smallest relation ⊇ R′R (in terms of the ⊆) that has property p the p-closure of R. ABox Defined along with terminology ABox Defined along with ontology ABox Defined along with D-ontology ADT See abstract data type AI See Artificial Intelligence AI Defined along with Artificial Intelligence AI See Artificial Intelligence

AJAX JSON is for JavaScript as (nested) dictionaries are for python. – The browser can directly read JSON and use it via JavaScript. – AJAX =b JavaScript can query the backend for JSON data to update parts of the DOM; .(lightweight interaction)

2 AJAX See Ajax

ALU Defined along with central processing unit API See application programming interface

Ajax Ajax, (also AJAX; short for “Asynchronous JavaScript and XML”) is a set of client-side techniques for creating asynchronous web applications.

American Standard Code for Information Interchange The American Standard Code for Information Interchange( ASCII) is a character code that assigns characters to 0-127

Code ···0 ···1 ···2 ···3 ···4 ···5 ···6 ···7 ···8 ···9 ···A ···B ··· ···D ···E ···F 0··· NUL SOH STX ETX EOT ENQ ACK BEL BS HT LF VT FF CR SO SI 1··· DLE DC1 DC2 DC3 DC4 NAK SYN ETB CAN EM SUB ESC FS GS RS US 2··· !"#\$%&’()*+,-./ 3··· 0123456789:;<=>? 4··· @ABCDEFGHIJKLMNO 5··· PQRSTUVWXYZ[\]^_ 6··· ‘abcdefghijklmno 7··· p q r s t u v w x y z { | } ~ DEL

Anti-Counterfeiting Trade Agreement The Anti-Counterfeiting Trade Agreement (ACTA) is a multinational treaty on interna- tional standards for intellectual property rights enforcement.

Artificial Intelligence Artificial Intelligence(AI) is intelligence exhibited by machines

Artificial Intelligence Artificial Intelligence(AI) is a sub- of Computer Science that is concerned with the automation of intelligent behavior.

Artificial Intelligence Artificial Intelligence(AI) studies how we can make the computer do things that humans can still do better at the moment.

Berne convention The Berne convention process is a of international treaties that try to harmonize internationalIP laws. It started with the original Berne convention 1886 and went through revision in 1896, 1908, 1914, 1928, 1948, 1967, 1971, and 1979. Boolean Defined along with

CC provision The CC licenses stipulate that (cf. http://www.creativecommons.org)

– Creators retain the copyright on their works. – Creators license their works to the world with under the CC provisions: +/- attribuition(must reference the author) +/- commercial use(can be restricted) +/- works(can allow modification) +/- share alike(copyleft)(modifications must be donated back)

CIDOC CRM CIDOC CRM provides an extensible ontology for concepts and information in cultural heritage and museum documentation. It is the international standard (ISO 21127:2014) for the controlled exchange of cultural heritage information. The central classes include – space-time specified by title/identifier, place, era/period, time-span, and relationship to persistent items – events specified by title/identifier, beginning/ending of existence, participants (people, either individually or in groups), creation/modification of things (physical or concep- tional), and relationship to persistent items

3 – material things specified by title/identifier, place, the information object the material thing carries, part-of relationships, and relationship to persistent items – immaterial things specified by title/identifier, information objects (propositional or symbolic), conceptional things, and part-of relationships CLI See command-line interface CMS See content management system CPU See central processing unit CS See computer science CWA See closed world assumption

Cartesian product The Cartesian product of an arbitrary (possibly infinite) indexed family of sets is defined Q S as i∈I Xi := {f : I → i∈I Xi | f(i) ∈ Xi}.

Cartesian product Cartesian product: A × B := {(a, b) | a ∈ A ∧ b ∈ B}, call (a, b) pair.

Cascading Style Sheets The Cascading Style Sheets(CSS), is a style sheet language that allows authors and users to attach style (e.g., fonts, colors, and spacing) to HTML and XML documents. Content MathML Defined along with Mathematics Markup Language

Creative Commons license The Creative Commons licenses are – a common legal vocabulary for sharing content – to create a kind of “public domain” using licensing – presented in three layers (human/lawyer/machine)-readable

DAG We will sometimes use the abbreviation DAG for “directed acyclic graph”. DAG Defined along with cyclic DBMS See management system DDL See data definition language DELETE Defined along with method DOM See document object model DTM Defined along with nondeterministic Turing machine DUPLICATE Defined along with issue ERD See entity relationship diagram

EU directive A EU directive is a legal act of the European Union which requires member states to achieve a particular result without dictating the means of achieving that result.

EU regulation A EU regulation is a legal act of the European Union that becomes immediately enforceable as law in all member states simultaneously.

Erlangen CRM/OWL Erlangen CRM/OWL implements CIDOC CRM in OWL Extensible Markup Language See XML

FAIR Research data should be FAIR:

4 – Findable: easy to identify and find for both humans and computers, e.g. with metadata that facilitate searching for specific datasets, – Accessible: stored for long term so that they can easily be accessed and/or downloaded with well-defined access conditions, whether at the level of metadata, or at thelevelof the actual data, – Interoperable: ready to be combined with other datasets by humans or computers, without in the meanings of terms and values, – Reusable: ready to be used for future research and to be further processed using com- putational methods. Consensus in the research data community; for details see [FAIR; WilDumAal:FAIR16].

FIXED Defined along with issue number FLOSS See Free/Libre/Open-Source Software

Free/Libre/Open-Source Software Free/Libre/Open-Source Software(FLOSS or just open source) is software that is and licensed via licenses that ensure that its source code is available. GDPR See General Data Protection Regulation

GET Defined along with method GFM See GitHub flavored markdown

GIT flow [gitflow:url] suggests GIT flow, which includes: – A main branch called main that all other branches merge into. – New functionality is developed “feature-by-feature” on feature branches. – A development branch (usually called devel) that integrates all feature branches and is merged into master once the integrated functionality is stable. – (possibly) release branches for every release; they collect bugfixes, but no new features.

GND But there are some sources that are useful – the GND(Gemeinsame Normdatei[ GND:on]), an authority file for personal/corporate names and keywords from literary catalogs, – geonames[ geonames:on], a geographical database with more than 25M names and locations – Wikipedia Gemeinsame Normdatei See GND

General Data Protection Regulation The General Data Protection Regulation(GDPR) is a EU regulation created in 2016 to harmonize information privacy regulations within Europe. The GDPR applies to data controllers, i.e organizations that process personal data of EU citizens (the data subjects). It sanctions violations to GDPR mandates with substantial punishments – up to 20Me or 4% of annual worldwide turnover.

General Public License The General Public License (GPL) is a copyleft license for FLOSS software originally writ- ten by Richard Stallman in 1989. It requires that the source code of GPL-licensed software be made available.

5 GitHub flavored markdown GitHub flavored markdown(GFM) is a markdown dialect extended for the use in GIT-based issue tracking systems; see [GFM:on] for the specification.

Gregorian calendar The Gregorian calendar is a solar calendar that takes the birth of Christ is taken as the year 1 and has a complicated rule for leap years: Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100; the centurial years that are exactly divisible by 400 are still leap years. HTML See HyperText Markup Labnguage

HTML5 See HyperText Markup Language HTTP See Hypertext Transfer Protocol

HTTP authentication HTTP basic authentication introduces a HTTP header Authorization for base64-encoded pairs ⟨⟨username⟩⟩:⟨⟨password⟩⟩ and a couple of challenge/response messages.

HTTP request Defined along with user agent HTTPS See Hypertext Transfer Protocol Secure

HyperText Markup Labnguage The HyperText Markup Labnguage(HTML), is a representation format for web pages[ W3C:html5].

HyperText Markup Language The HyperText Markup Language(HTML5), is believed to be the next generation of HTML. It is defined by the W3C and the WhatWG.

Hypertext Transfer Protocol The Hypertext Transfer Protocol(HTTP) is an application layer protocol for distributed, collaborative, hypermedia information systems.

Hypertext Transfer Protocol Secure Hypertext Transfer Protocol Secure(HTTPS) is an extension of the Hypertext Transfer Protocol(HTTP) for secure communication over a computer network. HTTPS achieves this by running HTTP over a TLS connection.

6 IANA See Internet Assigned Numbers Authority

ICH Defined along with cultural heritage IDE See integrated development environment INVALID Defined along with issue number

IP See Internet Protocol

IP address An IP address is a numerical label that is assigned to devices participating in a computer network, that uses the Internet Protocol for communication between its nodes. IPv4 See Internet Protocol Version 4 IPv4 address Defined along with Internet Protocol Version 4

IPv6 See Internet Protocol Version 6 IPv6 address Defined along with Internet Protocol Version 6 IRI See internationalized resource identifier

ISO-Latin 16 Extensions of ASCII to 8- (256 characters) ISO-Latin1 =b “Western European”, ISO-Latin 6 =b “Arabic”,ISO-Latin 7 =b “Greek”. . .

International System of Units The International System of Units(SI) is the modern form of the metric system and is gen- erally a system of units of measurement devised around seven units and corresponding dimensions.

Internet The Internet is a worldwide computer network that connects hundreds of thousands of smaller networks. (The mother of all networks)

Internet Assigned Numbers Authority The global IP address space allocations are managed by the Internet Assigned Numbers Authority(IANA), delegating allocate IP address blocks to five Regional Internet Registries (RIRs) and further to Internet service providers (ISPs).

Internet Protocol The Internet Protocol(IP) is a protocol used for communicating data across a packet- switched internetwork. The Internet Protocol defines addressing methods and structures for datagram encapsulation. The Internet Protocol also routes data packets between networks

Internet Protocol Version 4 The Internet mainly uses Internet Protocol Version 4(IPv4)[ RFC760], which uses 32-bit numbers (IPv4 address es) for identification of network interfaces of Computers.

Internet Protocol Suite The Internet Protocol Suite (commonly known as TCP/IP) is the set of communications protocols used for the Internet and other similar networks. It structured into 4 layers.

Internet Protocol Version 6 Internet Protocol Version 6(IPv6)[ DeeHin:RFC2460], which uses 128-bit numbers (IPv6 address es) for identification. Isa-Hierarchy See terminology

JQuery JQuery is a feature-rich JavaScript library that simplifies tasks like HTML document traver- sal and manipulation, event handling, animation, and Ajax.

JSON JSON(JavaScript Object Notation is an open standard file format, for interchange of struc- tured data. JSON uses human-readable text to store and transmit data objects consisting of attribute–value pairs and .

7 JavaScript JavaScript is an object-oriented scripting language mostly used to enable programmatic acce ss to the DOM in a web browser. JavaScript Object Notation See JSON

Kleene closure The of passing from an alphabet A to A∗ is called Kleene closure, Kleene opera- tion, or Kleene star. The operation ·+ is called Kleene plus. Kleene operation See Kleene closure Kleene plus See Kleene closure Kleene star See Kleene closure

Kronecker delta The Kronecker delta is a of two . The function is 1 if the variables are equal, and 0 otherwise:  1 (i = ) δ := if i j 0 else

Landau set The three Landau sets O(g), Ω(g), Θ(g) are defined as

– O(g) = {f | ∃ k>0 f ≤a k · g}

– Ω(g) = {f | ∃ k>0 f ≤a k · g} – Θ(g) = O(g) ∩ Ω(g)

Landau set Let g : N → N, then we define the three Landau sets O(g),Ω(g),Θ(g) as

– O(g) := {g : N → N | ∃ k>0 f ≤a k · g} – Ω(g) := {g : N → N | ∃ k>0 f ≥a k · g} – Θ(g) := O(g) ∩ Ω(g)

If G ∈ {O(g), Ω(g), Θ(g)}, we often say that f : N → N is (of complexity) G, iff f ∈ G, accordingly we often write f = G by a certain abuse of notation. Given a particular function, e.g. g : N → N; n 7→ n3, we often write O(g) as O(n3), and analogously for Ω(g) and Θ(g).

Let’s Encrypt Let’s Encrypt is a not-for-profit certificate authority that does this and issues free TLS certificates. (to encourage HTTPS adoption) MAC address See media access control address

MathTalk Abbreviations for Mathematical statements in MathTalk – ∧ and ∨ are common notations for and and or – not is in mathematical statements often denoted with ¬ – ∀ x P (∀ x ∈ S P ) stands for condition P holds for all x (in S) – ∃ x P (∃ x ∈ S P ) stands for there exists an x (in S) such that proposition P holds – ̸∃ x P (̸∃ x ∈ S P ) stands for there exists no x (in S) such that proposition P holds – ∃1 x P (∃1 x ∈ S P ) stands for there exists one and only one x (in S) such that proposition P holds – iff as abbreviation for if and only if, symbolized by ⇔ – the symbol ⇒ is used a as shortcut for implies

8 Mathematics Markup Language The Mathematics Markup Language (MathML) is an integrated framework for content and presentation in web-based mathematics. Presentation MathML covers the basic font, box, grouping primitives for presenting the two-dimensional layout of mathematical formulae Content MathML provides the an infrastructure for marking up the functional/logical struc- ture of formulae as applications, variables, constants, and binding expressions.

Matrix addition is defined pointwise: Given two n×m matrices A := [ai,j]1≤i≤n,1≤j≤m and B := [bi,j]1≤i≤n,1≤j≤m, the matrix sum A + B is defined as [ai,j + bi,j]1≤i≤n,1≤j≤m.

Model A first-order Model M = ⟨Dι, I⟩ consists of a universe Dι and an interpretation I. NIC See network interface controller NTM See nondeterministic Turing machine

NoSQL Defined along with mongoDB ODF Defined along with Office Open XML OOP See object-oriented programming OOXML See Office Open XML

OS See operating system OWA Defined along with closed world assumption

Office Open XML Popular word processors include – MS Word, an elaborated word processor for Windows, whose native format is Office Open XML(OOXML; file extension .docx). – OpenOffice and LibreOffice are similar word processors using the ODF format (Open Office Format; file extension .odf) natively, but can also import other formats.. – Pages, a word processors for Mac OS X it uses a proprietary format. – Office Online and GoogleDocs are browser-based real-time collaborative word pro- cessors.

Open Data Commons Defined along with open Open Office Format Defined along with Office Open XML PDF See Protable document format

PERL CGI is a scripting language with good string manipulation facilities. PERL CGI is an early server-side scripting framework based on this. PGS work Defined along with copyrightable work

PHP PHP (originally “Programmable Home Page Tools”, later “PHP: Hypertext Processor”) is a server-side scripting language with a C-like syntax. PHP code is embedded into HTML via special “tags”

PII See personally identifiable information POST Defined along with method PUT Defined along with method

9 Peano axioms The following set of axioms are called the Peano axioms( ∗1858, †1932) Presentation MathML Defined along with Mathematics Markup Language

Proposition Propositions: A ∈ wff o(Σ) (denote truth values: type o)

p i 1 k – if p ∈ Σk and A ∈ wff ι(Σι) for i≤k, then p(A ,..., A ) ∈ wff o(Σ),

– if A, B ∈ wff o(Σ) and X ∈ Vι, then T , A ∧ B, ¬ A, ∀X A ∈ wff o(Σ).

Protable document format Protable document format(PDF) is a document format that mixes text and graphics with a variety of content including logical structuring elements, interactive elements such as anno- tations and form-fields, layers, rich media (including video content), and three-dimensional objects using U3D or PRC, and various other data formats. The PDF specification also provides for encryption and digital signatures, file attachments, and metadata to enable workflows requiring these features. RCS See revision control system RDBMS See relational database management system RDF graph Defined along with statement RDF store See triplestore REPL See read–eval–print loop

RGB Colors are usually represented in RGB format, i.e. as triples ⟨R, G, B⟩ with three channels (also called bands).

RTFM RTFM( =b “read those fine manuals”)

RTFM RTFM( =b “read the fine manuals”) RWD See responsive web design

Resource Description Framework The Resource Description Framework( RDF) is a framework for describing resources on the web. It is an XML vocabulary developed by the W3C. SI See International System of Units

SQL SQL, the structured query language is a domain-specific language for managing data held in a RDBMS. SQL instructions are directly executed by the RDBMS to change the database state or compute answers to SQL queries.

SQL injection attack We call this an SQL injection attack. SQL-sanitizes Defined along with parameter substitution

SQLite shell this opens a command line interpreter: the SQLite shell.(all DBs have one) test it with .help that tells you about more “dot commands”. SVG See Scalable Vector Graphics

Scalable Vector Graphics Scalable Vector Graphics(SVG) is an XML-based markup format for vector graphics.

Simple Mail Transfer Protocol The Simple Mail Transfer Protocol(SMTP) is a for electronic mail transmission based on telnet. Skolem constant Defined along with first-order signature

10 Sobel filter Given a 3 × 3 matrix M, the Sobel filter computes a new pixel value by getting the pixel value of each neighbor in 3x3 window, multiply with the components in M and adding everything up. TBox See terminology TBox Defined along with ontology

TBox An TBox is a finite set of concept definitions and concept axioms. It iscalled acyclic, iff it does not contain recursive definitions. TBox Defined along with D-ontology TCP/IP See Internet Protocol Suite TLS See Transport Layer Security

Transmission Control Protocol The internet protocol mainly uses suite the Transmission Control Protocol( TCP) and User Datagram Protocol( UDP) protocols at the transport layer.

Transport Layer Security Transport Layer Security(TLS) is a cryptographic protocol designed to provide privacy – by symmetric cryptography – and authentication – by public key cryptography – over a computer network.

Turing complete An information processing system is said to be Turing complete or computationally uni- versal if it can be used to simulate any Turing machine.

Turing machine A Turing machine consists of

– An tape with infinitely many cells, each of which contains a symbol from a finite al- phabet A with #(A)≥2. – A head that can read/write symbols on the tape and move left/right. – A state register that stores the state of the Turing machine. The set of states is finite, the state register is initialized with a special start state. – An action table (or program ]) that – given the symbol it has just read from the tape and the state it is currently in – specifies the next action, i.e. what symbol to write, how to move the head and the next state. If no entry applicable the machine halts. Turing-acceptable See recursively enumerable

Turing-recognizable See recursively enumerable UCS See universal character set UI See user interface UNA Defined along with closed world assumption

URI See uniform resource identifier URI decoding Defined along with URI encoding

URI encoding URI encoding maps non-ASCII characters to a ASCII strings: 1. map character to its UTF-8 representation 2. represent each of the UTF-8 representation by three characters. 3. The first character is the percent sign (%),

11 4. and the other two characters are the hexadecimal representation of the byte.

URI decoding is the dual operation.

URL A uniform resource locator(URL) is a URI that that gives access to a web resource, by specifying an access method or location. All other URIs are called uniform resource names (URN). URL See uniform resource locator

URN Defined along with uniform resource locator

UTF-8 The UTF-8 encoding encodes each character in one to four octets (8-bit ): 1. One byte is needed to encode the 128 US-ASCII characters (Unicode range U+ 0000 to U+ 007F ). 2. Two bytes are needed for Latin letters with diacritics and for characters from Greek, Cyrillic, Armenian, Hebrew, Arabic, Syriac and Thaana alphabets (Unicode range U+ 0080 to U+ 07FF ). 3. Three bytes are needed for the rest of the Basic Multilingual Plane (which contains virtually all characters in common use). 4. Four bytes are needed for characters in the other planes of Unicode, which are rarely used in practice.

Universe We fix the Universe Do = {T, F} of truth values. User Datagram Protocol Defined along with Transmission Control Protocol WCMS Defined along with content management system WFH See work made for hire

WONTFIX Defined along with issue number WORKSFORME Defined along with issue number WWW See World Wide Web

WWWeb See World Wide Web

WissKI WissKI is a virtual research environment (VRE) for managing scholarly data and docu- menting cultural heritage.

WissKI commons We call the part of this resource that can be created by aggregating WissKI exports the WissKI commons.

World Wide Web The World Wide Web(WWW or WWWeb) is an open source information space where documents and other web resources are identified by URLs, interlinked by hypertext links, and can be accessed via the Internet.

XHTML XHTML is the XML version of HTML.(just make it valid XML)

XML XML (short for Extensible Markup Language) is a framework for markup formats for electronic documents and structured data.

XML document tree The XML document tree is made up of element nodes, attribute nodes, text nodes(and namespace declarations, comments,. . .)

12 XML literal We call any string that is well-formed XML an XML literal.

XML namespace An XML namespace is a string that identifies an XML vocabulary. Every element and attribute name in XML consists of a local name and a namespace.

XML path language The XML path language(XPath) is a language framework for specifying fragments of XML trees. XPath See XML path language

absolute URI To distinguish them from relative URIs, we call URIs absolute URIs.  r if r≥0 The absolute value |r| of an integer r is defined as . − (r) else

a |a| absolute value The absolute value |r| of an b is defined as |b| .

absolute value Real absolute value, addition, , , , and exponentiation, roots, r-th roots, and the ordering relations are extended to the real numbers, so that they respect limits.  r if r≥0 absolute value The absolute value |r| of a number r is defined as . −(r) else

abstract data type An abstract data type(ADT) is a mathematical model for a data types, which specifies a container by its behavior from the point of view of a user of the data, specifically in terms of possible value, possible operations on data of this type, and the behavior of these operations. accept Defined along with report

accepted unit Some units that have important contemporary application worldwide, or are otherwise commonly encountered worldwide and can be expressed as scalar multiples of derived units. They have been given the status of accepted units in theSI system. accepting Defined along with current cell accepting state Defined along with nondeterministic Turing machine

accepts A Turing machine M acceptsa word w (in n steps), if it halts (after n steps) with an accepting configuration on a tape that encodes W , and it rejects w otherwise. M accepts a formal language L (in n steps), iff it accepts all words w ∈ L (in n steps). If M is total, then we say that decides L (in n steps).

access control Access control is the selective restriction of access to a resource, access management de- scribes the corresponding process. access management Defined along with access control

accessible Defined along with FAIR action Defined along with Turing machine action table Defined along with Turing machine

acyclic Defined along with TBox acyclic Defined along with cyclic

13 acyclic Defined along with cyclic

addition Addition is extended to the integers by defining the sum as   |a| + |b| if a, b ∈ N  ( − (|a| + |b|) a, b ∈ − a + b := if Z |a| + ( − ( |b| )) if (a≥b)   |b| + ( − ( |a| )) if (a

a c a·d + b·c addition We define addition on the rational numbers: the sum b + d is b·d . addition Defined along with absolute value

addition Addition + computes the sum of a + b of natural numbers a and b. It defined by the equations x + 0 = x and x + s(y) = s(x + y), where s is the .

addition Addition + computes the sum of a + b of numbers a and b.

addition operation We “define” the addition operation ⊕ procedurally (by an ) – adding zero to a number does not change it. written as an equation: n ⊕ o = n – adding m to the successor of n yields the successor of m ⊕ n. written as an equation: m ⊕ s(n) = s(m ⊕ n) admits weakening Defined along with derivation relation

algorithm An algorithm is a formal or informal specification for solving a problem by executing afinite of instructions (concrete or imaginary/abstract) information processing systems.

alpha We introduce a fourth channel: A (for alpha). Alpha is the opacity (inverse of transparency). A pixel is now ⟨R, G, B, A⟩. alphabet Defined along with formal language

alphabet An alphabet A is a finite set; we call each element a ∈ A a character, and an n-tuple of n s ∈ A a word (or string) of over A. We will often write a string ⟨c1, . . . , cn⟩ as "c1 . . . cn" 0 or even as c1 . . . cn. We write the empty word(empty string) in A with ϵ. alphabet Defined along with nondeterministic Turing machine amount Defined along with length

ancestor The ancestor and descendant relations are the transitive closures of the parent and child relations respectively.

anonymized Error: The defi does not appear to be inside a definition environment. line23:18 anonymous function python also allows to make anonymous functions via the lambda constructor for function objects:

14 lambda (p1,...,pn): ⟨⟨expr⟩⟩

anti-aliasing On the edges of ?ex.rasterization?, we see pixels whose barycenter is outside the triangle but that are colored in a very light variant of the adjoining pixels. This technique is called anti-aliasing and is used to make the jagged lines created by rasterization less noticeable to the human eye. anti-reflexive Defined along with reflexive antisymmetric Defined along with symmetric antisymmetric Defined along with reflexive app Defined along with application software application Defined along with application software application Defined along with partial function application Defined along with expression language

application layer The application layer of the internet protocol suite contains all protocols and methods that fall into the realm of process-to-process communications via an Internet Protocol (IP) net- work using the Transport Layer protocols to establish underlying host-to-host connections.

application ontology A WissKI application ontology is one that extends CIDOC CRM, without changing it. application operator Defined along with applicative structure application programming interface An application programming interface(API) is an interface that defines interactions be- tween multiple software intermediaries. It defines the kinds of calls or requests that canbe made, how to make them, the data formats that should be used, the conventions to follow, etc.

application software Application software is a program or of programs (individually called an application or app) designed for end users.

applicative structure Let U be a set, and let @: U × U ⇀ U and Λ: U → U ⇀ U partial functions, such that ((aΛb)@a) = b, then we call A := ⟨U, @, Λ⟩ an applicative structure. U is called the universe, @ the application operator, and Λ the binding operator of A. arbitrary Defined along with variable arc Defined along with graph archaic Defined along with periodization architectural work Defined along with copyrightable work area Defined along with image map argument Defined along with subroutine argument Defined along with partial function argument Defined along with expression language /logic unit Defined along with central processing unit

A python function is defined by a code snippet of the form

15 def f (p1,...,pn): """docstring, what does this function do on parameters :param pi: document arguments} """ ⟨⟨body⟩⟩ # it can contain p1, . . . , pn, and even f return ⟨⟨value⟩⟩ # value of the function call (e.g text or number) ⟨⟨more code⟩⟩

– the indented part is called the body of f,( : whitespace matters in python)

– the pi are called parameters, and n the arity of f.

A function f can be called on arguments a1, . . . , an by writing the expression f(a1, ..., an). This executes the body of f where the (formal) parameters pi are replaced by the arguments ai. arity Defined along with subroutine

assertion We define the assertions for ALC – a: φ (a is a φ) – a R b (a stands in relation R to b) assertions make up the ABox in ALC. assertion Defined along with D-ontology assertions Defined along with terminology

assertions Defined along with ontology assign Defined along with variable assignment assign Defined along with report

assignee Defined along with issue number associative array See dictionary asymmetric Defined along with symmetric asymmetric Defined along with reflexive asymmetric-key cryptosystem In an asymmetric-key cryptosystem, the key needed to encrypt a message is different from the key for decryption. Such a method is called a public-key cryptosystem if the decryption key (the private key) is very difficult to reconstruct from encryption key (called the public key). We speak of a (cryptographic) key pair. asymptotically bounded Let f, g : N → N, we say that f is asymptotically bounded by g, written as f ≤a g, iff there is an n0 ∈ N, such that f(n)≤g(n) for all n>n0. asymptotically bounded Let f, g : N → N, we say that f is asymptotically bounded by g (write f ≤a g), iff there is an n0 ∈ N, such that f(n)≤g(n) for all n>n0.

asynchronous A process p is called asynchronous, iff the parent process (i.e. the one that spawned p) continues processing without waiting for p to terminate. atom See atomic

16 atomic Propositional formulae without connectives are called atomic (or an atoms) and complex otherwise.

atomic formula Call formulae without connectives or quantifiers atomic else complex. attachment Defined along with issue atto Defined along with prefixes

attribuition Defined along with CC provision attribute Defined along with opening tag attribute Defined along with relational database management system attribute Defined along with entity relationship diagram

attribute Defined along with object-oriented programming attribute node Defined along with XML document tree audiovisual work Defined along with copyrightable work aural markup Defined along with visual markup

authentication Authentication is the process of ascertaining that somebody really is who they claim to be.

authentication Authentication is the process of ascertaining that somebody really is who they claim to be. authentication factor Authentication can be performed by assertaining an authentication factor, i.e. testing for something the user – knows, e.g. a password or answer to a security question – kwowledge factor – has, e.g. an ID card, key, implanted device, software token, – ownership factor – is or does, e.g. a fingerprint, retinal pattern, DNA sequence, or voice – inheritance factor. authority Defined along with uniform resource identifier authorization Defined along with permission level

authorization Authorization refers to a set of rules that determine who is allowed to do what.

auxiliary storage See secondary storage

availability control Availability control: Personal data have to be protected against loss and accidental destruction. ( physical/building safety, backups) ; axiom Defined along with ontology

axiom An axiom (or postulate) is a statement about mathematical objects that we assume to be true.

back end Defined along with front end band Defined along with RGB bare See headless

base Defined along with positional number system

17 base Defined along with positional number system base Defined along with exponentiation base Defined along with exponentiation base Defined along with positional number system base Defined along with exponentiation base Defined along with exponentiation base Defined along with

base equation Error: The defi does not appear to be inside a definition environment. line75:3 base name Defined along with file system base set Defined along with

base set We call a structure ⟨S, ≤⟩ of a set S (the base set) equipped with a preorder r an preordered set or proset. base unit Defined along with International System of Units

base64 base64 is a group of binary-to-text encoding schemes that represent binary data in an ASCII string format by translating it into a radix-64 representation. Each Base64 digit represents exactly 6 of data. basic multilingual plane Most (non-Chinese) characters have code points in [1, 65536] (the basic multilingual plane). begin tag Defined along with tag biimplication Defined along with formulae bijection Defined along with bijective bijective Defined along with injective

bijective A function f : S → T is called bijective (or a bijection or a one-to-one correspondence), iff f is injective and surjective. binary Defined along with source binary Defined along with unary

binary A code is a called binary iff B = {0, 1}. binary file Defined along with text file

binary The following binary unit prefix es are used for because they are similar to the SI unit prefixes.

prefix symbol 2n ~SI prefix Symbol kibi Ki 210 1024 kilo k mebi Mi 220 1048576 mega M gibi Gi 230 1.074 × 109 giga G tebi Ti 240 1.1 × 1012 tera T pebi Pi 250 1.125 × 1015 peta P exbi Ei 260 1.153 × 1018 exa E zebi Zi 270 1.181 × 1021 zetta Z yobi Yi 280 1.209 × 1024 yotta Y

18 binding Defined along with expression language binding operator Defined along with applicative structure

bit A bit (a contraction of “binary digit”) is the basic unit of capacity of a data storage device or communication channel. The capacity of a system which can exist in only two states, is one bit (written as 1 b) blank symbol Defined along with nondeterministic Turing machine

blended learning Blended learning is an approach to education that combines online educational materials and opportunities for interaction online with traditional place-based classroom methods.

block Drupal allows to configure web pages modularly from content blocks, which can be – static content, i.e. supplied by a module, – user-supplied content, or – views, i.e. listings of content fragments from other blocks. These can be assembled into web pages via a visual interface: the config bar.

body Defined along with loop body Defined along with function definition body Defined along with subroutine border Defined along with width

bottle WSGI Bottle WSGI supplies the template engine stpl (Simple Template Engine).(documentation at [stpl:on]) bottom concept Defined along with top concept bound Defined along with bound variable occurrence

bound An occurrence of a variable v is called bound in an expression E, iff it is in a variable binding that binds v. Variables that are not bound in an expression E are called free in E.

We often write an expression E in which variables x1, . . . , xn occur freely, as E[x1, . . . , xn]. bound variable occurrence We call an occurrence of a variable X bound in a formula A, iff it occurs in a sub-formula ∀X B of A. We call a variable occurrence free otherwise. For a formula A, we will use BVar(A) (and free(A)) for the set of bound(free) variables of A, i.e. variables that have a free/bound occurrence in A. box Defined along with width

branch A branch is a copy of an object under revision control (such as a source code file or a directory tree) so that it can be developed in parallel. branch Defined along with graph

branch A path in a tree that starts with the root is called a branch. branches Defined along with conditional execution

19 branching factor Defined along with in-degree

browsing Defined along with hypertext bug report See issue bugtracker See issue tracker

bundle Drupal has a special data type called a bundle, which is essentially a dictionary: it contains key/value pairs called fields.

– bundles can be nested sub-bundles. – fields also have data type; information, etc. to support editing.

byte The byte is a derived unit for information capacity: 1 B = 8 b.

calendar A calendar is a system of organizing dates. This is done by giving names to periods of time, typically days, weeks, month and years.A date is the designation of a single, specific day within such a system.

called Defined along with subroutine canonical projection Defined along with equivalence class canonical surjection Defined along with equivalence class

cardinality Defined along with finite

cell Jupyter notebooks consist of cells which come in three forms – a raw cell shows text as is – a markdown cell interprets the contents as markdown text (later more) – a code cell interprets the contents as (e.g. python) code

cell Defined along with Turing machine centi Defined along with prefixes central processing unit A central processing unit(CPU), also called a central processor or main processor, is the electronic circuitry within a computer that carries out the instructions of a program by performing the basic arithmetic, logic, controlling, and input/output (I/O) operations specified by the instructions. A CPU that consists of a – control unit that interprets the program and controls the flow of machine instructions and – a arithmetic/logic unit(ALU) that does the actual computations internally.

central processor See central processing unit

centralized A centralized revision control system features – a single, central repository server(for current revision and reverse diffs) – local working copies(asynchronous checkouts, updates, commits)

20 They are kept synchronized by passing around diffs and patching the repository and working copies. Conflicts are resolved by (three-way) merge. The revision control actions are those of a local RCS plus

– clone: fetch the current revision from repository server and checkout a new working copy. – pull: fetch the pending differences between the revision of the working copy and the revision of the repository server and merges them into the working copy. – push: if the working copy and the repository are based on the same revision, then transmit the differences to the repository server and update the revision there. fetch and push are dual operations. Just as fetch is integrated into the pull, push is usually integrated into commit for centralized RCS. certificate authority Defined along with public key infrastructure

certificate authority In a typical public key infrastructure scheme, the signature will be of a certificate authority, an organization chartered to verify and issue public key certificates. channel Defined along with RGB character Defined along with universal character set character Defined along with alphabet

character code Let A and B be alphabets, then we call an injective function c: A → B+ a character code. A string c(w) ∈ {c(a) | a ∈ A} is called a codeword.

character encoding A character encoding is a mapping from bit strings to UCS code points. character name Defined along with code point character properties Defined along with code point

Defined along with floating point number checkout Defined along with local child Defined along with tree child Defined along with tree

child table Defined along with foreign key choreographic work Defined along with copyrightable work

civil law tradition Legal systems in the civil law tradition are usually based on explicitly codified laws (civil codes).

class A vocabulary often includes names for classes and relationships (also called concepts, and properties).

21 class In object-oriented programming, a class is a program construct for creating objects as well as providing the fields with initial values and the methods with implementations. classical antiquity Defined along with periodization

client A client is a piece of computer hardware or software that accesses a service made available by a server. client-server architecture In the client-server architecture a single overall computation is distributed across multiple processes or computers. A single server can serve multiple clients, and a single client can use multiple servers.A client may run on the same computer or may connect over a network to a server on a different computer. clone Defined along with centralized close Defined along with report

closed Defined along with opened

closed We call a formula A closed or ground, iff free(A) = ∅. We call a closed proposition a sentence, and denote the set of all ground terms with cwff ι(Σι) and the set of sentences with cwff o(Σι).

closed An expression is called closed or ground, iff it does not contain free variables. closed world assumption Database: Ontology: – Closed world assumption – Open world assumption (CWA) (OWA) ∗ Missing information ∗ Missing information treated as false treated as unknown – Unique name assumption – No UNA (UNA) ∗ Individuals may have ∗ Each individual has a sin- more than one name gle, unique name – Ontology axioms behave like – Schema behaves as constraints implications (inference rules) on structure of data ∗ Entail implicit informa- ∗ Define legal database tion states closing tag Defined along with opening tag

cloud IDE See web IDE code See computer code

code A code is a system of rules to convert information – such as a letter, word, sound, image, or gesture – into another form, sometimes shortened or secret, for communication via a communication medium or storage in a storage medium. The process of encoding applies a code for communication or storage, whereas the process of decoding applies it in reverse to restore the original information

22 code block Defined along with template file

code cell Defined along with cell code line Defined along with template file

code point Each UCS character is identified by an unambiguous name and an integer number called its code point.

code point For each character UniCode defines a code point (a number written in hexadecimal as U+ ABCD), a character name, and a set of character properties.

codeword Defined along with character code

coding The implementation of an algorithm in a chosen is called coding. codomain Defined along with domain codomain Defined along with partial function

coefficient Defined along with floating point number coefficient Defined along with collection See container column Defined along with relational database management system

column name Defined along with table name

column specification The SQL statement CREATE TABLE\$\pmetavar{name}\$ (\$\pmetavar{coldefs}\$) creates a table with name ⟨⟨name⟩⟩. ⟨⟨coldefs⟩⟩ are column specifications that specify the columns: it is a comma-separated list of column names and SQL data types. The totality of all column specifications of all tables in a database is called the database schema.

command Defined along with command-line interface command line Defined along with command-line interface command-line interface A command-line interface(CLI) is a means of interacting with a computer program where the user (or client) issues instructions (called commands in a CLI) to the program in the form of successive lines of text (command line). The program which handles this user interface is called a command-line interpreter or command-line processor. command-line interpreter Defined along with command-line interface command-line processor Defined along with command-line interface commercial use Defined along with CC provision

commit Defined along with local common law tradition Legal systems in the common law tradition are usually based on case law, they are often derived from the British system. common mathematical language Defined along with formulae

communication Communication is the act of conveying information from one group of subjects to another.

23 communication medium A communication medium is a channel or system of communication – the means by which information (the message) is transmitted between a speaker or writer (the sender) and an audience (the receiver). compile Defined along with compiler

compiler A compiler is a program that translates (compiles)code written in one programming lan- guage (the source language) into another language (the target language). complement Defined along with concept complement See set difference complex Defined along with atomic complex formula Defined along with atomic formula

complex numbers The set C of complex numbers contains expressions of the form c = (a + bi), where a, b ∈ R. Re(c) := a is called the real part and Im(c) := b the imaginary part of c; we call i the . complexes Defined along with integer component Defined along with uniform resource identifier component Defined along with

composable We call two relations R ⊆ A × B and S ⊆ C × D composable, iff B = C compose Defined along with composition principle

composition The composition of two relations R ⊆ A × B and S ⊆ B × C is defined as

S ◦ R := {(a, c) ∈ A × C | there is a b ∈ B with (a, b) ∈ R and (b, c) ∈ S}

composition The composition of R ⊆ A × B and S ⊆ B × C is defined as S ◦ R := {(a, c) ∈ A × C | ∃ b ∈ B (a, b) ∈ R ∧ (b, c) ∈ S}

composition principle All programming languages provide composition principles that allow to compose smaller program fragments into larger ones in such a way, that the semantics of the larger is deter- mined by the semantics of the smaller ones and that of the composition principle employed. computation See run computationally universal See Turing complete computer See computing device

computer code We call any well-formed fragments of a program computer code or program code, or just code.

computer monitor A computer monitor (or just monitor)is an output device for visual information. Computer programming (or just programming) is the process of designing and building a program for accomplishing a specific computing task. It involves sub-processes, such as: analysis, generating , profiling algorithms’ re- source consumption, proving algorithm properties, coding, and program verification.

computer science Computer science (or shortCS) is the study of algorithms and information processing system in theory and practice. ACS professional is called a computer scientist.

24 computer scientist Defined along with computer science computer-created Defined along with human-organized

computing device A computing device or simply a computer is an physical (usually electrical or electronic) information processing system that can automatically executea sequence of machine instruc- tions i.e. arithmetic or logical operations that change state of the system. A computer consists of physical parts (its hardware) and a set of programs and data, its software.

concatenation The concatenation conc(L1,L2) of two languages L1 and L2 over the same alphabet is defined as conc(L1,L2) := {s1s2 | s1 ∈ L1 ∧ s2 ∈ L2}.

n m concatenation The concatenation conc(s, t) of two strings s=⟨s1, . . . , sn⟩∈A and t=⟨t1, . . . , tm⟩∈A is (n + m) defined as ⟨s1, . . . , sn, t1, . . . , tm⟩ ∈ A . We will often write conc(s, t) as s + t or simply st. concept Defined along with semantic network concept Defined along with ontology concept See class concept Defined along with D-ontology

0 concept Let PLDL be given by the grammar

0 PLDL :== C | ⊤ | ⊥ | L | L ⊓ L | L ⊔ L | L ⊑ L | L ≡ L

0 i.e. PLDL formed from

– concepts( =b propositional variables) – concept intersection( ⊓)(=b conjunction ∧) – concept complement( ·)(=b negation ¬) – concept union( ⊔), subsumption( ⊑), and equality( ≡) defined from these. (=b ∨, ⇒, and ⇔) concept Defined along with ontology concept axiom Defined along with D-ontology

concept axiom A concept axiom is a formula A that is assumed to be true in the world.

concept definition A concept definition is a pair c = C, where c is a new concept name and C ∈ C is a D-formula.

concrete data Concrete data: digital representations of artefacts in terms of simple data, – e.g. images as pixel arrays in JPEG. (see above) – e.g. books identified by author/title/publisher/pubyear. (see above)

condition A condition is a Boolean expressionina control structure. conditional execution Conditional execution allows to execute (or not to execute) certain parts of a program (the branches) depending on a condition. We call a code block that enables conditional execution a conditional statement.

25 conditional statement Defined along with conditional execution

cone Defined along with lens config bar Defined along with block configuration Defined along with current cell configuration transition function Defined along with current cell conflict Defined along with three-way merge conflict marker Defined along with three-way merge

conjecture Error: The defi does not appear to be inside a definition environment. line43:51

conjunction Defined along with formulae connective Defined along with formulae connective Defined along with formulae connective Defined along with first-order signature

constant A constant is a memory location which contains a value that cannot be altered by the program during normal execution. It is referenced by an identifier – the constant name. constant Defined along with expression language constant name Defined along with constant

container A container or collection is a grouping of some variable number (possibly zero) of data items – the elements of the container – that need to be operated upon together in some controlled fashion. content Defined along with width content management system A content management system(CMS) is a software application that can be used to manage the creation and modification of digital content by users with little knowledge of program- ming languages or markup languages. A web content management system(WCMS) is a content management system for web con- tent. Web content management consists of website authoring, collaboration, and adminis- tration.

control flow The control flow of a program is the sequence of execution of the program instructions. It is specified via special program instructions called control structures. control structure Defined along with control flow

control unit Defined along with central processing unit control word Defined along with document markup conversation Defined along with issue

converse R−1 := {(y, x) | (x, y) ∈ R} is the converse relation of R.

converse relation R−1 := {(y, x) | (x, y) ∈ R} is the converse relation of R ⊆ A × B.

26 cookie A cookie is a text file stored on the client hard disk by the web browser. Web servers can request the browser to store and send cookies.

copyleft A copyleft license is a license which requires that allows derivative works, but requires that they be licensed with the same license. copyright Defined along with intellectual property

copyright holder The copyright holder is the legal entity that owns the copyright to a copyrighted work. copyright infringement The use of a copyrighted material, by anyone other than the owner of the copyright, amounts to copyright infringement only when the use is such that it conflicts with any one or more of the exclusive rights conferred to the owner of the copyright.

copyrightable work A copyrightable work is any artefact of human labor that fits into one of the following eight categories: – Literary works: Any work expressed in letters, numbers, or symbols, regardless of medium. (Computer source code is also considered to be a literary work.) – Musical works: Original musical compositions. – Sound recordings of musical works. (different licensing) – Dramatic works: literary works that direct a performance through written instructions. – Choreographic works must be “fixed,” either through notation or video recording. – Pictorial, graphic and sculptural work(PGS works): Any two-dimensional or three- dimensional art work – Audiovisual works: work that combines audio and visual components. (e.g. films, television programs) – Architectural works.(copyright only extends to aesthetics) copyrighted Defined along with public domain

corollary Error: The defi does not appear to be inside a definition environment. line49:3

countable We say that a set A is countable (otherwise uncountable), iff there isan bijective function f : A → N with N ⊆ N.

countably infinite We say that a set A is countably infinite, iff there is a bijective function f : A → N.

cryptography Cryptography is the practice of transmitting a plain text t by encoding it into a cypher text t′, to hide its content from anyone but the legitimate reciever who can decode t′ to t.

cultural artefact Defined along with cultural heritage

cultural heritage Cultural heritage is the legacy of physical artifacts – cultural artefacts – and practices, representations, expressions, knowledges, or skills – intangible cultural heritage(ICH) – of a group or society that is inherited from past generations. current Defined along with length

current cell Let M := ⟨A, S, b, Σ, s0, F, R⟩ be a nondeterministic Turing machine, then we call a triple ⟨w, n, s⟩, where – w ∈ A∗ is the word encoded by the current tape,

27 – n the number of the cell being scanned by the head (we call it the current cell), and – s the current state a configuration of M, we denote the set of configurations of M with C(M) (or just C). A configuration ⟨w, n, s⟩ is called final or accepting, iff s ∈ F. Obviously, the transition function R can be reformulated as a function R: C(M) → C(M), we call it the configuration transition function.

cursor A cursor is a named object that encapsulates a set of query results in a (virtual) database table. cycle Defined along with cyclic cycle Defined along with cyclic

cyclic Given a graph G = ⟨V,E⟩, then – a path p is called cyclic (or a cycle) iff start(p) = end(p).

– a cycle ⟨v0, . . . , vn⟩ is called simple, iff vi ̸= vj for 1 ≤ i, j ≤ n with i ̸= j. – graph G is called acyclic iff there is no cyclic path in G.

cyclic Given a directed graph G := ⟨V,E⟩, – a path p is called cyclic (or a cycle) iff start(p) = end(p).

– a cycle ⟨v0, . . . , vn⟩ is called simple, iff vi ̸= vj for 1≤i, j≤n with i ̸= j. – G is called acyclic (or a DAG: directed acyclic graph) iff there is no cycle in G. cypher text Defined along with cryptography

dashboard A dashboard is a user interface that organizes and presents system information give an overview over the state of a complex system and its services.

data Data is information that is used to represent objects by giving values to their relevant attributes and stating their relationships. data controller Defined along with General Data Protection Regulation data definition language The data definition language(DDL) is a of SQL instructions that address the creation and deletion of database objects.

data language A data language is a formal language for specifying data in an information processing system. data languages are not Turing complete.

data structure A data structure is a data organization, management, and storage format that enables efficient access and modification. data subject Defined along with General Data Protection Regulation

data transfer control Data transfer control: Personal data may not be copied during transmission between sys- tems. ( encryption) ;

data type A data type or simply type is an programming language attribute of data which tells the compiler or interpreter how the programmer intends to use the data. A type constrains the valuesa variable or function can might take and defines the operators that can be applied to it.

28 database A database is an organized collection of data, stored and accessed electronically from a computer system.

database browser A database browser is a graphical user interface for a RDBMS that (typically) bundles an SQL instruction editor with displays for results and the database schema. database management system A database management system(DBMS) is program that interacts with end users, appli- cations, and a database to capture and analyze the data and provides facilities to administer the database.

database record Defined along with relational database management system database schema Defined along with column specification

database transaction The general solution to the problem of accessing a database from multiple programs or processes in parallel is solved by a complex technology called database transactions, which allow users’ to define a sensible unit of work (via begin/end bracketing) called a transaction and makes sure that the process

– behaves as if the user’s process has sole access to the database system for the duration of the transaction(isolation) – any changes made during the transaction can be rolled back if an error occurs during processing (integrity).

Transactions are an essential, but complex technology that is beyond the scope of the IWGS course. For our understanding, db.commit is essentially just the end of a transaction.

database view A database view (or simply view) is a virtual table based on the result-set of a query.A view contains rows and columns, just like a real table. The fields in a view are fields from one or more real tables in the database. date Defined along with calendar

day Defined along with minute deca Defined along with prefixes deci Defined along with prefixes

decidable See recursive decides Defined along with accepts decimal Defined along with unary decimal point Defined along with floating point number

declaration A CSS declaration block consists of a semicolon-separated list of declarations in curly braces. Each declaration itself consists of a property, a colon, and a value. declaration block Defined along with rule decode Defined along with cryptography decode key Defined along with public key cryptography

decoding Defined along with code default namespace declaration Defined along with namespace declaration

29 default value Defined along with keyword argument

defined at We call a partial function f : X ⇀ Y

– defined at x ∈ X, iff (x, y) ∈ f for some y ∈ Y and – undefined at x ∈ X (write f(x) = ⊥), iff (x, y) ̸∈ f for all y ∈ Y .

defined piecewise A function m is defined piecewise, we write  a1 if A1   . . m(x) = . .  an if An   o else

where Ai are conditions involving x, if m(x) = ai for all x with Ai and o otherwise.

definiendum Error: The defi does not appear to be inside a definition environment. line22:26

definiendum Defined along with definitional equation

definiens Error: The defi does not appear to be inside a definition environment. line23:3

definiens Defined along with definitional equation R a definite integral Given a function f : R → R and an interval [a, b] ⊂ R, then the definite integral b f(x)dx is defined to be the signed area of the region in the plane bounded by thegraphof f, the x-axis, and the vertical lines x = a and x = b, such that area above the x-axis adds to the total, and that below the x-axis subtracts from the total. definition by description Error: The defi does not appear to be inside a definition environment. line58:16

definitional equation If a does not occur in A, we call a pair a := A a definitional equation and a :⇔ A a definitional equivalence with definiendum a and definiens A. definitional equivalence Defined along with definitional equation

delete The SQL delete statement allows to change existing records. DELETE FROM \$\pmetavar{table}\$ WHERE \$\pmetavar{condition}\$;

deleted Defined along with hunk denominator Defined along with rational number

dependencies Defined along with issue number

depth The depth of a node n in a tree t is the length of the path that links n with the root of t. dereferencing Defined along with reference derivation Defined along with inference

derivation relation ! Let S := ⟨L, K, |=⟩ be a logical system, then we call a relation ⊢ ⊆ P(L) × L a derivation relation for S, if it

30 – is proof-reflexive, i.e. H ⊢ A, if A ∈ H; – is proof-transitive, i.e. if H ⊢ A and H′ ∪ {A} ⊢ B, then H ∪ H′ ⊢ B; – monotonic (or admits weakening), i.e. H ⊢ A and H ⊆ H′ imply H′ ⊢ A. derivative works Defined along with CC provision derive Defined along with relation

derived Defined along with ontology

derived unit A derived unit is formed as a product of integer powers of base units. descendant Defined along with tree descendant Defined along with ancestor

description Defined along with issue description logic Defined along with ontology

description logic A description logic is a formal system for talking about sets and their relations that is at least as expressive as PL0 with set-theoretic semantics and offers individuals and relations. A description logic has the following four components – a formal language L with logical con- PL1 stants ⊓, ·, ⊔, ⊑, and ≡. undecideable ψ decideable – a set-theoretic semantics ⟨D, [[·]]⟩   DL  C 7→ pα→o  – a translation into first-order logic ψ := ⊓ 7→ ∩  · 7→ D\·  that is compatible with ⟨D, [[·]]⟩. φ    Xo 7→ C  φ := ∧ 7→ ⊓ – a calculus for L that induces a deci- 0 PL  ¬ 7→ ·  sion procedure for L-satisfiability. description logic reasoner A description logic reasoner implements of reaonsing services based on a satisfiabiltiy test for description logics. deterministic Turing machine Defined along with nondeterministic Turing machine developer Defined along with guest development Defined along with GIT flow

development history Defined along with revision control system diagonal See identity function

dictionary A dictionary (also called associative array, map, symbol table) is an abstract data type composed of a set of key/value pairs, such that each possible key appears at most once in the container.

diff Defined along with difference

difference diff is a file comparison utility that computes differences between two strings or text files: the source f1 and the target f2. Differences are output linewise in a diff δ(f1, f2). difference Defined along with subtraction difference Defined along with subtraction

31 difference Defined along with subtraction

difference Defined along with subtraction digit Defined along with positional number system digit Defined along with positional number system

digit Defined along with positional number system

digital signature A digital signature consists of a plaintext together with its ciphertext – encoded with the sender’s pri- vate key. A message signed with a sender’s private key can be verified by anyone who has access to the sender’s public key, thereby proving that the sender had access to the private key (and therefore is likely to be the person associated with the public key used), and the part of the message that has not been tam- pered with.

digital text An electronic document that contains a digital encoding of textual material that can be read by the end user by simply presenting the encoded characters is called digital text. digraph Defined along with graph digraph Defined along with directed graph

dimension Defined along with n-fold Cartesian product dimension Defined along with International System of Units direct identifier Defined along with personally identifiable information directed acyclic graph Defined along with cyclic directed edge Defined along with directed graph directed graph Defined along with graph

directed graph A directed graph (also called digraph) is a pair ⟨V,E⟩ such that – V is a set of vertices – E ⊆ V × V is the set of its directed edges

disambiguation point A disambiguation point in a path marks an entity that can be re-used in data acquisition.

discharge We can discharge a variable X from a substitution σ by σ−X := σ, [X/X]. disjunction Defined along with formulae

distributed We call a revision control system distributed, iff it allows multiple repositories that can exchanged patches.

division The division operator computes the a / b of a ∈ Q and b ∈ Q. On Q we define a c a·c b / d := b·d . division Defined along with absolute value

32 division Division computes the modulus ndivm of two natural numbers n and m. ndivm is defined as that q ∈ N, such that n = m · q + r for some r≤0

division Division computes the quotient a / b of a and b. It is defined as is that c – if it exists, such that a c = b. division Defined along with field

document format A document format is a file format for electronic documents.

document markup Document markup (or just markup) is the process of adding control words (special character sequences also called markup codes) to a plain text to control the structure, formatting, or the relationship among its parts, making it a formatted text. All characters of a formatted text that are not control words constitute its textual content. document object model The document object model(DOM) is a data structure for storing marked-up electronic documents as trees together with a standardized set of access methods for manipulating them. document renderer Defined along with electronic document

document root As a document is a tree, the XML specification mandates that there must be a unique document root. document type Defined along with markup format domain Defined along with model

domain Let D be a given set (called the domain) and φ: Vo → P(D), then we define – [[P ]] := φ(P ), (remember φ(P ) ⊆ D).   – [[A ⊓ B]] := [[A]] ∩ [[B]] and A := D\[[A]] ...

domain call X the domain (write dom(f)), and Y the codomain( codom(f))(come with f) domain Defined along with partial function dot notation Defined along with object

double star operator The double star operator unpacks a dictionary into a sequence of keyword arguments. downstream Defined along with remote repositories dramatic work Defined along with copyrightable work

drupal Drupal is an open source web content management application. It combines CMS func- tionality with knowledge management via RDF.

drupal core Drupal functionality is structured into – drupal core– the basic CMS functionality – modules– which contribute e.g. new block types (∼ 45.000) – themes– which contribute new UI layouts (∼ 2800) Drupal core is the vanilla system as downloaded, modules and themes must be installed and configured separately via the config bar.

33 222 CHAPTER 12. IMAGE PROCESSING

221

Edge Detection

dynamic route A dynamic route is a route annotation that contains named wildcards, which can be picked 222 Goal:up in Find the interesting route function. parts of image (features).CHAPTER 12. IMAGE PROCESSING edge Find edges, i.e. image sections, where color changes rapidly. Example: Find edges, i.e. sections, where color changes rapidly.

Example Image: Edge Detection

Slide 319 Goal: Find interesting parts of image (features). In this (admittedly simple) example image, we can clearly see, that there is an edge present, where the color shiftsExample: fast Find from edges dark, i.e. to sections, light. We where will color now explore,changes rapidly how we. can detect such an edge automatically.

Example Image:

Edge Detection

Goal: Find interesting parts of image (features). Clearly there is an edge in this image. How do we detect it automatically? Example: FindClearly edges there, i.e. is ansections, edge in where this image. color changes rapidly. How do we detect it automatically?

Example Image: Slide 319

In this (admittedly simple) example image, we can clearly see, that there is an edgeSlide present, 318 where the color shifts fast from dark to light. We will now explore, how we can detect such an edge automatically.

Decide for each pixel, whether it is on an edge. Here: Is marked pixel an edge pixel? Decide for each pixel, if it is an edge. Here: Is marked pixel an edge pixel? We will now look at more interesting image operations. A typical example especially important for object recognition in images is to ﬁnd features. Features are areas in the image, which are recognizable.

For example, let’s say we want to ﬁnd so-called edges in our image, i.e. areas where the color changes rapidly. Edges often correspond to object outlines. We will see an example later. Inspect neighbor pixels. edge Defined along with graph

34 edge labelling Defined along with label

edge-labeled Defined along with label

electronic document An electronic document is any electronic media content that is intended to be used via a document renderer, i.e. a program or computing device that transforms it into a form that can be directy perceived by the end user. element Defined along with set

element Defined along with set element Defined along with container element node Defined along with XML document tree

elementhood Defined along with set

embedded system An embedded system is a computing device with a dedicated function within a larger mechanical or electrical system. empty Defined along with empty set empty element tag Defined along with opening tag

empty set the empty set: ∀ x x ̸∈ ∅

empty set The empty set ∅ (also written as {}) is the set without elements. A set is called empty, iff it is ∅, and non-empty or (inhabited) otherwise. empty string Defined along with alphabet empty tag Defined along with tag empty word Defined along with alphabet

encode We say that a tape t encodesa word w ∈ A∗, if w can be obtained from t by dropping all leading and trailing b. encode key Defined along with public key cryptography encoding Defined along with cryptography

encoding Defined along with code

encoding scheme UniCode defines various encoding schemes for characters, the most important is UTF-8. end Defined along with path end Defined along with path end tag Defined along with tag

end user An end user is a person who ultimately uses or is intended to ultimately use a computation device or program. end-user license agreement Software vendors usually license software under extensive end-user license agreement (EULA) entered into upon the installation of that software on a computer. The license authorizes the user to install the software on a limited number of computers.

35 entailment relation Let S := ⟨L, K, |=⟩ be a logical system, then we define the entailment relation |= ⊆ P(L) × L. We say that a set H ⊆ L of formulae entails B (written H |= B), iff we have M |= B for all A ∈ H and models M ∈ K with M |= A. entails Defined along with entailment relation entities Defined along with entity relationship diagram entity relationship diagram An entity relationship diagram(ERD) illustrates the logical structure of . It consists of entities that characterize (sets of) objects by their attributes and relations between them. entries Defined along with matrix

equal Two sets A and B are equal (written A ≡ B), iff they have the same elements.

equal We call two mathematical objects a and b equal, (written a = b), iff there are no properties that discern them. equality Defined along with concept equivalence Defined along with formulae

equivalence class Let S be a set and R be an equivalence relation on S, then for any we call x ∈ S we call the set [x]R := {y ∈ S | R(x, y)} the equivalence class of x (under R), and the set S/R := {[x]R | x ∈ S} the quotient space or quotient set of S (under R), it is often read as S “modulo R”. The element x is called the representative of [x]R ∈ S/R.

The mapping πR : S → S/R; x 7→ [x]R is called the canonical projection or canonical surjec- tion of S to S/R.

equivalence class Let S be a set and R be an equivalence relation on S, then for any we call x ∈ S we call the set [x]R := {y ∈ S | R(x, y)} the equivalence class of x (under R), and the set S/R := {[x]R | x ∈ S} the quotient space of S (under R).

equivalence relation A relation R ⊆ A × A is an equivalence relation on A, iff R is reflexive, symmetric, and transitive. equivalence relation Defined along with reflexive escape character Defined along with string literal escape sequence Defined along with string literal evaluation Defined along with expression

event The first key concept we need to understand here is that the browser essentially actsas an user interface: it presents the HTML pages to the user, waits for actions by the user – usually mouse clicks, drags, or gestures; we call them events– and reacts to them. The second is that all events can be associated to an element node in the DOM: consider an HTML anchor node, as we have seen above, this corresponds to a rectangular area in the browser window. Conversely, for any point p in the browser window, there is a minimal DOM element e(p) that contains p – recall that the DOM is a tree. So, if the user clicks while the mouse is at point p, then the browser triggers a click event in e(p), determines how e(p) handles a click event, and if e(p) does not, bubbles the click event up to the parent of e(p) in the DOM tree. There are multiple ways a DOM element can handle an event: some elements have default event handlers, e.g. an HTML anchor will handle a click event by issuing

36 a HTTP GET request for ⟨⟨URI⟩⟩. Other HTML elements can carry event-handler attributes whose JavaScript content is executed when the corresponding event is triggered on this element. Actually there are more events than one might think at first, they include: 1. Mouse events; click when the mouse clicks on an element (touchscreen devices gener- ate it on a tap); contextmenu: when the mouse right-clicks on an element; mouseover / mouseout: when the mouse cursor comes over / leaves an element; mousedown / mouseup: when the mouse button is pressed / released over an element; mousemove: when the mouse is moved. 2. Form element events; submit: when the visitor submits a

exception An exception is a special python object. Raising an exception e terminates computation and passes e to the next higher level. execute Defined along with interpreter execute Defined along with computing device exploitation rights Defined along with personal rights exponent Defined along with floating point number exponent Defined along with exponentiation exponent Defined along with exponentiation exponent Defined along with exponentiation exponent Defined along with exponentiation

exponentiation The exponentiation operation raises a number a (the base) to the power n (the exponent). We define it as  bn a ∈ − (n = 2 · k) an := if Z and ( − (bn) if a ∈ Z− and (n = 2 · k + 1)

exponentiation Exponentiation raises a number a ∈ Q (the base) to the power n ∈ Q (the exponent). We define √ n m n a m a := √ b m bn

37 exponentiation Defined along with absolute value

exponentiation Exponentiation raises a a (the base) to the n-th power an (n ∈ N is called the exponent). We define a0 := 1 and as(n) := aan.

exponentiation Exponentiation raises a number a (the base) to the n-th power an (n is called the exponent). expression Defined along with template file

expression An expression in a programming language is a combination of one or more constants, variables, operators, and functions that the programming language computes to produce a value. This process is called evaluation.

expression An expression is a finite construction composed of variables and names of mathematical objects/concepts composed by operator application and variable binding according to rules that depend of the (mathematical) context.

expression language An expression language is a formal language whose words (called exressions, terms, well formed formulae, or just wffs or formulae) are composed from constants and variables by application and binding. The set wff (Σ, V) of formulae is determined by the signature Σ – i.e., the set of constants– and the set V of variables (usually assumed to be countably infinite). The application of an expression o – called the in an application– operator to a sequence n t1, . . . , tn of exressions – called operands or arguments– is written as o t1 . . . tn (or o t ). exression Defined along with expression language extended assignment Let φ be a variable assignment and a ∈ Dι, then we denote with φ, [a/X] the extended assignment {(Y, b) ∈ φ | Y ̸= X} ∪ {(X, a)}.(φ, [a/X] coincides with φ off X, and gives the result a there)

extension The extension of a code (on characters) c: A → B+ to a function c′ : A∗ → B∗ is defined ′ as c (⟨a1, . . . , an⟩ = ⟨c(a1), . . . , c(an)⟩). extension Defined along with file system

extension If σ is a substitution, then we call σ, [A/X] the extension of σ by [A/X].

external memory See secondary storage f-string See formatted string literal f-string See formatted string literal fact Defined along with ontology

fair use doctrine Case law in common law traditions has established a fair use doctrine, which allows e.g.

– making safety copies of software and audiovisual data, – lending of books in public libraries, – citing for scientific and educational purposes, or – excerpts in search engine.

Fair use is established in court on a case-by-case taking into account the purpose (com- mercial/educational), the nature of the work the amount of the excerpt, the effect on the marketability of the work.

38 false Defined along with truth value false Defined along with model falseDefined under alongφ with true under φ falseDefined under alongφ with true under φ falsehood Defined along with model falsifiable Defined along with true under φ falsifiable Defined along with true under φ falsifiable Defined along with satisfied falsified Defined along with satisfied falsum Defined along with truth value

feature We will now look at more interesting image operations. A typical example especially im- portant for object recognition in images is to find features– i.e. areas in the image, which are recognizable. For example, let’s say we want to find so-called edges in our image, i.e. areas where the color changes rapidly. Edges often correspond to object outlines. We will see an example later.

feature Find interesting parts of image (features). feature branch Defined along with GIT flow feature branch Defined along with master branch feature request A feature request is an issue that only specifies the expected behavior and proposes ways of implementing that. femto Defined along with prefixes fetch Defined along with centralized field Defined along with relational database management system field Defined along with bundle field Defined along with object-oriented programming

field A field is a where multiplication is commutative all elements x except zero have a x−1. We define division as a / b := ab−1.

file A file is a resource for recording data in a storage device.

file format A file format is a standard way that information is encoded for storage in a computer file. It specifies how bits are used to encode information ina storage device.

file object python uses file objects to encapsulate all file input/output functionality.

file system A file system is a program that organizes space on a storage device and makes it acessible as files.A file name usually consists of a base name and an extension separated by a dot. final Defined along with current cell final state Defined along with nondeterministic Turing machine

39 findable Defined along with FAIR

finite We say that a set A is finite and has cardinality (or size) #(A) ∈ N, iff there is a bijective function f : A → {n ∈ N | n<#(A)}. The cardinality of a set A is also written as |A|, card(A), n(A), or A. finite sequence Defined along with sequence

first component Let p := (a, b) be a pair, then we call p1 := a the first component and p2 := b the second component of p.

first-order logic First-order logic( PL1), is a formal logical system extensively used in mathematics, philos- ophy, linguistics, and computer science. It combines propositional logic with the ability to quantify over individuals.

first-order signature A first-order signature consists of (all disjoint; k ∈ N) – connectives: Σo = {T , F , ¬, ∨, ∧, ⇒, ⇔,...} (functions on truth values) f – function constants: Σk = {f, g, h, . . .} (functions on individuals) p – predicate constants: Σk = {p, q, r, . . .} (relations among inds.) sk k k – (Skolem constants: Σk = {f1 , f2 ,...})(witness constructors; countably ∞) f p sk ∗ S ∗ – We take Σι to be all of these together: Σι := Σ ∪ Σ ∪ Σ , where Σ := k∈ Σk and o N define Σ := Σι ∪ Σ .

flipped classroom A flipped classroom is an instructional strategy and a type of blended learning focused on student engagement and active learning. Usually, students prepare plenary sessions with online materials and use classroom time for discussions, applications and worked exercises. float Defined along with integer float See floating point number floating point number A floating point number (or short a float) is a quintuple n := ⟨σ, s1, s2, b, e⟩, where

1. the sign σ is unit sequence − or the empty sequence, and the si are sequence of digits of base b. Together, (i.e. concatenated with a decimal point between s1 and s2) σ, s1, and s2 make up the s (also called the mantissa or coefficient. 2. an exponent e ∈ Z (also referred to as the characteristic, or scale), which modifies the magnitude of the number n.

s e The number ⟨σ, s1, s2, b, e⟩ represents the rational number bp − 1 · b . The length p := len(s1) + len(s2) of the significand determines the precision to which numbers can be represented.

for loop A for loop iteratesa program fragment over a sequence; we call the process iteration. python uses the following general syntax for ⟨⟨var⟩⟩ in ⟨⟨range⟩⟩: ⟨⟨body⟩⟩ ⟨⟨other code⟩⟩

foreign key A foreign key is a column (or collection of columns) in one table (called the child table) that refers to the primary key in another table (called the reference table or parent table). fork Defined along with remote repositories

40 fork If you want to contribute to a repository R you have no push-rights on,

1. clone R to a new repository R′ you own (i.e. fork it; R′ is a fork of R) 2. develop your contribution on R′. 3. ask Rs owners to pull from R′ (pull request) GIT repository management systems like GitHub and GitLab support this.

fork A branch controlled by a different developer or not intended tobe merged back is called a fork. form action Defined along with input element

form data The HTML form element groups the layout and input elements: – specifies the form action in terms of a HTTP request ⟨⟨req⟩⟩ to the URI ⟨⟨URI⟩⟩.

– The form data consists of a string ⟨⟨data⟩⟩ of the form n1=v1&···&nk=vk, where

∗ ni are the values of the name attributes of the input fields ∗ and vi are their values at the time of submission. – triggers the form action: it composes a HTTP request ∗ If ⟨⟨req⟩⟩ is get (the default), then the browser issues a GET request ⟨⟨URI⟩⟩?⟨⟨data⟩⟩. ∗ If ⟨⟨req⟩⟩ is post, then the browser issues a POST request to ⟨⟨URI⟩⟩ with document content ⟨⟨data⟩⟩.

formal language A set L ⊆ A∗ is called a formal language in A.

formal language A formal language (or simply language) over an alphabet A is a set L ⊆ A∗ of words over A.

formal system We call ⟨L, K, |=, ⊢⟩ a formal system, iff S := ⟨L, K, |=⟩ is a logical system, and ⊢ a derivation relation for S. formatted string literal Formatted string literals (aka. f-strings) are string literals can contain python expressions that will be replaced with their values at runtime. F-strings are prefixed by a prefix f or F, the expressions are delimited by curly braces, and the characters { and } themselves are represented by {{ and }}. formatted text Defined along with plain text

formula Defined along with logic formula Defined along with expression language

formulae Mathematicians use a stylized language that

R 0 3 / 2 – uses formulae to represent mathematical objects, e.g. 1 x dx – uses math idioms for special situations (e.g. iff, hence, let. . . be. . . , then. . . ) – classifies statements by role (e.g. Definition, Lemma, Theorem, Proof, Example)

We call this language mathematical vernacular or common mathematical language. For the use in formulae we use abbreviations (special symbols) for many of the connectives: – ∧ and ∨ and ¬ are common notations for and and or

41 – not is in mathematical statements often denoted with ¬ – iff as abbreviation for if and only if, symbolized by ⇔ – the symbol ⇒ is used a as shortcut for implies or if. . . , then . . . . and quantifiers: – ∀ x P (∀ x ∈ S P ) stands for P holds for all x (in S) – ∃ x P (∃ x ∈ S P ) stands for there exists an x (in S) such that P holds – ̸∃ x P (̸∃ x ∈ S P ) stands for there exists no x (in S) such that P holds – ∃1 x P (∃1 x ∈ S P ) stands for there exists one and only one x (in S) such that P holds

formulae The formulae of propositional logic (write PL0) are made up from

1 2 – propositional variables: Vo := {P, Q, R, P ,P ,...} (countably infinite)

– constants/constructors called connectives: Σo := {T , F , ¬, ∨, ∧, ⇒, ⇔,...}

We define the set wff o(Vo) of well-formed propositional formulas as – propositional variables – the logical constants T and F , – negations ¬ A, – conjunctions A ∧ B, – disjunctions A ∨ B, – implications A ⇒ B, and – equivalences (or biimplications). A ⇔ B,

where A, B ∈ wff o(Vo) themselves. formulae Defined along with logical system fraction Defined along with rational number fragment identifier Defined along with uniform resource identifier free Defined along with bound variable occurrence free Defined along with bound

free variable We define the set free(A) of free variables of a formula A inductively:

free(X) := {X} S free(f(A1,..., An)) := 1≤i≤n free(Ai) S free(p(A1,..., An)) := 1≤i≤n free(Ai) free(¬ A) := free(A) free(A ∧ B) := free(A) ∪ free(B) free(∀X A) := free(A)\{X} free variable occurrence Defined along with bound variable occurrence

front end A web application consists of two parts – A front end that handles the user interaction. – A back end that stores, computes and serves the application content.

42 Front End Back End JavaScript e.g. python computation read Web Browser Database interact HTTP Server

Both parts rely on (separate) computational facilities. A database as a persistence layer is optional. function Defined along with subroutine

function If we do not want to specify whether a partial function is total, then we simply speak of a function.

function constant Defined along with first-order signature

function definition The function definition f(a1, . . . , an) := B[a1, . . . , an] defines a n-ary function f by its behavior on the (formal) arguments a1, . . . , an. Here we call f(a1, . . . , an) the function pattern and B[a1, . . . , an] the body– an expression that can contain the arguments a1, . . . , an as free variables.

A relation p is defined analogously via definitional equivalence p(a1, . . . , an):⇔ B[a1, . . . , an].

function object Defined along with anonymous function function pattern Defined along with function definition

function space Given sets A and B We will call the set A → B (A ⇀ B) of all (partial) functions from A to B the (partial) function space from A to B. function space Defined along with partial function space function/argument notation Function/argument notation for semantic networks – interprets node as arguments (reification to individuals) – interprets link as functions (predicates actually)

functional syntax But there are also other syntaxes in regular use. We show the functional syntax which is inspired by the of relations. general-purpose computer A general-purpose computer is one that, given the appropriate Software and the required time, should be able to perform arbitrary computing tasks.

geonames Defined along with GND gibi Defined along with binary unit prefix giga Defined along with prefixes

graph A graph is a pair G := ⟨V,E⟩ such that V is a set and E ⊆ V × V is a relation on V . We call V the vertices (or nodes, points, junctions) and E the edges (or lines, branches, arcs) of G. If E is symmetric, we call G an undirected graph, else a directed graph or digraph. In the former we consider the pairs (a, b), (b, a) ∈ E together as an unordered pair {a, b}.

43 graphical user interface A graphical user interface is a user interface that includes graphical elements, such as windows, icons, and buttons.

grayscale A color is called grayscale, iff R = G = B

grayscale conversion To convert an image to an grayscale image (grayscale conversion), we compute Gray = 0.21R + 0.71G + 0.08B

greater than Defined along with less than ground Defined along with closed

ground See closed group Defined along with project

guest GitLab has five permission levels for repositories: 1. guests can clone and see/report issues... 2. reporters can also assign issues... 3. developers can also push, create branches... 4. maintainers can also assign permission levels... 5. owners can also delete repository...

halt Defined along with Turing machine

halts Given an input tape t, we say that M halts after n steps, iff c(i) is undefined for all runs c of M on t and i>n. handle See identifier

handled Exceptions are first-class citizens in python, in particular they – are classified by their classes in a hierarchy. – exception classes can be defined by the user (they inherit from the Exception class) class DivByZero (Exception) pass

– can be raised when an abnormal condition appears if denominator == 0 : raise DivByZero else ⟨⟨computation⟩⟩

– can be handled in a try/except block (there can be multiple) try: ⟨⟨tentative computation⟩⟩ except : ⟨⟨err⟩⟩1, ..., ⟨⟨err⟩⟩n : ⟨⟨errorhandling⟩⟩ finally : ⟨⟨cleanup⟩⟩

hardware Defined along with computing device

44 head Defined along with Turing machine head revision Defined along with local

headless We call a repository headless (or bare), if used without a working copy. hecto Defined along with prefixes height Defined along with width

height The height of a node n in a tree t is the length of the longest path that links n to a leaf of t. The height of t is the height of its root. height Defined along with height hexadecimal Defined along with unary higher-order function We call a functiona higher-order function, iff it takes a function as argument.

horizontal edge pixel We call a pixela horizontal edge pixel, iff (lB − IT ) + (IBL − ITL) + (IBR − ITL) > τ for some threshold τ and a vertical edge pixel, iff (lR − IL) + (ITR − ITL) + (IBR − IBL) > τ.

host A web server can host – i.e serve resources for – multiple domains (via configurable hostnames) that can be addressed in the authority components of URLs. This usually includes the special hostname localhost which is interpreted as “this computer”. hostname Defined along with host hour Defined along with minute

human-organized We call a web search engine – human-organized, if documents are categorized by subject-area experts, (e.g. Open Directory, About) – computer-created, if software spiders crawl the web for documents and categorize pages, (e.g. Google) – hybrid if it combines the two categories above – a metasearch engine if it sends direct queries to multiple search engines and aggre- gates/clusters results, (e.g. Copernic, Vivisimo, Mamma)

hunk A diff consists of a sequence of hunks that in turn consist of a locator which indicates the source line number followed by the lines deleted in the source and added in the target. hybrid Defined along with human-organized

hyperlink A hyperlink is a reference to data that can immediately be followed by the user or that is followed automatically by a user agent.

hypertext A collection text documents with hyperlinks that point to text fragments within the col- lection is called a hypertext. The action of following hyperlinks in a hypertext is called browsing or navigating the hypertext.

idempotent We call a HTTP request idempotent, iff executing it twice has the same effect as executing it once.

identifier An identifier (also called handle) is reference to a resource.

45 identity function The identity function on a set A is defined as IdA := {(a, a) | a ∈ A}.

identity function For a set A, the identity function IdA : A → A on A maps any a ∈ A to itself. If we think of IdA as a relation on A, then we call it the identity relation or diagonal on A and write it as ∆A.

identity matrix We call the matrix In := [δi j]1≤i≤n,1≤j≤n the identity matrix of size n. identity relation See identity function iff Defined along with formulae iff Defined along with MathTalk

image Let f : A → B be a function, A′ ⊆ A, and B′ ⊆ B, then we call – f(A′) := {b ∈ B | (a, b) ∈ f for some a ∈ A′} the image of A′ under f, – Im(f) := f(A) the image of f, and – f −1(B′) := {a ∈ A | (a, b) ∈ f for some b ∈ B′} the pre-image of B′ under f. image Defined along with image

image map HTML image map allow you to mark areas in an image and assign names and links to them. imaginary part Defined along with complex numbers imaginary unit Defined along with complex numbers immaterial thing Defined along with CIDOC CRM immutable Defined along with mutable implication Defined along with formulae implicit Defined along with relation implicit definition Error: The defi does not appear to be inside a definition environment. line57:56

in-degree Given a graph G = ⟨V,E⟩. The in-degree indeg(v) and the out-degree outdeg(v) (or branching factor) of a vertex v ∈ V are defined as – indeg(v) = #({w | (w, v) ∈ E}) – outdeg(v) = #({w | (v, w) ∈ E})

inclusion We call links labeled by – “isa” an inclusion or isa link(inclusion of concepts) – “inst” instance or inst link(concept membership)

indegree Let G := ⟨V,E⟩ be a directed graph and v ∈ V a node in G, then we define – indegree indeg(v) of v as #({w | (w, v) ∈ E}) – outdegree outdeg(v) of v as #({w | (v, w) ∈ E}) individual Defined along with D-ontology individual Defined along with universe

46 individual Defined along with ontology

individual Defined along with truth value

1 2 individual variable We assume a set of individual variables: Vι = {Xι,Yι,Zι,Xι ,Xι ,...} (countably ∞) induced undirected graph Let G := ⟨V,E⟩ be a graph, and E′ the symmetric closure of E, then we call ⟨V,E′⟩ the induced undirected graph of G. industrial design right Defined along with intellectual property

inference Defined along with relation inference Defined along with logic

inference We call a sequence of inferencesa derivation or a proof (of the last statement).

infinite A set that is not finite is called infinite. infinite sequence Defined along with sequence

Infinity (written ∞) is an abstract concept describing something without any . In mathematics is is usually treated like a number.

information Information consists of a sequence of symbols or states. information access control Information access control: Users may only access those data they are authorized to access. ( access control lists, safe boxes for storage media, encryption) ; information privacy The principle of information privacy comprises the idea that humans have the right to control who can access their personal data. information processing system An information processing system (or information processor) is a stateful system (be it electrical, mechanical or biological) which takes information in one form and transforms it into another form. An information processing system S is made up of four subsystems: 1. the input subsystem channels information into S, 2. the processor executes the transformation in a sequence of operations called instructions on the processor state, 3. the storage subsystem stores information, and 4. the output subsystem channels the transformed information out of S. information processor See information processing system inhabited Defined along with empty set

inheritable Defined along with inherits inheritance factor Defined along with authentication factor

inherits If an element is fully contained in another, the inner inherits some properties (called inheritable) of the outer. In a nutshell – text-related properties are inheritable; e.g. color, font, letter−spacing, line−height, list−style, and text−align

47 – box-related properties are not; e.g. background, border, display, float, clear, height, width, margin, padding, position, and text−align.

initial Let G := ⟨V,E⟩ be a directed graph, then we call a node v ∈ V – initial (or a source) in G, iff there is no w ∈ V such that (w, v) ∈ E. – terminal (or a sink) in G, iff there is no w ∈ V such that (v, w) ∈ E.

initial Let G = ⟨V,E⟩ be a directed graph, then we call a node v ∈ V – initial, iff there is no w ∈ V such that (w, v) ∈ E.(no predecessor) – terminal, iff there is no w ∈ V such that (v, w) ∈ E.(no successor) In a graph G, node v is also called a source(sink) of G, iff it is initial (terminal) in G. initial state Defined along with nondeterministic Turing machine initialize Defined along with local

i injection Given a tuple v ∈ A1 × ... × A(i − 1) × A(i + 1) × ... × An we call the function ιv : Ai → th A1 × ... × An; ai 7→ ⟨a1, . . . , an⟩ the (i ) injection induced by v.

injective A function f : S → T is called – injective iff ∀ x, y ∈ S f(x) = f(y) ⇒ x = y. – surjective iff ∀ y ∈ T ∃ x ∈ S f(x) = y. – bijective iff f is injective and surjective.

injective A function f : S → T is called injective or one-to-one, iff f(x) = f(y) entails x = y for all x, y ∈ S. inner node Defined along with path

input control Input control: It must be possible to review retroactively who entered, changed, or deleted personal data. ( authentication, journaling) ; input element The HTML form element groups the layout and input elements: – specifies the form action(as a web page address). – triggers the form action: it sends the form data to web page specified there. input subsystem Defined along with information processing system input symbol Defined along with nondeterministic Turing machine

inserting SQL provides the INSERT INTO command for inserting records into a table. This comes in two forms: 1. INSERT INTO \$\pmetavar{table}\$ VALUES (\$\pmetavar{vals}\$); where ⟨⟨vals⟩⟩ is a comma- separated list of values given in the order the columns were declared in the CREATE TABLE instruction. 2. INSERT INTO \$\pmetavar{table}\$ (\$\pmetavar{cols}\$) VALUES (\$\pmetavar{vals}\$) where ⟨⟨vals⟩⟩ is a comma-separated list of values given in the order of ⟨⟨cols⟩⟩ (a subset of columns) all other fields are filled with NULL inst link Defined along with inclusion

48 instance Defined along with inclusion

instruction Defined along with SQL instruction Defined along with information processing system intangible cultural heritage Defined along with cultural heritage

integer python has the following five basic data types

Data type Keyword contains Examples integers int bounded integers 1, −5, 0,... floats float floating point numbers 1.2, .125, −1.0,... strings str strings "Hello", ’Hello’, "123", ’a’,... Booleans bool truth values True, False complexess complex complex numbers 2+3j,. . .

integer See integer number

integer division Integer division computes the integer quotient (or modulus) n div m of two integers. n div m is defined as that q ∈ Z, such that nm · q + r for some 0≤r

integer interval We define the integer interval as a set of consecutive integers: [a, b] := {x ∈ Z | x≤a≤b}

integer number The set Z of integer numbers (or integers) is defined as Z := N ∪ {− n | n ∈ N+}. integer quotient Defined along with integer division integrated development environment An integrated development environment(IDE) is a program that provides comprehensive facilities to computer programmers for software development. An IDE normally consists of at least a source code editor, build automation tools, and a debugger. integrity Defined along with database transaction

intellectual property The concept of intellectual property motivates a set of laws that regulate property rights rights on intangible objects, in particular – Patents grant exploitation rights on original ideas. – Copyrights grant personal and exploitation rights on expressions of ideas. – Industrial design rights protect the visual design of objects beyond their function. – Trademarks protect the signs that identify a legal entity or its products to establish brand recognition. interactive toplevel See read–eval–print loop interface See user interface

internal Defined along with private internationalized resource identifier Internationalized resource identifiers(IRIs) extend the ASCII-based URIs to the universal character set. interoperable Defined along with FAIR interpretation Defined along with logic

interpretation An interpretation I assigns values to constants, e.g.

49 0 – I(¬): Do → Do with T 7→ F, F 7→ T, and I(∧) = ... (as in PL ) f k – I :Σk → Dι → Dι (interpret function symbols as arbitrary functions) p k – I :Σk → P(Dι ) (interpret predicates as arbitrary relations) interpretation Defined along with model interpretation Defined along with model

interpretation Let wff (Σ, V) be an expression language with signature Σ and A := ⟨U, @, Λ⟩ an applicative structure, then we call a mapping I :Σ → U an interpretation.

interpreter An interpreter is a program that directly executes instructions written in a programming language, without requiring them previously to have been compiled into a machine language program. intersection Defined along with concept

intersection intersection: A ∩ B := {x | x ∈ A ∧ x ∈ B}

intersection Let A and B be sets, then the intersection A ∩ B of A and B is {x | x ∈ A and x ∈ B}. T intersection Let I be a set and Si a family of sets indexed by I, then the intersection i∈I Si over I is {x | x ∈ Si for all i ∈ I}. intersection over a collection intersection over a collection: Let I be a set and Si a family of sets indexed by I, then T i∈I Si := {x | ∀ i ∈ I x ∈ Si}.

interval We define four kinds of intervals as of the real numbers:

– [a, b] := {x ∈ R | (a≤x) and (x≤b)} – [a, b) := {x ∈ R | (a≤x) and (x

inventory book An inventory book is a ledger that identifies, describes, and records provenance of the artefacts in the collection of a museum.

If f is bijective, call the converse relation inverse function, we (also) write it as f −1.

inverse function If f : A → B is injective, then the converse relation is a partial function f −1 : B ⇀ A, we call it the inverse function of f. If f is bijective total function, then f −1 is a total function. inverse matrix Defined along with invertible

invertible We say that an n × n matrix A is invertible, iff there is an n × n matrix B, such that AB = BA = In. If this is the case, then we call B the inverse matrix of A and denote it with A−1. The corresponding (partial) operation on matrices is called matrix inversion invoke Defined along with subroutine invoker Defined along with subroutine irreflexive Defined along with reflexive irreflexive Defined along with reflexive

50 is (of complexity) Defined along with Landau set

isa link See inclusion isolation Defined along with database transaction issue Defined along with issue tracker

issue An issue (or bug report) specifies

– title: a short and descriptive overview (one line) – description: a precise description of the expected and actual behavior, giving exact reference to the component, version, and environment in which the bug occurs. (bugs must be reproducible and localizable) – issue metadata: who, when, what, why, state, . . . (see below) – conversation: a forum-like facility for disussing an issue. – attachment: e.g. a screen shot, set of inputs, etc. issue metadata Defined along with issue

issue number Issue metadata can specify

– issue number: for referencing with e.g. #15 – an assignee: a developer currently responsible – participants: people who get notified of changes/comments – labels: for specializing bug search – a state: e.g. one of new, assigned, fixed/closed, reopened. – a resolution for fixed bugs, e.g. ∗ FIXED: source updated and tested ∗ INVALID: not a bug in the code ∗ WONTFIX: “feature”, not a bug ∗ DUPLICATE: already reported elsewhere; include reference ∗ WORKSFORME: couldn’t reproduce issue – dependencies: which issues does this one depend on/block?

issue tracker An issue tracker (also called issue tracking system simply bugtracker) is a software appli- cation that keeps track of reported issues– i.e. software bugs, tasks, and feature requests – in software development projects. issue tracking system See issue tracker iterate Defined along with for loop

iterate Let S be a set, n ∈ N, and f : S → S be a function. We define the n-th iterate f n of f by 0 n (n − 1) f := IdS and f := f ◦ f for n>0. iteration Defined along with for loop

join See table join junction Defined along with graph key Defined along with dictionary

51 key pair Defined along with asymmetric-key cryptosystem keyword argument The last k≤n of n parameters of a function can be keyword arguments of the form pi=⟨⟨val⟩⟩i: If no argument ai is given in the function call, the default value ⟨⟨val⟩⟩i is taken. keyword argument python functions can take keyword arguments: if k is a sequence of key/value pairs then def f(p1,...,pn,∗∗k), binds the keys to values in the body of f. kibi Defined along with binary unit prefix

kilo Defined along with prefixes kwowledge factor Defined along with authentication factor label Defined along with issue number

label Given a graph G := =⟨V,E⟩ and a set L of labels,a vertex labelling is a function from V to L; a graph with such a function defined is called a vertex-labeled graph. Likewise, an edge labelling is a function from E to L. In this case, the graph is called an edge-labeled graph. A graph is called labeled, iff it has a vertex and/or edge labelling. labeled Defined along with label language See formal language

language shell See read–eval–print loop late antiquity Defined along with periodization

layer Sometimes we want to overlay images layers. ; leaf Defined along with tree

leaf Defined along with tree leap year Defined along with year

lemma Error: The defi does not appear to be inside a definition environment. line47:67

length Defined along with sequence

length Defined along with path

length The length |s| of a word s ∈ An is n. length Defined along with path

length The seven dimensions ofSI base units are length( L), mass( M), time( T ), current( I), temperature( Θ), luminous intensity( J), and amount( N).

lens Light from our surroundings enters our eye through the lens and then hits the retina on the back of our eye.

52 The retina has cones and rod, which are responsible for color and brightness vision, respec- tively.

less than We define the order relation

− +

We define the relation >Z (greater than) via (n>m):⇔ (m

less than The < relation is the transitive closure of the relation {(n, s(n)) | n ∈ N}, and ≤ its transi- tive-reflexive closure. > and ≤ are the corresponding converse relations. For a

library A python library is a python file with a collection of functions, classes, and methods. It can be loaded via the import command.

licensor Defined along with license line See text line line Defined along with graph

line feed character Defined along with text line line number Defined along with text line

linear ordering We call a partial ordering R a linear ordering (or simple ordering or total ordering), iff a≤b or b≤a for all a, b ∈ A. linearly ordered set We call a structure ⟨S, ≤⟩ of a set S and a total ordering ≤ a linearly or totally ordered set.

link Defined along with semantic network

link block Let p be a drupal page for an ontology group g, then a WissKI link block is a special drupal block with associated path builder, whose ontology paths all end in g. linked Defined along with path

1EdNote: continue for the others

53 linked data Linked data is structured data in which classified objects are interlinked via relations with other objects so that the data becomes more useful through semantic queries and access methods.

linked open data Linked open data(LOD) is linked data which is released under an open license, which does not impede its reuse by the community. linked open data cloud Given the Semantic Web technology stack, we can create interoperable ontologies and interlinked data sets, we call their totality the linked open data cloud.

list A list or sequence is an abstract data type that represents a finite number of ordered elements, where the same value may occur more than once.

list constructor We call [⟨⟨seq⟩⟩] the list constructor. literary work Defined along with copyrightable work

local A local RCS supports the following revision control actions: 1. initialize: creates a new repository with empty head revision (a.k.a. head). 2. checkout: given a revision identifier – by default the head – creates a new working copy from the reposi- tory.

3. add: places a file in the working copy under control of the RCS. 4. commit: transmits the differences between the head and the working copy to the repository, which patches the head. local name Defined along with XML namespace localhost Defined along with host

locator Defined along with hunk

l logarithm The logarithm logb(x) of a number x is to the base b is that l such that b = x. If the base b is clear from the context, we simply write log(x) for logb(x). The logarithm function log the inverse function to the .2 EdN:2 logarithm function See logarithm

logic Logic =b formal languages, inference and their relation with the world – Formal language FL: set of formulae( 2 + 3/7, ∀x.x + y = y + x) – Formula: sequence/tree of symbols (x, y, f, g, p, 1, π, ∈, ¬, ∧ ∀, ∃) – Model: things we understand (e.g. ) – Interpretation: maps formulae into models( [[three plus five]] = 8) – Validity: M |= A, iff [[A]] = T (five greater three is valid) – Entailment: A |= B, iff M |= B for all M |= A.(generalize to H |= A) – Inference: rules to transform (sets of) formulae( A, A ⇒ B ⊢ B)

2 EdNote: MK: We should define the logarithm function as x 7→ logb(x) and make a view of the inverse statement.

54 – Syntax: formulae, inference (just a bunch of symbols) – Semantics: models, interpr., validity, entailment(math. structures) logical constant Defined along with formulae logical constant Defined along with model

logical reasoning Error: The defi does not appear to be inside a definition environment. line42:54

logical system A logical system is a triple S := ⟨L, K, |=⟩, where L is a formal language, K is a set and |= ⊆ K × L. Members of L are called formulae of S, members of K models for S, and |= the satisfaction relation.

logical system Error: The defi does not appear to be inside a definition environment. line51:5

loop A loop is a control structure that allows to execute certain parts of a program (the body) multiple times depending on conditions. lower bound Defined along with luminous intensity Defined along with length machine instruction Defined along with computing device main branch Defined along with GIT flow main processor See central processing unit maintainer Defined along with guest mantissa Defined along with floating point number mantissa Defined along with scientific notation map See dictionary margin Defined along with width

markdown Markdown is a family of markup formats whose control words are unobtrusive and easy to write in a text editor. It is intended to be converted to HTML and other formats for display, e.g. in markdown cell Defined along with cell markup See document markup markup code Defined along with document markup

markup format The control words and composition rules for a particular kind of markup system determine a markup format. The markup format used in an electronic document is called its document type. mass Defined along with length

master branch In software development we profit from separate – master branch/trunk– main line of development, used for integration. – release branch– only bug fixing; no new features

55 – feature branch– develop a new feature; close branch upon merge – staging branch– integrate multiple fixes/features material thing Defined along with CIDOC CRM math idiom Defined along with formulae

math idiom Mathematicians use a stylized language that

R 0 3 / 2 – uses formulae to represent mathematical objects, e.g. 1 x dx – uses math idioms for special situations (e.g. iff, hence, let. . . be. . . , then. . . ) – classifies statements by role (e.g. Definition, Lemma, Theorem, Proof, Example) We call this language mathematical vernacular. mathematical structure A mathematical structure combines multiple mathematical objects (the components) into a new object. Structures are usually given as finite enumerations, where the components have names by which they can be referenced. mathematical vernacular Defined along with formulae mathematical vernacular Defined along with math idiom

matrix Let V be a vector space over a field K := ⟨F, +, 0, −, ∗, 1,/⟩, then a matrix is a rectangular m × n arrangement of members of F : A matrix is given doubly indexed values ai,j ∈ K (the entries) for 1≤i≤m and 1≤j≤n; we write a matrix as [ai,j]1≤i≤n,1≤j≤m.

matrix inversion Defined along with invertible Defined along with matrix product

matrix product Given matrices A := [ai,j]1≤i≤k,1≤j≤l and B := [bi,j]1≤i≤l,1≤j≤m, the matrix product AB Pl is defined via matrix multiplication as [ n=1 (ai,n ∗ bn,j)]1≤i≤k,1≤j≤m. matrix sum Defined along with Matrix addition maximum Defined along with minimum maximum Defined along with minimum

mebi Defined along with binary unit prefix media See medium media access control address Each NIC contains a unique number, the media access control address(MAC address), identifies the device uniquely on the network.

media content Defined along with medium

media query CSS-based layout with relative sizes and media queries– CSS conditionals based on client screen size/resolution/. . . medieval Defined along with periodization

medium A medium (plural media) is a communication medium or storage medium. The information conveyed or stored is called the media content.

mega Defined along with prefixes

56 member Defined along with set membership Defined along with set

memory The memory (also primary storage) is a storage subsystem in a computer that stores infor- mation for immediate use by its CPU.

merging There are basically two ways of merging the differences of files into one. message Defined along with communication medium

metadata Metadata: “data about data”, e.g. who has created these facts, images, or documents, how do they relate to each other? (not covered yet) metasearch engine Defined along with human-organized metasyntactic variable Defined along with pseudocode

method Most important HTTP request methods.(5 more less prominent)

GET Requests a representation of the specified re- safe source. PUT Uploads a representation of the specified resource. idempotent DELETE Deletes the specified resource. idempotent POST Submits data to be processed (e.g., from a web form) to the identified resource.

method Defined along with object-oriented programming micro Defined along with prefixes middle ages Defined along with periodization

milestone For timing work plans, most issue trackers provide milestones that issues can be targeted to. milli Defined along with prefixes

minimum The minimum min S (maximum max S) of an ordered set S is that element m (if it exists), such that all other members of S are smaller (larger) than m. We write min (a1, . . ., an) for min {a1, . . . , an} and max (a1, . . ., an) for max {a1, . . . , an}. If e is an expression and φ a condition (in a variable x), we write max (e) for max {e | φ} φ and call it the maximum for e over φ. Analogously, we write min (e) for min {φ | e} and call φ it the minimum for e over φ minimum Defined along with minimum

minute A minute is 60 seconds, an hour is 60 minutes, a day is 24 hours, and a week is seven days.

model Let ⟨D, [[·]]⟩ be a model for ALC, then we define – [[a: φ]] = T, iff [[a]] ∈ [[φ]], and – [[a R b]] = T, iff ([[a]], [[b]]) ∈ [[R]]. model Defined along with logic

model A model for ALC is a pair ⟨D, [[·]]⟩, where D is a non-empty set called the domain and [[·]] a mapping called the interpretation, such that

57 Op. formula semantics [[c]] ⊆ D = [[⊤]] [[⊥]] = ∅ [[r]] ⊆ D × D · [[φ]] = [[φ]] = D\[[φ]] ⊓ [[φ ⊓ ψ]] = [[φ]] ∩ [[ψ]] ⊔ [[φ ⊔ ψ]] = [[φ]] ∪ [[ψ]] ∃ R [[∃ R φ]] = {x ∈ D | ∃y ⟨x, y⟩ ∈ [[R]] and y ∈ [[φ]]} ∀ R [[∀ R φ]] = {x ∈ D | ∀y if ⟨x, y⟩ ∈ [[R]] then y ∈ [[φ]]}

model A model M := ⟨Do, I⟩ for propositional logic consists of

– the universe Do = {T, F} – the interpretation I that assigns values to essential connectives

– I(¬): Do → Do; T 7→ F, F 7→ T

– I(∧): Do × Do → Do; ⟨α, β⟩ 7→ T, iff α = β = T

We call a constructor a logical constant, iff its value is fixed by the interpretation

model Defined along with logical system

model A model is an applicative structure, whose universe contains special elements T (true for truth) and F (false) for falsehood. modern era Defined along with periodization module Defined along with drupal core

modulo Defined along with equivalence class modulus Defined along with integer division modulus Defined along with division

mongoDB mongoDB is the most popular NoSQL database system. (no SQL inside)

monitor See computer monitor monotonic Defined along with derivation relation

month A month is between 27 and 31 day, depending on which month of the calendar and year it is. multi-relation expression A multi-relation expression is built up from binary relations via conjunction: aRbSc. . . holds, iff R(a, b) holds and also bSc. . ..

multigraph A multigraph is a pair G := ⟨V,E⟩ where V is a set and V ⊆ 3 EdN:3

multiplication Multiplication is extended to Z by defining the product by cases:  |a| · |b| a, b ∈ a, b ∈ − a · b := if N or Z ( − (|a| · |b|) else

a c a·c multiplication We define multiplication on Q: The product b · d is b·d . multiplication Defined along with absolute value

3EdNote: continue; how do we do generalizations well? All we have already done for graphs should (with restrictions where necessary) also apply to multigraphs

58 multiplication Multiplication · computes the product a · b (also written as ab or a × b) of natural numbers a and b. It is defined by the equations x · 0 = 0 and x + s(y) = x + x · y.

multiplication Multiplication computes the product a b of numbers a and b. multiplicative inverse Defined along with field musical work Defined along with copyrightable work

mutable The last two items touch a somewhat delicate subject in programming. Mutable an immutable data structures: the former can be changed in-place – as we have above with the .set method, and the latter cannot. Both have their justification and respective ad- vantages. Immutable data structures are “safe” in the sense that they cannot be changed unexpectedly by another part of the program, they have the disadvantage that every time we want to have a variant, we have to copy the whole object. Mutable ones do not – we can change in place – but we have to be very careful about who accesses them when. This is also the reason why we spoke of “dictionary-like interface” to XML trees in lxml: dictionaries are immutable, while XML trees are not. mutually recursive Defined along with recursive name Defined along with subroutine

named wildcard Defined along with dynamic route namepsace prefix Defined along with namespace declaration namespace Defined along with project namespace declaration Defined along with XML document tree namespace declaration namespace declaration is an attribute xmlns:⟨⟨prefix⟩⟩|=| whose value is an XML names- pace n on an XML element e. The first associates the namepsace prefix ⟨⟨prefix⟩⟩ with the namespace n in e: Then, any XML element in e with a prefixed name ⟨⟨prefix⟩⟩:⟨⟨name⟩⟩ has namespace n and local name ⟨⟨name⟩⟩. A default namespace declaration xmlns=d on an element e gives all elements in e whose name is not prefixed, the namepsace d. Namespace declarations on subtrees shadow the ones on supertrees. nano Defined along with prefixes

narrative data Narrative data: documents and text fragments used for communicating knowledge to hu- mans. – e.g. plain text and formatted text with markup codes(see above)

natural number The set N of natural numbers is the set {0, 1, 2,...}. They are constructed by iteration of the successor function over zero. navigating Defined along with hypertext negation Defined along with formulae negative integer Defined along with non-negative integer negative rational number Defined along with positive rational number negative Defined along with positive real number

59 network interface A network interface is a software component in the operating system that implements the higher levels of the network protocol (the NIC handles the lower ones). network interface controller A network interface controller(NIC) is a hardware device that handles an interface to a computer network and thus allows a network-capable device to access that network. network packets Defined along with packet-switched network node Defined along with graph node Defined along with undirected graph non-empty Defined along with empty set

+ − non-negative integer We use Z0 := N and Z0 := {x ∈ Z | x = ( − y) for some y ∈ N} and call them the non- + + negative integers and non-positive integers respectively. Analogously, we use Z := {x ∈ Z0 | x ̸= 0} − − and Z := {x ∈ Z0 | x ̸= 0} for the positive integers and negative integers. non-negative rational number Defined along with positive rational number non-negative real number Defined along with positive real number non-positive integer Defined along with non-negative integer non-positive rational number Defined along with positive rational number non-positive real number Defined along with positive real number nondeterministic Turing machine A nondeterministic Turing machine(NTM) is a septuple M := ⟨A, S, b, Σ, s0, F, R⟩, where – A is a set called the alphabet, – S is a set of states, – b ∈ A the blank symbol. – Σ ⊆ A the input symbols

– s0 ∈ S is the initial state, – F ⊆ S is the set of accepting or final states, – and R ⊆ ((S\F) × A) × (S × A × {R,L}); it is called the transition relation. M is called a deterministic Turing machine(DTM) if R is a function R:(S\F) × A → S × A × {R,L}, then it is called the transition function. If it is irrelevant – or clear from the context – whether M is deterministic or not, we often just speak of Turing machines without a qualifier.

+ S i A A := + A nonempty string Let be an alphabet, then we define the sets i∈N of nonempty strings and A∗ := A+ ∪ {ϵ} of strings.

+ S i A A := + A nonempty word Let be an alphabet, then we define the sets i∈N of nonempty words (nonempty strings) and A∗ := A+ ∪ {ϵ} of words(strings).

normalized A formula A is called normalized wrt. an TBox T , iff it does not contain concept names defined in T .(convenient) normalized Defined along with scientific notation

normalized color Normalized colors use pixel values between 0 and 1. not fully specified Defined along with variable

60 null value Defined along with relational database management system

null vector Defined along with vector space

number A number is a mathematical object used to count or measure other objects.

number system A number system is simply a set of numbers.

numeral The representation of a number in a numeral system is called a numeral.

numeral system A numeral system (or system of numeration) is a writing system for expressing numbers, that is, a mathematical notation for representing numbers of a given set, using symbols in a consistent manner.

numerator Defined along with rational number

object In python all values belong to a class, which provide special functions we call methods. Values are also called objects, to emphasise class aspects. Method application is written with dot notation: ⟨⟨obj⟩⟩.⟨⟨meth⟩⟩(⟨⟨args⟩⟩) corresponds to ⟨⟨meth⟩⟩(⟨⟨obj⟩⟩,⟨⟨args⟩⟩). object Defined along with semantic network

object Defined along with ontology object Defined along with statement object Defined along with object-oriented programming object-oriented programming Object-oriented programming(OOP) is a programming paradigm based on the concept of an objects. Objects can contain data, in the form of fields (often known as attribute or properties) to represent object properties. Object behavior is specified via procedures (called methods in OOP). obligation of separation Obligation of separation: Personal data that was acquired for separate purposes has to be processed separately. octal Defined along with unary

on Defined along with path one Defined along with zero one-to-one See injective one-to-one correspondence See bijective

one-way function A one-way function is a function that is “easy” to compute on every input, but “hard” to invert given the image of a random input. onto See surjective

ontology An ontology is a formal model of (an aspect of) the world. It – introduces a vocabulary for the objects, concepts, and relations of a given domain, – specifies intended meaning of vocabulary in a description logic using ∗ a set of axioms describing structure of the model ∗ a set of facts describing some particular concrete situation

61 The vocabulary together with the collection of axioms is often called a terminology (or TBox) and the collection of facts an ABox(assertions). In addition to the represented axioms and facts, the description logic determines a number of derived ones.

ontology An ontology is a representation of the types, properties, and interrelationships of the entities that really or fundamentally exist for a particular domain of discourse.

ontology An ontology consists of a logical systems ⟨L, K, |=⟩ and concept axioms (expressed in L) about

– individuals: concrete instances of objects in the domain, – concepts: classes of individuals that share properties and aspects, and – relations: ways in which classes and individuals can be related to one another ontology group Defined along with ontology path

ontology group Defined along with path builder

pi ontology path We call sequence of facts si −→ oi, where si = oi−1 an ontology path and any subtree an ontology group. ontology web language OWL (the ontology web language) is a language for encoding TBox information about RDF classes. opacity Defined along with alpha

opaque Defined along with transparent

open Adapt the FLOSS license ideas to the particular domain X open X. ; – Open content: pictures, music, video, documents, . . . Creative Commons – Open data: data from science, government, and organizations,; . . . Open Data Commons[ OpenDataCommons:on]. – Open; licenses for many other domains X. open content Defined along with open open data Defined along with open open license Defined along with open

open source See Free/Libre/Open-Source Software open world assumption Defined along with closed world assumption

opened Once a file has been opened, the CPU can write to it and read from it. After use a file should be closed to protect it from accidental reads and writes.

opening tag For communication this tree is serialized into a balanced bracketing structure, where

– an inner element node is represented by the (called the opening tag) and (called the closing tag), – the leaves of the XML tree are represented by empty element tags (serialized as , which can be abbreviated as , – and text nodes (serialized as a sequence of UniCode characters).

62 – An element node can be annotated by further information using attribute nodes— serialized as an attribute in its opening tag. operand Defined along with expression language

operating system An operating system(OS) is a system program that manages computer hardware, software resources, and provides common services for computer programs. operation Defined along with vector space

operator An operator is a function that differs syntactically (e.g. by using infix notation) orseman- tically (in evaluation strategy or argument passing mode) from usual functions. operator Defined along with expression language operator application Defined along with expression out-degree Defined along with in-degree

outdegree Defined along with indegree output subsystem Defined along with information processing system

owner There are various legal entities (e.g. persons, states, companies, associations, . . . ) that can have ownership over a property p. We call them the owners of p.

owner Defined along with guest

ownership Ownership is the state or fact of exclusive rights and control over property, which may be a physical object, land/real estate or intangible object. ownership factor Defined along with authentication factor packet-switched network A packet-switched network divides messages into small network packets that are transported separately and re-assembled at the target.

page inspector The page inspector tool gives you an overview over the internal state of the browser. pair Defined along with set of pairs pair Defined along with Cartesian product

pair set See unordered pair

paper prototype Displayed here is our goal behavior, which we will pursue on the following slides. As we have not implemented this, we could have created this in an image program, e.g. photoshop or GIMP. We call such a mockup for informing our design intuition a paper prototype. The rectangles mark certain parts of our image and react to the mouse being moved over them. On the one hand the area is highlighted by the white rectangles. Additionally descrip- tive text is displayed below the image (in this case the name of the respective president). parameter Defined along with subroutine parameter substitution sqlite3 supplies a parameter substitution that SQL-sanitizes parameters (removes problem- atic SQL instructions). parent Defined along with three-way merge

63 parent Defined along with tree

parent Defined along with tree parent table Defined along with foreign key

partial function f ⊆ X × Y , is called a partial function, iff for all x ∈ X there is at most one y ∈ Y with (x, y) ∈ f.

partial function A relation f ⊆ X × Y , is called a partial function with domain X (write dom(f)) and codomain Y (write codom(f)), iff for all x ∈ X there is at most one y ∈ Y with (x, y) ∈ f. We write f : X ⇀ Y ; x 7→ y and f(x) = y instead of (x, y) ∈ f. We say that f(x) is the application of f to x and call x the argument of f. partial function space Given sets A and B we will call the set A → B (A ⇀ B) of all (partial) functions from A to B the (partial) function space from A to B. partial order See partial ordering

partial ordering We call a preorder ≤ ⊆ A × A on A a partial ordering (or partial order), iff it is antisym- metric. We associate with ≤ a strict ordering < := {(a, b) ∈ ≤ | a ̸= b}. We often also use the converse relations ≥ and >. partially decidable See recursively enumerable

partially ordered set We call a structure ⟨S, ≤⟩ of a set S and a partial ordering ≤ an partially ordered set or poset.

participant Defined along with issue number

patches patch is a sister utility that applies a diff δ := δ(f1, f2) to f1 – resulting in f2; we say it patches f1 with δ. patent Defined along with intellectual property

n+1 path Given a directed graph G = ⟨V,E⟩, then we call a vector p = ⟨v0, . . . , vn⟩ ∈ V a path in G iff (vi−1, vi) ∈ E for all 1≤i≤n, n>0.

– v0 is called the start of p (write start(p))

– vn is called the end of p (write end(p)) – n is called the length of p (write len(p)) path Defined along with uniform resource identifier

n + 1 path Given a directed graph G := ⟨V,E⟩a we call a n + 1-tuple p=⟨v0, . . . , vn⟩∈V a path in G iff (vi − 1, vi) ∈ E for all 1≤i≤n and n>0.

– We say that the vi are nodes on p and that v0 and vn are linked by p.

– v0 and vn are called the start and end of p (write start(p) and end(p)), the other vi are called inner nodes of p. – n is called the length of p (write len(p)). – We denote the set of paths in G with Π(G)

path builder The WissKI path builder maps ontology groups and ontology paths to drupal bundles and fields.

64 – ontology groups become data entry forms (bundles) for the root entities, – their fields are mapped to ontology paths. – subtrees in the ontology become sub-bundles.(shared objects) pebi Defined along with binary unit prefix

periodization The periodization of history gives names to notable periods in human history, here are some:

– The pre-historic period is the period of (human) history before the 8th century BC – The archaic period is the period between 8th and the 6th century BC. – Classical antiquity is commonly dated from the 6th century BC to the 5th century AD. – The term late antiquity describes the time of transition from classical antiquity to the Middle Ages, is commonly dated from the 3rd to the 7th century AD. – The middle ages or medieval time period ranges from the 5th to the 15th century AD. – The (European) renaiscance ranges from the 14th to the 17th century AD. – The modern era is the commonly dated from the 16th century AD to the present day.

permission level Authorization is often operationalized by assigning permission levels and binding the authorization to execute particular interactions to permission levels.

persistence layer Defined along with front end personal group Defined along with project

pillow Pillow is a fork (a version) of the old python library PIL (Python Image Library). (hence the name)

pixel Defined along with raster place-value notation Defined along with positional number system plain text Defined along with cryptography

plain text Digital text is subdivided into plain text, where all characters carry the textual information and formatted text, which also contains instructions to the document renderer.

plenary session Defined along with flipped classroom point Defined along with graph

port To separate the services and protocols of the network application layer, network interfaces assign them specific port, referenced by a number.

poset See partially ordered set Defined along with positional number system positional number system A positional number system N is a pair N = ⟨Db, φb⟩ with

– Db is a finite alphabet of b digits. b is called the base or radix of N

– assign each digit d ∈ Db a number φb(d) between 0 and b − 1. Pk i−1 – Extend φb to sequences of digits by φb(⟨nk, . . . , n1⟩) := i=1 φb(ni) · b positional number system A positional number system N is a triple N = ⟨Db, φb, ψb⟩ with

– Db is a finite alphabet of b digits.(b := #(Db) base or radix of N ) [b−1] – φb : Db → {ϵ, /, . . . , / } is bijective (first b unary numbers) + ∗ Lk [b] [i−1] – ψb : Db → {/} ; ⟨nk, . . . , n1⟩ 7→ i=1 φb(ni) ⊙ exp(/ ,/ ) (extends φb to string code) positional number system A positional number systemisa numeral system that uses positional notation (also called place-value notation) to encode a number by a sequence of digits. A positional number system for a number system N is given as a pair P := ⟨D, φ⟩, where D is a finite set D of digits (we call b := #(D) the base or radix of P ) and a injective mapping from D to N. Positional Notation extends φ to a bijective mapping from finite sequences over D to N using the of N by interpreting a finite sequence a0, . . . , an as a sum of successive i powers b multiplied by φ(ai). Details vary with N. positive integer Defined along with non-negative integer positive natural number The set N+ of positive natural numbers is the set {1, 2, 3,...}.

66 + p − p positive rational number We use Q := { q ∈ Q | p>0} and Q := { q ∈ Q | p<0} sets of positive rational numbers − p − p and negative rational numbers and Q0 := { q ∈ Q | p≤0} and Q0 := { q ∈ Q | p≥0} sets of non-positive rational numbers and non-negative rational numbers.

+ − − positive real number We use R and R sets of and negative real numbers and R0 and + R0 sets of non-positive real numbers and non-negative real numbers. Here a real number is called positive/negative, iff all rational numbers that approximate it are. postulate See axiom power Defined along with exponentiation

power Defined along with exponentiation power Defined along with exponentiation power Defined along with exponentiation

the power set: P(A) := {S | S ⊆ A}

power set Let A be a set, then the power set P(A) of A is {S | S ⊆ A}.

pre-historic Defined along with periodization pre-image Defined along with image precision Defined along with floating point number predecessor Defined along with successor

predicate Defined along with statement predicate constant Defined along with first-order signature

prefix A string p is a called a prefix of s (write p⊴s), iff there is a string t, such that s = conc(p, t). p is a proper prefix of s (write p ◁ s), iff t ̸= ϵ. prefix Defined along with subword

prefix code A (character) code c: A → B+ is a prefix code iff none of the codewords is a proper prefix to an other codeword, i.e.,

∀ x, y ∈ A x ̸= y ⇒ (c(x)̸◁ c(y) ∧ c(y)̸◁ c(x))

prefixed name Defined along with namespace declaration

prefixed unit Defined along with prefixes

prefixes TheSI system defines a set of 19 prefixes, which transform a unit into a prefixed unit by multiplying it with a .

67 Prefix Symbol 10n yottaY 1024 zettaZ 1021 exaE 1018 petaP 1015 teraT 1012 gigaG 109 megaM 106 kilok 103 hectoh 102 deca da 101 decid 10−1 centic 10−2 millim 10−3 micro µ 10−6 nanon 10−9 picop 10−12 femtof 10−15 attoa 10−18 zeptoz 10−21 yoctoy 10−24

preorder We call a binary relation ≤ ⊆ A × A on A a preorder (or quasiorder), iff itis reflexive and transitive. preordered set Defined along with base set presentation MathML Defined along with Mathematics Markup Language

primary key A column in a table can be designated as a primary key. This constrains its values to be non-null and unique i.e. all distinct. In DDL, we just add the keyword PRIMARY KEY to the column specification. primary storage See memory

primitive In a programming language, a primitive is a “basic unit of processing”, i.e. the simplest element that can be given a procedural meaning (its semantics) of its own.

private Group/project visibility can be one of three states:

– Private: Project access must be granted explicitly to each user. – Internal: The project can be accessed by any authenticated user. – Public: The project can be accessed without any authentication. Private and public make most sense in our setting.

private key Defined along with asymmetric-key cryptosystem procedure Defined along with subroutine

process A process is an instance of a program that is being executed. processor Defined along with information processing system

product Defined along with multiplication product Defined along with multiplication

68 product Defined along with multiplication product Defined along with multiplication program Defined along with programming language program Defined along with Turing machine program code See computer code

programmer A person involved in programming is called a programmer. programming See computer programming programming language A programming language L is a formal language for specifying sequences information pro- cessing system instructions.A word in L is called a program of L. programming paradigm Programming paradigms are a way to classify programming languages based on their fea- tures. Languages can be classified into multiple paradigms.

project Often, repository management systems organize repositories (called projects in GitLab) hierarchically into groups (also called namespaces) and provide a personal group to all users.

th projection We call the function πi : A1 × ... × An → Ai; ⟨a1, . . . , an⟩ 7→ ai the (i ) projection. proof Defined along with inference proof-reflexive Defined along with derivation relation proof-transitive Defined along with derivation relation proper prefix Defined along with prefix proper prefix Defined along with subword proper subgraph Defined along with subgraph

proper subset A set A is a proper subset of a set B (written A ⊂ B), iff A ⊆ B but A ̸≡ B. proper substring Defined along with subword proper subword Defined along with subword proper suffix Defined along with subword

proper superset A set A is a proper superset of a set B (written A ⊃ B), iff B ⊂ A. properties Defined along with class property Defined along with declaration property Defined along with ownership

property A property is a resource that has a name, such as author or homepage, and a property value is the value of a property, such as Michael Kohlhase or http://kwarc.info/kohlhase.(a property value can be another resource) property Defined along with object-oriented programming

property right Ownership involves multiple rights (the property rights), which may be separated and held by different parties.

69 property value Defined along with property

propositional logic Defined along with formulae propositional variable Defined along with formulae proset Defined along with base set

pseudocode Pseudocode is a plain language description of the steps in an algorithm or another system. Pseudocode often uses structural conventions of a normal programming language, but is intended for human reading rather than machine reading. In pseudocode we often use metasyntactic variables, i.e. is a specific word or set of words identified as a placeholder that is intended to be modified or substituted before real-world usage.

pseudonymized Error: The defi does not appear to be inside a definition environment. line24:18

public Defined along with private

public domain A work is said to be in the public domain, if no copyright applies, otherwise it is called copyrighted. public key Defined along with asymmetric-key cryptosystem

public key certificate A public key certificate is an electronic document which uses a digital signature to bind a public key with an identity, e.g. the name of a person or an organization. public key cryptography Public key cryptography split the key into an encode key e and a decode key d – key e can encode a text t to t′, but only d can decode t′ to t. public key infrastructure In a public key infrastructure, the TLS certificate is issued bya certificate authority, an organization chartered to verify identity and issue TLS certificates. public-key cryptosystem Defined along with asymmetric-key cryptosystem

pull Defined along with centralized pull request Defined along with fork

punch card A punch card is a piece of stiff paper that contains digital information represented bythe presence or absence of holes in predefined positions.

push Defined along with centralized

python console The JupyterLab python console, i.e. a python interpreter in your browser.(use this for python interaction and testing.)

70 quantifier Defined along with formulae quasi-identifier Defined along with personally identifiable information quasiorder See preorder

query We call a SELECT instructiona query. query Defined along with uniform resource identifier

quotient Defined along with division quotient Defined along with division quotient Defined along with rational number quotient set Defined along with equivalence class quotient space Defined along with equivalence class quotient space Defined along with equivalence class radix Defined along with positional number system

radix Defined along with positional number system radix Defined along with positional number system raising Defined along with exception

range A range is a finite sequence of numbers it can conveniently be constructed by the range function: range(⟨⟨start⟩⟩,⟨⟨stop⟩⟩,⟨⟨step⟩⟩) construts a range from ⟨⟨start⟩⟩ to ⟨⟨stop⟩⟩ with step size ⟨⟨step⟩⟩.

range Defined along with variable

raster We call the grid raster and each entry in it pixel (from “picture element”).

rasterized For monitors, vector graphics must be rasterized– i.e. converted into a raster image – before display.

71 + rational number The set Q of rational numbers is defined as (Z × N )/∼, where ((p1, q1) ∼ (p2, q3)), iff n p1 q2 = q2 q1. We call m := (n, m) a fraction or quotient; it denotes the rational number n [(n, m)]∼. In a fraction d , n is called the numerator and d the denominator. raw cell Defined along with cell raw string literal Defined along with string literal read Defined along with opened

read–eval–print loop A read–eval–print loop(REPL), also termed an interactive toplevel or language shell, is a simple, interactive user interface that takes single user inputs (i.e., single expressions or instructions), evaluates or executes) them, and returns the result to the user.

real number The set R of real numbers is defined as the completion of Q. real part Defined along with complex numbers receiver Defined along with communication medium recognizable See recursively enumerable recursion Defined along with recursive

recursive A concept definition c = C is called recursive, iff c occurs in C.

recursive We call a problem recursive, if its solution depends on solutions to smaller instances of the same problem. Recursion solves recursive problems by (mutually) recursive functions or types.

We call a set F = {f1, . . . , fn} of functions or types mutually recursive if they call each other in their bodies. We call a functions or types f recursive, iff {f} is mutually recursive. recursive Defined along with recursive

recursive A formal language is called recursive (or decidable), iff there is a total Turing machine that accepts it and undecidable iff there is not. recursively enumerable A formal language L is recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable), if there exists a Turing machine that accepts all strings of L but none outside of L. refer Defined along with reference

reference A reference is a value that enables a program to indirectly access a particular datum in the computer’s memory or in some other storage device. The reference is said to refer to the datum, and accessing the datum is called dereferencing the reference. reference table Defined along with foreign key

reflexive A relation R ⊆ A × A is called – reflexive on A, iff (a, a) ∈ R for all a ∈ A, and – irreflexive (or anti-reflexive) on A, iff (a, a) ̸∈ R for all a ∈ A.

reflexive A relation R ⊆ A × A is called – reflexive on A, iff ∀ a ∈ A (a, a) ∈ R

72 – irreflexive on A, iff ∀ a ∈ A (a, a) ̸∈ R – symmetric on A, iff ∀ a, b ∈ A (a, b) ∈ R ⇒ (b, a) ∈ R – asymmetric on A, iff ∀ a, b ∈ A (a, b) ∈ R ⇒ (b, a) ̸∈ R – antisymmetric on A, iff ∀ a, b ∈ A ((a, b) ∈ R ∧ (b, a) ∈ R) ⇒ a = b – transitive on A, iff ∀ a, b, c ∈ A ((a, b) ∈ R ∧ (b, c) ∈ R) ⇒ (a, c) ∈ R – equivalence relation on A, iff R is reflexive, symmetric, and transitive.

reflexive extension A relation R on A is reflexive, iff IdA ⊆ R, so we call R ∪ IdA the reflexive extension of R. regexp See regular expression

regular expression A regular expression (also called regexp) is a formal expression that specifies a set of strings. rejects Defined along with accepts relation Defined along with entity relationship diagram

relation We call all link labels except “inst” and “isa” in a semantic network relations. isa R inst Let N be a semantic network and R a relation in N such that A −→ B −→ C or A −→ R R B −→ C, then we can derivea relation A −→ C in N. The process of deriving new concepts and relations from existing ones is called inference and concepts/relations that are only available via inference implicit (in a semantic network). relation Defined along with ontology relation Defined along with ontology

relation R ⊆ A × B is a (binary) relation between A and B. If A = B then R is called a relation on A.

relation R ⊆ A × B is a (binary) relation between A and B. relation on Defined along with relation

relation on If A = B then R is called a relation on A. relational database management system In a relational database management system(RDBMS), data are represented as tables: every datum is represented by a row (also called database record), which has a value for all columns (also called an attributes) or fields). A null value is a special “value” used to denote a missing value. relationship Defined along with class

relative URI URIs can be abbreviated to relative URIs; missing parts are filled in from the context. relative complement See set difference release branch Defined along with GIT flow release branch Defined along with master branch remainder Defined along with integer division remainder Defined along with division

remote repositories GIT is a distributed revision control system that features

73 – local repositories for each working copy. – multiple remote repositories connected to a local repository ∗ clonea remote repository make local repository+working copy ∗ local repository changes can; be fetched from and pushed to a remote repository (the upstream/downstream repositories). – branches and forks(remote upstream repository) renaiscance Defined along with periodization

renewal provision Defined along with term provision

report supported by all bugtrackers – user reports issue(files report in the system) – other users extend/discuss/up/downvote issue – QA engineer triages issues – classification, remove duplicates, identify dependencies, tie to component, . . . and assigns to developer. – developer accept or re-assigns issue(fixes who is responsible primarily) – project planning by identification of sub-issues, dependencies (new issues) – bug fixing (design, implementation, testing) – issue landing (sign-off, integration into code base) – release of the fix (in the next revision) – QA engineer or developer closes issue reporter Defined along with guest repositories Defined along with revision control system repository hosting service A repository hosting service is a web-based repository management system that also offers storage space for repositories. repository management system A repository management system is an web application that supports the administration of a repository server and manages authentication and authorization. repository server Defined along with centralized representative Defined along with equivalence class

represented Defined along with ontology

research data Research data is any information that has been collected, observed, generated or created to validate original research findings. Although usually digital, research data also includes non-digital formats such as laboratory notebooks and diaries. resolution Defined along with issue number

resolved In revision control systems conflicts must be resolved by choosing one of the alternatives or creating a manually merged revision before changes can be committed.

resource A resource is anything that can have a URI, such as http://www.fau.de. resource See system resource

74 responsive web design Responsive web design(RWD) designs web documents so that they can be viewed with a minimum of resizing, panning, and scrolling – across a wide range of devices (from desktop monitors to mobile phones) retina Defined along with lens return Defined along with subroutine

return value Defined along with subroutine reusable Defined along with FAIR revision Defined along with revision control system revision control action Defined along with local revision control system A revision control system(RCS) a software system that tracks the change process of a document collection via a federation of repositories. Each step in the development history is called a revision. rod Defined along with lens

role Roles name binary relations (like in PL1) role Defined along with D-ontology

root Defined along with tree √ √ b b 2 root For b ∈ Z√, r ∈ Z is a b-th root of a ∈ Z (we write a), if r = a. The a is written as a. root Defined along with tree √ √ b b 2 root For b ∈ Q√, r ∈ Q is a b-th root of a ∈ Q (we write a), if r = a. The square root a is written as a. root Defined along with absolute value √ n n root The n-th root√ a of a number√ a ∈ N is the r ∈ N – if it exists, such that r = a. The square root 2 a is written as a. √ n n root The n-th root a of a number a is that r – if√ it exists, such that r = a. The second root is also called the square root and is written as a.

route A server-side scripting framework solves two problems:

1. making the development of functionality that generates HTML pages convenient and efficient, usually via a template engine, and 2. binding such functionality to URLs – the routes, we call this routing. route Defined along with serverside routing

route filter Dynamic routes can be restricted by a route filter to make them more selective.

route function Defined along with serverside routing routine See subroutine routing Defined along with route

75 routing See serverside routing

row Defined along with relational database management system

rule A CSS style sheet consists of a sequence of rules that in turn consist of a set of selectors that determine which XML elements the rule applies to and a declaration block that specifies intended presentation.

run A run (or computation) of a nondeterministic Turing machine M := ⟨A, S, b, Σ, s0, F, R⟩ on a tape t: N → A is a sequence c: N ⇀ C(M) of configurations of M, such that c(0) = ⟨w, 0, s0⟩, where w is the word encoded by t and c(i + 1) ∈ R(c(i)) for i>0. i For a deterministic Turing machine we have c(i) = R ⟨w, 0, s0⟩.

safe We call a HTTP request safe, iff it does not change the state in the web server.(except for server logs, counters,. . . ; no side effects) satisfaction relation Defined along with logical system

satisfiable Defined along with true under φ satisfiable Defined along with true under φ satisfiable Defined along with satisfied

satisfied Let S := ⟨L, K, |=⟩ be a logical system, M ∈ K be a model and A ∈ L a formula, then we say that A is

– satisfied by M, iff M |= A. – falsified by M, iff M ̸|= A. – satisfiable in K, iff M |= A for some model M ∈ K. – valid in K (write |=M), iff M |= A for all models M ∈ K. – falsifiable in K, iff M ̸|= A for some M ∈ K. – unsatisfiable in K, iff M ̸|= A for all M ∈ K. scalar Defined along with vector space scalar field Defined along with vector space

scalar fraction Defined along with scalar multiple

scalar multiple For a quantity q ∈ Q and a scalar r we define the scalar multiple r · q of r and q to be r · q := r, su, if q = su for some u ∈ U. Similarly, we define the scalar fraction q/q′ of two quantities q and q′ to be that (r / r′) ∈ R, such that if q = ru and q′ = r′u for some u ∈ U. Note that both operations are well-defined by the axioms above. scalar multiplication Defined along with vector space scale Defined along with floating point number scheme Defined along with uniform resource identifier

scientific notation In scientific notation all numbers are written in the form of a × 10b,(a ∈ R times 10 raised to the power of b ∈ Z), a is called the significand, mantissa, or coefficient. a × 10b is called normalized, iff 1≤|a|<10

76 second Since 1967, the second has been defined as exactly the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom (at a temperature of 0◦K). second component Defined along with first component

secondary storage Secondary storage (also known as external memory or auxiliary storage), refers to any form of storage device and media that it is not directly accessible by the CPU.

selector Defined along with rule self-join Defined along with table join

semantic We call a query language semantic, iff query answering involves derived axioms and facts.

semantic network A semantic network is a directed graph for representing knowledge: – nodes represent objects and concepts (classes of objects) (e.g. John (object) and bird (concept)) – edges (called links) represent relations between these (isa, father_of, belongs_to)

semantic web The semantic web is a collaborative movement led by the W3C that promotes the inclusion of semantic content in web pages with the aim of converting the current web, dominated by unstructured and semi-structured documents into a machine-understandable “web of data”. semantic web technology stack This is facilitated and standardized by the semantic web technology stack: – URIs for representing objects, – RDF triples for representing facts, – RDFa for annotating RDF triples in XML documents, – OWL for representing TBoxes, – triplestores for storing (lots of) RDF triples, – SPARQL for querying ontologies, – description logic reasoners for deciding ontology consistency and concept subsumption, – Protégé for authoring and maintaining ontologies, semantics Defined along with primitive

semantics Defined along with logic semidecidable See recursively enumerable sender Defined along with communication medium sentence Defined along with closed

sequence python has more types that behave just like lists, they are called sequence types.

sequence See list

sequence A sequence, (an)n∈S, is a function whose domain is a countable, totally ordered set S (e.g. N, then we often write (ai)). If S is infinite, we call any sequence (ai)i∈S on S an infinite sequence, and finite sequence otherwise. Then the cardinality of S is called the length of (ai)i∈S. Sequences are writen as

77 – 1, 2, 3, 4 for a concrete finite sequence, – 1, 2, 3, 4,..., 10 for a finite sequence with ellipsis, 1 n – x , . . . , x and x1, . . . , xn for a sequence of upper/lower-indexed variables of length n, – 1, 2, 3, 4,... for an infinite sequence, 1 2 – x , x ,... and x1, x2,... for a sequence of upper/lower-indexed variables of length n,

th Given a sequence a: S → T , and a ∈ S we write the i element of a as Si.

server A server is a program or a computer that provides functionality – called a service– for other programs or computers, called clients. server-side scripting framework A server-side scripting framework is a web server extension that generates web pages upon HTTP requests.

serverside routing Serverside routing (or simply routing) is the process by which a web server connects a HTTP request to a function (called the route function) that provides a web resource.A single URI path/route function pair is called a route. service Defined along with server

set A set is a collection of elements. We can represent sets by 1. listing the elements (also called member) within curly brackets: e.g. {a, b, c} 2. describing the elements via selection from another set S using a property P : {x ∈ S | x has property P }. We use {x | x has property P } as a shorthand, if the set to be selected from is obvious from the context. 3. stating elementhood (also called membership; written a ∈ S) or not (b ̸∈ S) outright.

set comprehension Indeed it is very difficult to define something as foundational as a set. We want setsto be collections of objects, and we want to be as unconstrained as possible as to what their elements can be. But what then to say about them? Cantor’s intuition is one attempt to do this, but of course this is not how we want to define concepts in math. a AA b b So instead of defining sets, we will directly work with representations of sets. For that we only have to agree on how we can write down sets. Note that with this practice, we introduce a hidden assumption: called set comprehension, i.e. that every set we can write down actually exists. We will see below that we cannot hold this assumption.

set difference set difference: A\B := {x | x ∈ A ∧ x ̸∈ B}

set difference Let A and B be sets, then the set difference A\B of A and B is {x | x ∈ A and x ̸∈ B}. We also call A\B the relative complement or simply complement of B in A. If A is clear from the context, we write B for the complement of B in A. set inclusion Defined along with subset set of nonempty strings See nonempty word

set of pairs Let A and B be sets, then the set of pairs A × B of A and B is defined as {(a, b) | a ∈ A, b ∈ B}, we call (a, b) ∈ A × B a pair. (a, b) = (c, d), iff a = c and b = d. set of str ings Defined along with nonempty word

78 set of words Defined along with nonempty word

share alike Defined along with CC provision

shell A shell is a command-line interface for accessing the services of a computer’s operating system.

sibling operator The CSS sibling operator + modifies a selector so that it (only) affects following sibling elements (same level). sign Defined along with floating point number

signature Defined along with expression language significand Defined along with floating point number significand Defined along with scientific notation

simple Defined along with cyclic simple Defined along with cyclic simple definition Error: The defi does not appear to be inside a definition environment. line21:49

simple ordering See linear ordering

sink Defined along with initial sink Defined along with initial size Defined along with finite

size The size #(A) of a set A is the number of elements in A.

software Defined along with computing device

solar A solar or tropical year is the time between successive spring or autumn equinoxes, or winter or summer solstices, roughly 365 days, 5 hours, 48 minutes, and 46 seconds.

solar calendar A solar calendar assigns a day to each solar day and often aligns years with the solar years.

solar day A solar day is the length of time which elapses between the sun reaching its highest point in the sky two consecutive times. The solar day on Earth is roghly 86400s. sound recording Defined along with copyrightable work

source Compiler: translates a program (the source) into another program (the binary) in a much simpler programming language for optimized execution on hardware directly. source Defined along with difference source See initial

source Defined along with initial source language Defined along with compiler space Defined along with time space-time Defined along with CIDOC CRM

79 sparql endpoint A system is called a SPARQL endpoint, iff it answers SPARQL queries.

square root Defined along with root square root Defined along with root square root Defined along with absolute value

square root Defined along with root square root Defined along with root

staging GIT local workflow: staging files for commit using git add

Working Staging .git directory Copy Area (repository)

checkout

Your work here You collect/stage You commit normal file system changes locally changes locally

commits acts only on staged files git add foo. (GIT must know about them) ; staging branch Defined along with master branch

star operator The star operator unpacks a list into an argument sequence. start Defined along with path start Defined along with path state Defined along with issue number

state Defined along with stateful state Defined along with nondeterministic Turing machine state register Defined along with Turing machine

stateful A system S is described as stateful if it is designed to remember preceding events. The totality of remembered events is called the state of S.

statement A RDF statement s (also known as a triple) consists of a resource (the subject of s), a property (the predicate of s), and a property value (the object of s). A set of RDF triples is called an RDF graph. static content Defined along with block

step Defined along with halts

step equation Error: The defi does not appear to be inside a definition environment. line75:48

steps Defined along with accepts

80 storage device A storage device is any type of hardware that stores (i.e. records with the purpose of later returning) data in a (fixed or removable) storage medium.

storage medium A storage medium is a physical material that holds (stores) information. storage subsystem Defined along with information processing system store Defined along with storage device store Defined along with storage medium stpl python Defined along with template file

stream Many operating systems use files as a primary computational metaphor, also treating other resources like files. This leads to an abstraction of files called streams, which encompass files as well as e.g. keyboards, printers, and the screen, which are seen as objects that can be read from (keyboards) and written to (e.g. screens). This practice allows flexible use of programs, e.g. re-directing a the (screen) output of a program to a file by simply changing the output stream. strict ordering Defined along with partial ordering string Defined along with integer

string python strings are sequences of UniCode characters. string Defined along with nonempty string string Defined along with alphabet

string literal python uses string literals, i.e character sequences surrounded by one, two, or three sets of matched single or double quotes for string input. The content can contain escape sequences, i.e. the escape character backslash followed by a code character for problematic characters:

Seq Meaning Seq Meaning \\ Backslash (\) \’ Single quote (’) \" Double quote (") \a Bell (BEL) \b Backspace (BS) \f Form-feed (FF) \n Linefeed (LF) \r Carriage Return (CR) \t Horizontal Tab (TAB) \v Vertical Tab (VT)

In triple-quoted string literals, unescaped newlines and quotes are honored, except that three unescaped quotes in a row terminate the literal. Prefixing a string literal with a r or R turns it into a raw string literal, in which backslashes have no special meaning. structured query language See SQL

subgraph Let G := ⟨V,E⟩ and G′ := ⟨V ′,E′⟩ be two graphs. If V ′ ⊆ V and E′ ⊆ E, then G′ is a subgraph of G, written G′ ⊆ G. If G′ ⊆ G and G′ ̸= G, then G′ is a proper subgraph of G; we write G′ ⊂ G. subject Defined along with statement

subpixel In color monitors, pixels typically consist not of a single light source, but three distinct subpixels. subprogram See subroutine

81 subroutine A subroutine (also called routine or subprogram) is a program fragment in a program P that performs a specific task, packaged as a unit in so that it can be executed (called, or invoked) by P .

A subroutine p consists of an identifier (its name), a sequence xx1, . . . , xn of local identifiers called parameters, and a program fragment (called the body of p). The length n of x is called the arity of p. When P (the invoker) calls p, then it supplies a list of values (called arguments) to p: the parameters are replaced by the arguments, and the body is executed in the context where it is called. p may or may not return values v to P , the return values. If it does, it is called a function otherwise a procedure.

subset A set A is a subset of a set B (written A ⊆ B), iff all x ∈ A are members of B. The relation ⊆ is called set inclusion.

substring Let A be an alphabet, then we say that a string s ∈ A∗ is a substring of a string t ∈ A∗ (written s⊆t), iff there are strings v, w ∈ A∗, such that t = vsw. substring See subword subsumption Defined along with concept

subsystem An entity S′ in a system S that is a system itself is called a subsystem of S.

subtraction Subtraction computes the difference a − b of a and b which is defined as a + ( − (b)).

b subtraction The subtraction operator computes the difference a − b of a ∈ Q and c ∈ Q which is defined ( − (b)) as a + c . subtraction Defined along with absolute value

subtraction Subtraction − computes the difference ab of natural numbers a and b. It is defined as is that natural number c – if it exists, such that a + c = b.

subtraction Subtraction − computes the difference ab of a and b. It is defined as is that number c – if it exists, such that a + c = b.

subtree A subgraph of a tree that is itself a tree is called a subtree.

subword Let A be an alphabet, then we say that a word s ∈ A∗ is a subword(substring) of a word t ∈ A∗ (written s⊆t), iff there are words v, w ∈ A∗, such that t = vsw. If v ̸= ϵ or w ̸= ϵ, then we call s a proper subword(proper substring) of t and write s⊂t. If v = ϵ, then we call s a prefix of t and write s⊴t, if additionally w ̸= ϵ we call s a proper prefix of t and write s ◁ t. Similarly, if w ̸= ϵ, then we call s a suffix of t, if additionally v ̸= ϵ a proper suffix of t.

successor We call a unary natural number the successor(predecessor) of another, if it can be con- structing by adding (removing) a slash. (successors are created by the s-rule) successor function Defined along with natural number suffix Defined along with subword sum Defined along with addition sum Defined along with summation

82 sum Defined along with addition

summation Summation is iterated addition, we define the sum over a sequnce ai by

m X  0 if (n≤m) ai := Pm an + ( ai) else i=n i=(n + 1)

The variable i is called the summation index and n and m the lower bound and upper bound of the sum respectively, together the specify the range of summation. P P There are variant summation operators φ ai and i∈S ai. The first one specifies the range of the summation via a formula φ in i and the second one directly by giving a set S. summation index Defined along with summation summation range Defined along with summation

supergraph If G is a subgraph of G′, then we call G′ a supergraph of G.

superset A set A is a superset of a set B (written A ⊇ B), iff B ⊆ A.

supertree If T is a subtree of T ′, then we call T ′ a supertree of T .

surjective Defined along with injective

surjective A function f : S → T is called surjective or onto, iff for all y ∈ T there is a x ∈ S with f(x) = y.

symbol A symbol is a mark, sign or word that indicates, signifies, or is understood as representing an idea, object, or relationship. symbol table See dictionary

symbolic data Symbolic data: descriptions of object and facts in a formal language – e.g. 3+5 in python (see above)

symmetric A relation R ⊆ A × A is called – symmetric on A, iff (b, a) ∈ R for all a, b ∈ A with (a, b) ∈ R. – asymmetric on A, iff (b, a) ̸∈ R for all a, b ∈ A with (a, b) ∈ R. – antisymmetric on A, iff (a, b) ∈ R and (b, a) ∈ R imply a = b. symmetric Defined along with reflexive symmetric difference The symmetric difference A∆B of sets A and B is defined as (A\B) ∪ (B\A); it is also written as A ⊕ B or A ⊖ B.

syntax Programming language syntax describes the surface form of the program: the admissible character sequences. It is also a composition of the syntax for the primitives.

syntax Defined along with logic

83 system A system is a group of interacting or interrelated entities that form a unified whole. A system is delineated by its spatial and temporal boundaries, surrounded and influenced by its environment, described by its structure and purpose and expressed in its functioning. system access control System access control: Unauthorized users may not use systems that process personal data. ( passwords, firewalls, . . .) ; system of numeration See numeral system

system resource A system resource, or simply resource, is any physical or virtual component of limited availability within a computer system or connected to it.

system software System software is software mainly intended for running the computer as a platform for other software, the application software. table Defined along with relational database management system

table join A table join (or simply join) is a means for combining columns from one (self-join) or more tables by using values common to each.

table name Tables are identified by table name and individual components of records by column name.

tag HTML marks up the structure and appearance of text with tags of the form (begin tag), (end tag), and (empty tag), where el is one of the following

structure html,head, body metadata title, link, meta headings h1, h2,..., h6 paragraphs p, br lists ul, ol, dl,..., li hyperlinks a multimedia img, video, audio tables table, th, tr, td,... styling style, div, span old style b, u, tt, i,... interaction script forms form, input, button Math MathML (formu- interactive vector graphics (SVG) lae) graphics and canvas (2D bitmapped)

tape Defined along with Turing machine tape See tape specification

tape specification A tape specification (also called tape) for a Turing machine M := ⟨A, S, b, Σ, s0, F, R⟩ is a sequence t: N → A, such that t−1(c) is finite for all c ∈ A except b. target Defined along with difference target language Defined along with compiler tebi Defined along with binary unit prefix

telnet protocol The telnet protocol uses TCP directly to send text-based messages two networked comput- ers. It customarily uses port 25. temperature Defined along with length template Defined along with template engine

template engine A template engine (or template processor) for a document format F is a program that transforms templates, i.e. strings or files (a template file) ith a mixture of program constructs and F -markup, into a F -strings or F -documents by executing the program constructs in the template(template processing).

84 template file A stpl template file mixes HTML with stpl python: – stpl python is exactly like python but ignores indentation and closes bodies with end instead. – stpl python can be embedded into the HTML as ∗ a code lines starting with a %, ∗ a code blocks surrounded with <% and %>, and ∗ an expressions {{⟨⟨exp⟩⟩}} as long as ⟨⟨exp⟩⟩ evaluates to a string. template file Defined along with template engine

template functions stpl python supplies the template functions 1. include(⟨⟨tpl⟩⟩,⟨⟨vars⟩⟩), where ⟨⟨tpl⟩⟩ is another template file and ⟨⟨vars⟩⟩ a set of variable declarations (for ⟨⟨tpl⟩⟩). 2. defined(⟨⟨var⟩⟩) for checking definedness ⟨⟨var⟩⟩ 3. get(⟨⟨var⟩⟩, default=⟨⟨val⟩⟩): return the value of ⟨⟨var⟩⟩, or a default ⟨⟨val⟩⟩. 4. setdefault(⟨⟨name⟩⟩,⟨⟨val⟩⟩) template processing Defined along with template engine template processor See template engine tera Defined along with prefixes

term Terms: A ∈ wff ι(Σι) (denote individuals: type ι)

– Vι ⊆ wff ι(Σι), f i 1 k – if f ∈ Σk and A ∈ wff ι(Σι) for i≤k, then f(A ,..., A ) ∈ wff ι(Σι). term Defined along with expression language

term provision a license is a regular contract (about intellectual property) that is handled just like any other contract. (it can stipulate anything the licensor and licensees agree on) in particular a license may – involve term, territory, or renewal provisions, – require paying a fee and/or proving a capability, or – require to keep the licensor informed on a type of activity, and to give them the oppor- tunity to set conditions and limitations.

terminal The JupyterLab terminal, i.e. a UNIX shell in your browser. (use this for managing files)

85 terminal Defined along with initial terminal Defined along with initial

terminal client Send shell instructions and responses as text messages between a terminal client (a program on the local host) and a terminal server (a program on the remote host). terminal server Defined along with terminal client

terminology We call the subgraph of a semantic network N spanned by the isa links and relations between concepts the terminology (or TBox, or the famous Isa-Hierarchy) and the subgraph spanned by the inst links and relations between objects, the assertions (or ABox) of N. terminology Defined along with ontology terminology Defined along with D-ontology territory provision Defined along with term provision

text editor A text editor is a program used for rendering and manipulating text files.

text file A text file is a file that is structured as a sequence of encoded characters. Computer files that are not text files are called binary files.

text line In practice, text files are often processed as a sequence of text lines (or just lines), i.e. sub- strings separated by the line feed character U+ 000A; LINE FEED (LF). The line number is just the position in the sequence. text node Defined along with XML document tree

text node The main remaining functionality in XML is the treatment of text. XML treats text as special kinds of node in the tree: text nodes. They can be treated just like any other node in the XML tree in the etree library. textual content Defined along with document markup theme Defined along with drupal core

theorem A theorem is a statement about mathematical objects that we know to be true. third party cookies Third party cookies are used by advertising companies to track users across multiple sites. (but you can turn off, and even delete cookies)

three-way merge In a three-way merge the files are f1 and f2 are assumed to be created by changing a joint original (the parent) p by editing.

If there are hunks h1 in δ(f1, p) and h1 in δ(f2, p) that affect the same line in p, then we call the pair (h1, h2) a conflict. 3 The result of a three-way merge are two diffs µi (f1, f2, p), which contain the non-conflicting differences of δ(fi, p) and (representations called conflict markers of) the conflicts.

time The time used by a computation c of a Turing machine is #(dom(c)) and the space is the number of distinct cells, the head visited.

time Time can be measured by observing a certain number of repetitions of one or another standard cyclical event. Every such event (e.g. the passage of a free-swinging pendulum) constitutes one standard unit. time Defined along with length

86 title Defined along with issue

top concept The top concept ⊤ (for “true” or “all”) and the bottom concept ⊥ (for “false” or “none”).

total A relation R ⊆ A × B is called total iff for all x ∈ A there is a y ∈ B, such that (x, y) ∈ R.

total We call a Turing machine total, if it halts on any input tape.

total R ⊆ A × B is called total iff ∀ x ∈ A ∃ y ∈ B (x, y) ∈ R.

total function If f : X ⇀ Y is a total relation, we call f a total function and write f : X → Y .(∀ x ∈ X ∃1 y ∈ Y (x, y) ∈ f)

total function If f : X ⇀ Y is a total relation (i.e. for all x ∈ X there is a unique y ∈ Y with (x, y) ∈ f), we call f a total function and write f : X → Y . total ordering See linear ordering totally ordered set See linearly ordered set trademark Defined along with intellectual property transaction Defined along with database transaction transition function Defined along with nondeterministic Turing machine transition relation Defined along with nondeterministic Turing machine

transitive A relation R ⊆ A × A is called transitive (else intransitive) on A, iff (a, c) ∈ R for all a, b, c ∈ A with (a, b) ∈ R and (b, c) ∈ R. transitive Defined along with reflexive

transitive closure Let R be a binary relation, then we call the smallest – the smallest transitive relation that contains R the transitive closure of R. – the smallest transitive and reflexive relation that contains R the transitive-reflexive closure of R we denote it with R∗. transitive-reflexive closure Defined along with transitive closure transitive-reflexive closure Let R be a binary relation, then we call the smallest transitive relation that contains R the transitive-reflexive closure of R we denote it with R∗. transparency Defined along with alpha

transparent Transparency is an important operation. In this example we want to layer two images on top of each other. We thus need to store for each pixel a measure of how transparent it is. We expand our RGB notion to RGBA, by introducing a fourth channel A. A stands for alpha and corresponds to the opacity of a pixel, i.e. a value of 0 means zero opacity (fully transparent), a value of 1 (normalized) means fully opaque (no transparency).

transport layer The transport layer is responsible for delivering data to the appropriate application process on the host computers by forming data packets, and adding source and destination port numbers in the header.

t transposed matrix Given a matrix A := [ai,j]1≤i≤n,1≤j≤m, then the transposed matrix of A is given as A := [aj,i]1≤i≤n,1≤j≤m

87 trap door function Asymmetric cryptosystems are based on trap door functions: one-way functions that can (only) inverted with a suitable key. trapdoor Defined along with trapdoor function

trapdoor function A trapdoor function is a one-way function that is easy to invert given a piece of information called the trapdoor.

tree A tree is a DAG G = ⟨V,E⟩ such that

– There is exactly one initial node vr ∈ V (called the root) – All nodes but the root have in-degree 1. We call v the parent of w, iff (v, w) ∈ E (w is a child of v). We call a node v a leaf of G, iff it is terminal, i.e. if it does not have children.

tree A tree is a directed acyclic graph G := ⟨V,E⟩ such that

– there is exactly one initial node vr ∈ V (called the root), and – all nodes but the root have indegree 1. We call v the parent of w, iff (v, w) ∈ E (w is a child of v). We call a node v a leaf of G, iff it is terminal, i.e. if it does not have children. An ancestor is an iterated parent, and a descendant an interated child. triage Defined along with report triple See statement

triplestore A triplestore or RDF store is a purpose-built database for the storage RDF graphs and retrieval of RDF triples usually through variants of SPARQL. tropical year See solar true Defined along with truth value

true A is true in domain D iff [[A]] = D true Defined along with model

true under φ Let L be a language with variables, K a class of models for L, M := ⟨U, I⟩ a model in K, and A ∈ L a formula, then we call A

φ – true under φ in M, iff Iφ(A) = T (write M |= A) φ – false under φ in M, iff Iφ(A) = F (write M ̸|= A)

– satisfiable in M, iff Iφ(A) = T for some assignment φ – valid in M, iff M |=φ A for all assignments φ (write M |= A)

– falsifiable in M, iff Iφ(A) = F for some assignments φ

– unsatisfiable in M, iff Iφ(A) = F for all assignments φ

true under φ Let wff (Σ, V) be an expression language, A := ⟨U, @, Λ⟩ an applicative structure, I :Σ → U an interpretation, and φ: V → U a variable assignment, then we a well formed formula A

φ – true under φ in M, iff Iφ(A) = T (we write M |= A) φ – false under φ in M, iff Iφ(A) = F; write M ̸|= A

– satisfiable in M, iff Iφ(A) = T for some assignment φ

88 – valid in M, iff M |=φ A for all assignments φ

– falsifiable in M, iff Iφ(A) = F for some assignments φ

– unsatisfiable in M, iff Iφ(A) = F for all assignments φ trunk See master branch truth Defined along with model

truth value There are two truth values: true (also called verum, denoted by T, 1, or ⊤) and false (or untrue, also falsum); written as F, 0, or ⊥). The set {T, F} of truth values is denoted with B. truth value Defined along with Universe

truth value PL1 talks about two kinds of objects: (so we have two kinds of symbols)

– truth values; sometimes annotated by type o (like in PL0) – individuals; sometimes annotated by type ι (numbers, foxes, Pokémon,. . .) twelve Defined along with zero two Defined along with zero

two-way merge In two-way merge, an automated procedure tries to combine two different files by copying over differences by guessing or asking the user. type See data type type Defined along with variable

unary The following positional number systems are in common use.

name set base digits example

unary N1 1 / /////1 binary N2 2 0,1 01010001112 octal N8 8 0,1,. . . ,7 630278 decimal N10 10 0,1,. . . ,9 16209810 or 162098 hexadecimal N16 16 0,1,. . . ,9,A,. . . ,F FF 3A1216

unary exponentiation The unary exponentiation operation can be defined by the equations exp(n, o) = s(o) and exp(n, s(m)) = n ⊙ exp(n, m).

unary multiplication The unary multiplication operation can be defined by the equations n ⊙ o = o and n ⊙ s(m) = n ⊕ n ⊙ m. unary natural numbers We call the representation of natural numbers by slashes on a surface the unary natural numbers unary natural numbers we call these representations unary natural numbers.

Jo Js(m) unary product The unary product operation can be defined by the equations i=o ni = s(o) and i=o ni = Jm ns(m) ⊙ i=o ni.

Lo Ls(m) unary summation The unary summation operation can be defined by the equations i=o ni = o and i=o ni = Lm ns(m) ⊕ i=o ni. uncountable Defined along with countable

89 undecidable Defined along with recursive

undefined at We call a partial function f : X ⇀ Y undefined at x ∈ X, iff (x, y) ̸∈ f for all y ∈ Y .(write f(x) = ⊥) undefined at Defined along with defined at undirected edge Defined along with undirected graph undirected graph Defined along with graph

undirected graph An undirected graph is a pair ⟨V,E⟩ such that – V is a set of vertices (or nodes)(draw as circles) – E ⊆ {{v, v′} | v, v′ ∈ V ∧ (v ̸= v′)} is the set of its undirected edges(draw as lines) unicode Standard Defined along with universal character set

unicode standard The unicode standard( UniCode) is an industry standard allowing computers to consistently represent and manipulate text expressed in any of the world’s writing systems. (currently about 100.000 characters) uniform resource identifier A uniform resource identifier(URI) is a global identifiers of local or network-retrievable documents, or media files (web resources). URIs adhere a uniform syntax (grammar) defined in RFC-3986 [BerFieMas:05]. A URI is made up of the following components:

– a scheme that specifies the protocol governing the resource – an authority: the host (authentication there) that provides the resource. – a path in the hierarchically organized resources on the authority. – a query in the non-hierarchically organized part of the host data. – a fragment identifier in the resource. uniform resource locator A uniform resource locator(URL) is a URI that that gives access to a web resource, by specifying an access method or location. All other URIs are called uniform resource names (URN). uniform resource name Defined along with uniform resource locator

union Defined along with concept

union Let A and B be sets, then the union A ∪ B of A and B is defined as {x | x ∈ A or x ∈ B}. S union Let I be a set and {Si | i ∈ I} a family of sets, then the union i∈I Si over the collection S is {x | x ∈ Si for some i ∈ I}.

union union: A ∪ B := {x | x ∈ A ∨ x ∈ B} S union over a collection union over a collection: Let I be a set and Si a family of sets indexed by I, then i∈I Si := {x | ∃ i ∈ I x ∈ Si}. unique Defined along with primary key unique name assumption Defined along with closed world assumption unit See unit of measurement

90 unit of measurement A unit of measurement (or just unit) is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement. universal character set A scalable architecture for representing all the worlds scripts – The universal character set(UCS) defined by the ISO/IEC 10646 International Stan- dard, is a standard set of characters upon which many character encodings are based. – The unicode Standard defines a set of standard character encodings, rules for normal- ization, decomposition, collation, rendering and bidirectional display order

universe We assume an arbitrary universe Dι ̸= ∅ of individuals(this choice is a parameter to the semantics) universe Defined along with model universe Defined along with applicative structure unknown Defined along with variable

unordered pair If A is a set and x, y ∈ A, then the unordered pair or pair set {x, y} is the p ⊆ A, such that A z ∈ p, iff z = x or z = y. The set of all pair sets is sometimes denoted with (( 2 )). unsatisfiable Defined along with true under φ unsatisfiable Defined along with true under φ unsatisfiable Defined along with satisfied untrue Defined along with truth value

update The SQL update statement allows to change existing records. UPDATE \$\pmetavar{table}\$ SET \$\pmetavar{column}_1\$ = \$\pmetavar{value}_1\$, \$\pmetavar{column}_2\$ = \$\pmetavar{value}_2\$, \$\ldots\$ WHERE \$\pmetavar{condition}\$;

upper bound Defined along with summation upstream Defined along with remote repositories user Defined along with user interface

user agent HTTP is used by a client (called user agent) to access web resources (addressed by uniform resource locators(URLs)) via a HTTP request. The web server answers by supplying the resource (and metadata).

user interface A user interface(UI or simply interface), is the means in which a person (the user) controls a software application or hardware device. user-supplied content Defined along with block valid Defined along with true under φ valid Defined along with true under φ valid Defined along with satisfied validity Defined along with logic

91 value Defined along with declaration

value Defined along with relational database management system value Defined along with dictionary value Defined along with variable

value A value is the representation of some entity that can be manipulated by a program.

value function Given a model ⟨D, I⟩, the value function Iφ is recursively defined: (two parts: terms & propositions)

– Iφ : wff ι(Σι) → Dι assigns values to terms.

∗ Iφ(X) := φ(X) and ∗ Iφ(f(A1,..., Ak)) := I(f)(Iφ(A1),..., Iφ(Ak))

– Iφ : wff o(Σ) → Do assigns values to formulae:

∗ Iφ(T ) = I(T ) = T, ∗ Iφ(¬ A) = I(¬)(Iφ(A)) 0 ∗ Iφ(A ∧ B) = I(∧)(Iφ(A), Iφ(B)) (just as in PL ) 1 k 1 k ∗ Iφ(p(A ,..., A )) := T, iff ⟨Iφ(A ), . . ., Iφ(A )⟩ ∈ I(p) ∗ Iφ(∀X A) := T, iff Iφ,[a/X](A) = T for all a ∈ Dι.

0 value function The value function Iφ : wff o(Vo) → Do assigns values to PL formulae. It is recursively defined,

– Iφ(P ) = φ(P ) (base case)

– Iφ(¬ A) = I(¬)(Iφ(A)).

– Iφ(A ∧ B) = I(∧)(Iφ(A), Iφ(B)).

value function Let wff (Σ, V) be an expression language, A := ⟨U, @, Λ⟩ an applicative structure, I :Σ → U an interpretation, and φ: V → U a variable assignment, then we call a function Iφ : wff (Σ, V) → U a value function, iff:

1. Iφ(X) := φ(X) for X ∈ V,

2. Iφ(c) := I(c) for c ∈ Σ, and

3. Iφ(f A) := (Iφ(f)@Iφ(A))

I Iφ(A) is often written as [[A]]φ or [[A]]φ if the interpretation is clear from the context. On closed terms, the variable assignment φ is often dropped.

variable A variable is a memory location which contains a value. It is referenced by an identifier – the variable name.

variable A variable is a memory location which contains a value. It is referenced by an identifier– the variable name.

variable A variable is an alphabetic character representing a mathematical object, called the value of the variable, which is either arbitrary (but fixed) or not fully specified or unknown – in this case the variable is called an unknown. The set of objects a variable v can stand for is called the range or type. variable assignment A variable assignment ⟨⟨var⟩⟩=⟨⟨val⟩⟩ assignsa value.

92 variable assignment A variable assignment φ: Vι → Dι maps variables into the universe. variable assignment A variable assignment φ: Vo → Do assigns values to propositional variables. variable assignment Let wff (Σ, V) be an expression language with variables V and A := ⟨U, @, Λ⟩ an applicative structure, then we call a mapping Φ: V → U a variable assignment. variable binding Defined along with expression variable name Defined along with variable

variable name Defined along with variable vector Defined along with vector space vector Defined along with n-dim Cartesian space vector Defined along with n-dimensional Cartesian space

vector addition Defined along with vector space

vector graphics Image representation formats that store shape information instead of individual pixels, are refered to as vector graphics.

vector space V := ⟨G, F, ·⟩ is called a vector space over a field F := ⟨F, ∗, +⟩ (the scalar field of V), if G := ⟨V, +, 0, −⟩ is an , and the following three conditions hold for scalar multiplication ·: F × V → V :

1. scalar multiplication is compatible with field multiplication (i.e. a ∗ bv = abv for all a, b ∈ F and v ∈ V ) 2. scalar multiplication is distributive w.r.t field addition (i.e. va + b = (av) + (bv) for all a, b ∈ F and v ∈ V ) 3. scalar multiplication is distributive w.r.t vector addition (i.e. au + v = (au) + (av) for all a ∈ F and v ∈ V ). V is called the base set of V, its members are called vectors, and + vector addition. +, −, and · are the operations and 0 is called the zero vector or null vector of V. Finally, the members of F are called scalars. vertex Defined along with graph

vertex Defined along with undirected graph vertex labelling Defined along with label vertical edge pixel Defined along with horizontal edge pixel

verum Defined along with truth value view See database view view Defined along with block

visual markup Markup is by no means limited to visual markup for documents intended for printing as ?document-markup.ex? may suggest. There are aural markup formats that instruct document renderers that transform documents to audio streams of e.g. reading speeds, intonation, and stress. vocabulary Defined along with ontology

93 web IDE A web IDE or cloud IDE, is a browser-based integrated development environment.

web application A web application is a program that runs on a web server and delivers its user interface as a web site consisting of programmatically generated web pages using a web browser as the client.

web browser A web browser is a software application for retrieving (via HTTP), presenting, and travers- ing information resources on the WWWeb, enabling users to view web pages and to jump from one page to another. web content management Defined along with content management system web content management system Defined along with content management system

web page A web page is a document (usually marked up in HTML) on the WWWeb that can include multimedia data and hyperlinks. web resource Defined along with uniform resource identifier

web search engine A web search engine is a web application designed to search for information on the World Wide Web. web server Defined along with user agent

web server A web server is a network program that delivers web resources to and receives content from user agents via the Hypertext Transfer Protocol(HTTP).

web site A web site is a collection of related web pages usually designed or controlled by the same individual or company. week Defined along with minute well formed formulae Defined along with expression language well-formed propositional formula Defined along with formulae wff Defined along with expression language

width For layout, CSS considers all HTML elements as boxes, i.e. document areas with a given width and height.A CSS box has four parts: – content: the content of the box, where text and images appear. – padding: clears an area around the content. The padding is transparent. – border a border that goes around the padding and content. – margin clears an area outside the border. The margin is transparent. The latter three wrap around the content and add to its size.

wiki A wiki is a web site on which authoring and editing can be done by anyone at anytime using simple browser tools. In a typical wiki, text is written using a simplified markup language (wiki markup) which is transformed into HTML by the underlying wiki engine. wiki engine Defined along with wiki wiki markup Defined along with wiki word Defined along with alphabet

94 word processor A word processor is a software application, that – apart from being a document renderer– also supports the tasks of composition, editing, formatting, printing of electronic documents. work made for hire A work made for hire(WFH) is a work created by an employee as part of his or her job, or under the explicit guidance or under the terms of a contract.

working copy In a RCS, users do not directly work on the repository, but on a working copy that is synchronized with the repository. write Defined along with opened

year A year is either 364 or 365 day depending whether is is a leap year or not.

yobi Defined along with binary unit prefix yocto Defined along with prefixes yotta Defined along with prefixes

zebi Defined along with binary unit prefix zepto Defined along with prefixes

zero We introduce some abbreviations – we “abbreviate” o and ‘ ’ by the symbol ’0’ (called “zero”) – we abbreviate s(o) and / by the symbol ’1’ (called “one”) – we abbreviate s(s(o)) and // by the symbol ’2’ (called “two”) – ... – we abbreviate s(s(s(s(s(s(s(s(s(s(s(s(o)))))))))))) and //////////// by the symbol ’12’ (called “twelve”) – ...

zero Defined along with natural number

zero Error: The defi does not appear to be inside a definition environment. line40:39

zero vector Defined along with vector space zetta Defined along with prefixes

95