Knowledge Representation Formalism For Building Semantic Web Ontologies
Basak Taylan
Department of Computer Science The Graduate Center, CUNY
Jan 4, 2018
1 / 71 Outline
1 Introduction Web Evolution Semantic Web
2 Knowledge Representation Knowledge Knowledge Representation Formalism
4 Some Applications
2 / 71 Question
IS A GIRAFFE BIGGER THAN AN APPLE?
3 / 71 Web Evolution - Motivation [1, 27, 34, 9, 4]
1.8+ billion websites/ 4.6+ billion web pages
Textual/graphical resources for mostly human consumption
Inadequacy of keyword-based searches
No result Irrelevant results Highly dependent on keywords Inability of question answering
Inefficiency of manual search
Access time
4 / 71 Web Evolution - Web-1.0 [78, 18, 17, 20, 16, 31, 29, 65, 93]
1996-2004
Tim Berners Lee
“Read Only, Hypertext Web”
Static Content
Millions of users
One directional
HTML Web1.0 version of yahoo Image source: https://ebusinessharper.wordpress.com
5 / 71 Web Evolution - Web-2.0 [31, 79, 29, 65, 93]
2004-2016
O’Reilly and MediaLive International
“Read-Write, People-Centric, Participative-Web”
Dynamic Content
Billions of users https://mariamkhatib.files.wordpress.com/2013/02/picture- 6.png Bi-directional
XML/ RSS
6 / 71 Web Evolution - Web-3.0 [31, 79, 29, 65, 93, 56]
2016-
Tim Berners Lee
“Semantic Web, Executable Web”
Dynamic Content + AI Web Learning
Trillions of users
Multi-User Virtual Environment "Linking Open Data cloud diagram 2017, by Andrejs Abele, John P. McCrae, Paul Buitelaar, Anja Jentzsch and Richard Cyganiak. http://lod-cloud.net/" RDF/RDFS/OWL
7 / 71 Web Evolution - Web-3.0 DBpedia Example
8 / 71 Web Evolution - Web-4.0 [29, 93, 48]
Near Future
“Symbiotic Web” (human-machine interaction)
Facial recognition for IoT
The ultra-intelligent personal agent with personality selection
Mind controlled interfaces
Small screenless smart devices
9 / 71 Semantic Web [19, 107, 4, 52, 29, 65]
Extension of current Web
Layered structure
Machine and human processable
Improved results compared to
absolute keyword-based searches Semantic Web Layer Cake [4]
Search engines as question answering platform
A common framework for data to be shared and reused across application, enterprise, and community boundaries
10 / 71 Unicode And Universal Resource Identifier(URI) [69]
Unicode : Standardized encoding for the character settings for the Semantic Web.
URI : identifiers for the resources on the Web.
11 / 71 Extensible Markup Language(XML) [4]
Nonmonotonic Reasoning: Context-Dependent Reasoning
by V. Marekand M. TruszczynskiSpringer 1993
ISBN 0387976892
Img source: https://images-na.ssl-images-amazon.com/images/I/41RXVgcRReL._SX327_BO1,204,203,200_.jpg
12 / 71 Resource Description Framework(RDF) [2, 35, 107, 4, 72, 111, 83]
Defines web-based resources
Consists of Subject(S)+Predicate(P)+Object(O)
Similar to entity-relationship or class diagrams is databases
XML defines individual objects
RDF draws the relations between objects created by XML
An RDF syntax: RDF/XML, N3, Turtle, and RDFa.
13 / 71 RDF Graphical Representation Example [2]
A simple RDF graph representation [35]
RDF statements can be modeled as directed, labelled graphs.
Nodes → S/O , arcs → predicates
14 / 71 RDF Turtle Representation [35]
@prefix s:
<“$62”>.
15 / 71 RDF Graphical Representation Example-2
A simple RDF graph representation [30]
16 / 71 RDF/XML Example
17 / 71 RDF Schema(RDFS)[4, 2]
Language that provides vocabulary used in RDF data models Organizes web objects into hierarchies such as classes, subclasses, properties, domain/range restrictions
Class hierarchy for the motor vehicles [4]
18 / 71 RDF Schema(RDFS)[4, 2]
19 / 71 SPARQL Protocol and RDF Query Language(SPARQL)[2, 83, 4]
Assume RDF Store consists of following triples: :JamesDean :playedIn :Giant
:JamesDean :playedIn :EastOfEden
:JamesDean :playedIn :RebelWithoutCause
Q1) SELECT ?who WHERE{?who :playedIn :Giant.} RebelWithoutCause
A1) JamesDean playedIn
playedIn Q2) SELECT ?what WHERE{:JamesDean :playedIn ?what} JamesDean EastOfEden playedIn A2) Giant, EastOfEden, RebelWithoutCause
Giant
A simple RDF relation [2]
20 / 71 Web Ontology Language(OWL) [93, 74, 46, 45]
An ontology is a language for representation of terms and their relations
Provides standard vocabulary for machine processable Web.
More expressive than XML, RDF, RDF(S).
OWL extends RDF for describing properties and classes (disjointness, cardinality, equality, symmetry, transitivity, inverse, enumerated classes, etc.)
Current version OWL2 is extended version of OWL.
21 / 71 OWL Examples
Examples are taken from:"LDK R Logics for Data and Knowledge Representation Web Ontology Language (OWL) Fausto Giunchiglia and Biswanath Dutta Fall’2011."
22 / 71 Rules, Proof, Logic, Trust [4, 93]
RIF/SWRL enables us to write rules beyond RDFS and OWL.
Logic ,Proof, and Trust layers are used for validation of trustability of inputs.
Digital signatures are used to verify origin of the sources for input data.
Trust layer will be created by validation of trusted agents through digital signatures, certifications and other kinds of knowledge.
23 / 71 Knowledge [24, 54, 63, 102, 37, 55, 103, 44]
Informally, the relation between knower and the known
Zagzebski: “a state of a person’s being in cognitive contact with reality”
Declarative: propositions of “what” is known (facts or assertions) Procedural: information about “how” to do things Heuristic: “shallow knowledge”, includes uncertainty, a chess player’s good guess Meta-knowledge: knowledge about how to use other knowledge
24 / 71 Knowledge Representation(KR) [23, 73, 32]
Despite their computational power, computers cannot learn from the scratch.
Computers should given information prior to task requires intelligence.
i.e. Diagnosing a disease requires knowing characteristics of the disease in advance
And information should be stored for future use.
Need for representing and storing information lead study of KR Formalism.
25 / 71 Knowledge Representation
26 / 71 Semantic Nets [97, 26, 86, 99, 96, 13, 61, 6]
27 / 71 Conceptual Graphs(CG) [94, 95]
Semantic Networks are insufficient in representing all features of logic.
“On Fridays, Bob drives his Chewy to St. Louis”
(∀x1:Friday)(∃x2:Drive)(∃x3:Chevy)(∃x4:Old) [Person Bob] [Chevy *x1] [Old *x2] (Poss Bob ?x1) (Attr
(Person(Bob) ∧ City("St. Louis") ∧ PTim(x2,X1) ?x1 ?x2) [[Friday @every*x3] [Drive *x4] [City "St. Louis"]
∧ Agnt(x2,Bob) ∧ Poss(Bob,x3) ∧ Thme(x2,x3) ∧ (PTim ?x4 ?x3) (Agnt ?x4 Bob) (Thme ?x4 ?x1) (Dest
Attr(x3,x4) ∧ Dest(x2,"St. Louis")) ?x2 "St. Louis")]
28 / 71 Frames [76, 40, 64, 43, 49, 12, 42, 12, 43, 82]
Data structure to represent stereotyped knowledge
Inspired from human memory and cognition: new information brings a frame from the memory and gets it updated
Sub/super-class relations are enabled by constructors
Frame (frame-name
29 / 71 Frames [40]
The Transportation Knowledge Base
30 / 71 KL-ONE Systems [110, 22, 7, 25, 108, 89, 90, 98]
Descendent of semantic nets and frames
To overcome ambiguity and inconsistency of semantic nets and frames
Ancestor of DLs
Subsumption is intractable or undecidable even for Truck and TrailerTruck concepts defined in KL-ONE simple languages
31 / 71 Propositional Logic [88, 60, 81, 80, 87]
Proposition: A statement evaluates to T/F
Atom:Simplest proposition denoted with P,Q,etc.
Complex statements can be created from atoms with logical connectors ∧, ∨,¬,→, and ↔
Not very expressive φ ψ ¬φ φ ∧ ψ φ ∨ ψ φ → ψ φ ↔ ψ T T F T T T T Checking validity of a logical T F F F T F F formula with n propositional F T T F T T F n variables requires having 2 lines in F F T F F T T truth table
32 / 71 First-order Logic [14, 88, 101, 106, 53, 47]
Extends PL with quantifiers
Building blocks:
Constant symbols(objects) : john, 2, paris,... Predicates(Relations): City(paris), CapitalOf(paris,france), ... Functions: maps individuals to individuals fatherOf(Mary) = John, plus(2,3)=5, etc.
Highly expressive
Suffers from complexity
33 / 71 Frame Logic (F-Logic) [58, 3, 57, 109, 28, 21, 15, 33, 71, 70]
KR formalism that combines advantage of object-oriented data model, frame-based languages and logic-based languages.
Initially designed as database language, but serves as knowledge representation and ontology language as well
More expressive than DLs
Closed world assumption
Generally undecidable
34 / 71 Frame Logic (F-Logic) [58, 3, 57, 109, 28, 21, 15, 33, 71, 70]
A simple ontology
35 / 71 Description Logics [7, 9, 62, 10, 8, 25, 51, 62, 104, 77, 45, 62]
A family of KR formalism
Decidable fragment of FOL, sufficiently expressive
FOL researchers → theorem proving
DL researchers → question answering in reasonable time
36 / 71 Description Logics [7, 9, 62, 10, 8, 25, 51, 62, 104, 77, 45, 62]
A family of KR formalism
Decidable fragment of FOL, sufficiently expressive
FOL researchers → theorem proving
DL researchers → question answering in reasonable time
37 / 71 Basic Buildings Of DLs
DLs provides means to model the relationship between entities and domain of interest. Three types of entities:
Individuals: individual names i.e. john
Concepts : set of individuals i.e. Parent(julia)
Roles : binary relation between individuals i.e. ParentOf(julia,john)
38 / 71 DL Languages
C U + E
S AL+C + Transitivity of Roles The most basic description language is U Concept Disjunction Attributive Language(AL). Concept and role E Full Existential Quantification(∃R.C) descriptions supported by (AL): H Role Hierarchies
O Nominals C:= A | > | ⊥ | ¬A | C u D I Inverse Roles R:= ∃R.> | ∀R.C N Number Restrictions (≤ nR)
Q Qualified number restrictions (≤ nR.C) A : atomic concept (D) Data types > :universal(top) concept
⊥ : bottom(empty) concept F Functional Roles
C, D : concept descriptions R Complex Role Inclusion
R : an atomic role. Constructors in Family of AL-Languages
39 / 71 SROIQ(D)- FORMAL SYNTAX [62, 7]
A SROIQ(D)concept C is defined by the grammar below, where n ∈ Z+,
NC is a set of concept names, and NI is a set of individual names:
C := NC | (C u C) | (C t C) | ¬C | > | ⊥ | ∃R.C | ∀R.C | ≥ nR.C | ≤
nR.C | ∃R.Self | {NI }
SROIQ(D) role expressions R is defined by the following grammar where U
is universal role and NR is a set of role names:
− R := U | NR | NR
40 / 71 SROIQ(D)- FORMAL SYNTAX
ABox : C(NI ) , R(NI , NI ) , NI ≈ NI , NI 6≈ NI
TBox : C v C , C ≡ C
RBox : R v R , R ≡ R , R ◦ R v R , Disjoint(R, R)
Formal Syntax of Axioms in SROIQ
41 / 71 Restrictions in SROIQ(D)
Structural restrictive rules are applied to the ontology in order to have a terminating and correct reasoning algorithms
In SROIQ following roles are restricted with simple roles, where a simple role is a role that does not contain role composition (e.g. if S ◦ T v R , then R is not simple):
Disjoint(R,R) , ∃R.Self , ≤ nR.C , ≥ nR.C
Besides simplicity restriction, there is regularity restriction. Regularity restriction limits cyclic dependencies between complex role inclusion axioms.
42 / 71 SROIQ(D)- FORMAL SEMANTICS [62]
43 / 71 SROIQ(D)- FORMAL SEMANTICS [62]
Formal Syntax and Semantics of SROIQ Axioms
44 / 71 The Open Mind Common Sense Project(OMCS) [92, 66]
Machine can easily calculate winning strategy from given chess position unlike human
It cannot draw simple conclusions about life.
CYC (1984-Early 2017) manually crafted database with 1+MM axioms
Still far from listing all possible axioms
OMCS distributed human project
8000+ volunteer
Human judgment, no guarantee for completeness or soundness. Project concludes having some incorrect and incomplete inferences.
ConceptNet is developed by OMCS Project
45 / 71 ConceptNet 3 [50]
Semi-automated, fill-in-the-blanks or a free form of the text (ConceptNet V5 reads from online resources i.e. Wiktionary)
Open Mind Commons(OMC) built on top of ConceptNet3 is a developed version of OMCS Project
46 / 71 WordNet [36, 38, 105, 75, 39]
A thesaurus: a book that contains list of words in groups of synonyms and related concepts.
Thesauri are the least formal form of an ontology
WordNet is the most well-known example for the thesauri.
Manually constructed Semantic Relations in WordNet
47 / 71 FrameNet [11, 5, 41, 12]
A human-/machine-readable lexical database for English
Started as toy project, less annotations than other lexical resources
Depends on “Frame Semantics”
Generalizes of group of words that are syntactically and semantically related
Based on annotating examples of how words are used in actual texts
48 / 71 VerbNet [67, 100, 59, 91]
A verb lexicon for verbs in English
VerbNet classes are organized in a way that every verb in each classes shares a common semantic, a common syntactic frames and common thematic roles
Each verb has a different class, which consist set of frames. i.e. For verb hit, hit class that consists of verbs like hit, kick, slap, tap, etc.
“John taught math to Mary” can be example to the following frame:
Type Frame Predicates
Theme and Recipient A V T to R transfer_info(during(E),A,R,T)
where A:agent, V:verb, T:thema, R: recipient and E:event
49 / 71 Brandies Semantic Ontology(BSO) [84, 85, 50, 68]
A large lexicon ontology and lexical database Similar to concept net
ConceptNet → BSO isA → formal relation partOf → constitutive usedFor → telic CapableOfReceivingAction → agentive relation
1) 4) [[drink activity]] [[Writer]] supertype = [[Take Nourishment Activity]] #telic = [[Write Activity]] #subject = [[Animate Living Entity]] #object = [[Beverage]] 5) [[Write Activity]] 2) #object = [[Book]] ’drink’ type = [[Drink Activity]] 6) 3) ’novelist’ ’chug’ type = [[Writer]] type = [[Drink Activity]] (#telic -> #object) = [[Novel]] #object = [[Alcoholic Beverage]]
50 / 71 Summary
IS A GIRAFFE BIGGER THAN AN APPLE?
51 / 71 Answer
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