A Translation Approach to Portable Ontology Specifications
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A Framework for Comparing the Use of a Linguistic Ontology in an Application
A Framework for Comparing the use of a Linguistic Ontology in an Application Julieanne van Zyl1 and Dan Corbett2 Abstract. A framework recently developed for understanding and “a body of knowledge about the world (or a domain) that a) is classifying ontology applications provides opportunities to review a repository of primitive symbols used in meaning the state of the art, and to provide guidelines for application b) organises these symbols in a tangled subsumption developers from different communities [1]. The framework hierarchy; and identifies four main categories of ontology applications: neutral c) further interconnects these symbols using a rich system of authoring, ontology as specification, common access to semantic and discourse-pragmatic relations defined among information, and ontology-based search. Specific scenarios are the concepts” [2]. described for each category and a number of features have been identified to highlight the similarities and differences between There has been some work on comparing ontology applications, them. In this paper we identify additional scenarios, describing the which refer to “the application that makes use of or benefits from use of a linguistic ontology in an application. We populate the the ontology (possibly directly)” [1]. A framework [3] was scenarios with a number of prominent research and industrial developed for comparing various projects in ontology design, applications from diverse communities such as knowledge-based which considered the differences and similarities in the way the machine translation, medical databases, heterogenous information projects treat some basic knowledge representation aspects. The systems integration, multilingual text generation, Web-based projects compared include three natural language ontologies, two applications, and information retrieval. -
An Axiomatic Approach to Physical Systems
' An Axiomatic Approach $ to Physical Systems & % Januari 2004 ❦ ' Summary $ Mereology is generally considered as a formal theory of the part-whole relation- ship concerning material bodies, such as planets, pickles and protons. We argue that mereology can be considered more generally as axiomatising the concept of a physical system, such as a planet in a gravitation-potential, a pickle in heart- burn and a proton in an electro-magnetic field. We design a theory of sets and physical systems by extending standard set-theory (ZFC) with mereological axioms. The resulting theory deductively extends both `Mereology' of Tarski & L`esniewski as well as the well-known `calculus of individuals' of Leonard & Goodman. We prove a number of theorems and demonstrate that our theory extends ZFC con- servatively and hence equiconsistently. We also erect a model of our theory in ZFC. The lesson to be learned from this paper reads that not only is a marriage between standard set-theory and mereology logically respectable, leading to a rigorous vin- dication of how physicists talk about physical systems, but in addition that sets and physical systems interact at the formal level both quite smoothly and non- trivially. & % Contents 0 Pre-Mereological Investigations 1 0.0 Overview . 1 0.1 Motivation . 1 0.2 Heuristics . 2 0.3 Requirements . 5 0.4 Extant Mereological Theories . 6 1 Mereological Investigations 8 1.0 The Language of Physical Systems . 8 1.1 The Domain of Mereological Discourse . 9 1.2 Mereological Axioms . 13 1.2.0 Plenitude vs. Parsimony . 13 1.2.1 Subsystem Axioms . 15 1.2.2 Composite Physical Systems . -
On the Boundary Between Mereology and Topology
On the Boundary Between Mereology and Topology Achille C. Varzi Istituto per la Ricerca Scientifica e Tecnologica, I-38100 Trento, Italy [email protected] (Final version published in Roberto Casati, Barry Smith, and Graham White (eds.), Philosophy and the Cognitive Sciences. Proceedings of the 16th International Wittgenstein Symposium, Vienna, Hölder-Pichler-Tempsky, 1994, pp. 423–442.) 1. Introduction Much recent work aimed at providing a formal ontology for the common-sense world has emphasized the need for a mereological account to be supplemented with topological concepts and principles. There are at least two reasons under- lying this view. The first is truly metaphysical and relates to the task of charac- terizing individual integrity or organic unity: since the notion of connectedness runs afoul of plain mereology, a theory of parts and wholes really needs to in- corporate a topological machinery of some sort. The second reason has been stressed mainly in connection with applications to certain areas of artificial in- telligence, most notably naive physics and qualitative reasoning about space and time: here mereology proves useful to account for certain basic relation- ships among things or events; but one needs topology to account for the fact that, say, two events can be continuous with each other, or that something can be inside, outside, abutting, or surrounding something else. These motivations (at times combined with others, e.g., semantic transpar- ency or computational efficiency) have led to the development of theories in which both mereological and topological notions play a pivotal role. How ex- actly these notions are related, however, and how the underlying principles should interact with one another, is still a rather unexplored issue. -
Semantics of First-Order Logic
CSC 244/444 Lecture Notes Sept. 7, 2021 Semantics of First-Order Logic A notation becomes a \representation" only when we can explain, in a formal way, how the notation can make true or false statements about some do- main; this is what model-theoretic semantics does in logic. We now have a set of syntactic expressions for formalizing knowledge, but we have only talked about the meanings of these expressions in an informal way. We now need to provide a model-theoretic semantics for this syntax, specifying precisely what the possible ways are of using a first-order language to talk about some domain of interest. Why is this important? Because, (1) that is the only way that we can verify that the facts we write down in the representation actually can mean what we intuitively intend them to mean; representations without formal semantics have often turned out to be incoherent when examined from this perspective; and (2) that is the only way we can judge whether proposed methods of making inferences are reasonable { i.e., that they give conclusions that are guaranteed to be true whenever the premises are, or at least are probably true, or at least possibly true. Without such guarantees, we will probably end up with an irrational \intelligent agent"! Models Our goal, then, is to specify precisely how all the terms, predicates, and formulas (sen- tences) of a first-order language can be interpreted so that terms refer to individuals, predicates refer to properties and relations, and formulas are either true or false. So we begin by fixing a domain of interest, called the domain of discourse: D. -
Formalizing Knowledge by Ontologies: OWL and KIF
Formalizing Knowledge by Ontologies: OWL and KIF Marchetti Andrea, Ronzano Francesco, Tesconi Maurizio, Minutoli Salvatore CNR, IIT Department, Via Moruzzi 1, I-56124, Pisa, Italy (andrea.marchetti, francesco.ronzano, maurizio.tesconi, salvatore.minutoli)@iit.cnr.it 2 I Abstract. During the last years, the activities of knowledge formaliza- tion and sharing useful to allow for semantically enabled management of information have been attracting growing attention, expecially in dis- tributed environments like the Web. In this report, after a general introduction about the basis of knowledge abstraction and its formalization through ontologies, we briefly present a list of relevant formal languages used to represent knowledge: CycL, F- Logic, LOOM, KIF, Ontolingua, RDF(S) and OWL. Then we focus our attention on the Web Ontology Language (OWL) and the Knowledge Interchange Format (KIF). OWL is the main language used to describe and share ontologies over the Web: there are three OWL sublanguages with a growing degree of expressiveness. We describe its structure as well as the way it is used in order to reasons over asserted knowledge. Moreover we briefly present three relevant OWL ontology editors: Prot´eg´e, SWOOP and Ontotrack and two important OWL reasoners: Pellet and FACT++. KIF is mainly a standard to describe knowledge among different com- puter systems so as to facilitate its exchange. We describe the main elements of KIF syntax; we also consider Sigma, an environment for cre- ating, testing, modifying, and performing inference with KIF ontologies. We comment some meaningful example of both OWL and KIF ontologies and, in conclusion, we compare their main expresive features. -
Solutions to Inclass Problems Week 2, Wed
Massachusetts Institute of Technology 6.042J/18.062J, Fall ’05: Mathematics for Computer Science September 14 Prof. Albert R. Meyer and Prof. Ronitt Rubinfeld revised September 13, 2005, 1279 minutes Solutions to InClass Problems Week 2, Wed. Problem 1. For each of the logical formulas, indicate whether or not it is true when the domain of discourse is N (the natural numbers 0, 1, 2, . ), Z (the integers), Q (the rationals), R (the real numbers), and C (the complex numbers). ∃x (x2 =2) ∀x ∃y (x2 =y) ∀y ∃x (x2 =y) ∀x�= 0∃y (xy =1) ∃x ∃y (x+ 2y=2)∧ (2x+ 4y=5) Solution. Statement N Z Q R √ C ∃x(x2= 2) f f f t(x= 2) t ∀x∃y(x2=y) t t t t(y=x2) t ∀y∃x(x2=y) f f f f(take y <0)t ∀x�=∃ 0y(xy= 1) f f t t(y=/x 1 ) t ∃x∃y(x+ 2y= 2)∧ (2x+ 4y=5)f f f f f � Problem 2. The goal of this problem is to translate some assertions about binary strings into logic notation. The domain of discourse is the set of all finitelength binary strings: λ, 0, 1, 00, 01, 10, 11, 000, 001, . (Here λdenotes the empty string.) In your translations, you may use all the ordinary logic symbols (including =), variables, and the binary symbols 0, 1 denoting 0, 1. A string like 01x0yof binary symbols and variables denotes the concatenation of the symbols and the binary strings represented by the variables. For example, if the value of xis 011 and the value of yis 1111, then the value of 01x0yis the binary string 0101101111. -
Representing and Using Ontologies
USC-CIT Technical Report 98-01 1 Representing and Using Ontologies Kuhanandha Mahalingam and Michael N. Huhns January 1998 Center for Information Technology Department of Electrical and Computer Engineering University of South Carolina Columbia, SC, U.S.A. 29208 (803) 777-5921 or [email protected] (803) 777-8045 FAX Keywords: Ontology, Java, Distributed Information Systems Abstract This paper discusses the representation of large ontologies, especially in a graphical format. It describes a tool, developed using Java, that incorporates several abstraction mechanisms that can help manage such ontologies. Furthermore, it briefly analyzes possible point-and-click approaches that can be used to form queries on these ontologies. 1 This research was partially done under a cooperative agreement between the National Institute of Standards and Technology Advanced Technology Program (under the HIIT contract, number 70NANB5H1011) and the Healthcare Open Systems and Trials, Inc. consortium. 1. Introduction The introduction of the World Wide Web (Web) and the consequent growth of other supporting technologies that, without doubt, have driven the Internet’s widespread usage have created many new problems. The most notable problem is how to manage efficiently the volume and heterogeneity of information produced on the Web each day. Further, most of the data produced is no longer just simple text, but also consists of multimedia objects. Multimedia objects require different policies, procedures, and conventions. They originate from and reside on a variety of different operating systems, and, most importantly, are large and complex. There are many approaches for coping with these problems. One of these approaches is to use ontologies for capturing the knowledge represented by the information sources, so that it can be viewed and manipulated declaratively. -
Discrete Mathematics for Computer Science I
University of Hawaii ICS141: Discrete Mathematics for Computer Science I Dept. Information & Computer Sci., University of Hawaii Originals slides by Dr. Baek and Dr. Still, adapted by J. Stelovsky Based on slides Dr. M. P. Frank and Dr. J.L. Gross Provided by McGraw-Hill ICS 141: Discrete Mathematics I – Fall 2011 4-1 University of Hawaii Lecture 4 Chapter 1. The Foundations 1.3 Predicates and Quantifiers ICS 141: Discrete Mathematics I – Fall 2011 4-2 Topic #3 – Predicate Logic Previously… University of Hawaii In predicate logic, a predicate is modeled as a proposional function P(·) from subjects to propositions. P(x): “x is a prime number” (x: any subject) P(3): “3 is a prime number.” (proposition!) Propositional functions of any number of arguments, each of which may take any grammatical role that a noun can take P(x,y,z): “x gave y the grade z” P(Mike,Mary,A): “Mike gave Mary the grade A.” ICS 141: Discrete Mathematics I – Fall 2011 4-3 Topic #3 – Predicate Logic Universe of Discourse (U.D.) University of Hawaii The power of distinguishing subjects from predicates is that it lets you state things about many objects at once. e.g., let P(x) = “x + 1 x”. We can then say, “For any number x, P(x) is true” instead of (0 + 1 0) (1 + 1 1) (2 + 1 2) ... The collection of values that a variable x can take is called x’s universe of discourse or the domain of discourse (often just referred to as the domain). ICS 141: Discrete Mathematics I – Fall 2011 4-4 Topic #3 – Predicate Logic Quantifier Expressions University of Hawaii Quantifiers provide a notation that allows us to quantify (count) how many objects in the universe of discourse satisfy the given predicate. -
Leibniz on Providence, Foreknowledge and Freedom
University of Massachusetts Amherst ScholarWorks@UMass Amherst Doctoral Dissertations 1896 - February 2014 1-1-1994 Leibniz on providence, foreknowledge and freedom. Jack D. Davidson University of Massachusetts Amherst Follow this and additional works at: https://scholarworks.umass.edu/dissertations_1 Recommended Citation Davidson, Jack D., "Leibniz on providence, foreknowledge and freedom." (1994). Doctoral Dissertations 1896 - February 2014. 2221. https://scholarworks.umass.edu/dissertations_1/2221 This Open Access Dissertation is brought to you for free and open access by ScholarWorks@UMass Amherst. It has been accepted for inclusion in Doctoral Dissertations 1896 - February 2014 by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. LEIBNIZ ON PROVIDENCE, FOREKNOWLEDGE AND FREEDOM A Dissertation Presented by JACK D. DAVIDSON Submitted to the Graduate School of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY September 1994 Department of Philosophy Copyright by Jack D. Davidson 1994 All Rights Reserved ^ LEIBNIZ ON PROVIDENCE, FOREKNOWLEDGE AND FREEDOM A Dissertation Presented by JACK D. DAVIDSON Approved as to style and content by: \J J2SU2- Vere Chappell, Member Vincent Cleary, Membie r Member oe Jobln Robison, Department Head Department of Philosophy ACKNOWLEDGEMENTS I want to thank Vere Chappell for encouraging my work in early modern philosophy. From him I have learned a great deal about the intricate business of exegetical history. His careful work is, and will remain, an inspiration. I also thank Gary Matthews for providing me with an example of a philosopher who integrates his work with his life. Much of my interest in ancient and medieval philosophy has been inspired by his work. -
Ontology and Information Systems
Ontology and Information Systems 1 Barry Smith Philosophical Ontology Ontology as a branch of philosophy is the science of what is, of the kinds and structures of objects, properties, events, processes and relations in every area of reality. ‘Ontology’ is often used by philosophers as a synonym for ‘metaphysics’ (literally: ‘what comes after the Physics’), a term which was used by early students of Aristotle to refer to what Aristotle himself called ‘first philosophy’.2 The term ‘ontology’ (or ontologia) was itself coined in 1613, independently, by two philosophers, Rudolf Göckel (Goclenius), in his Lexicon philosophicum and Jacob Lorhard (Lorhardus), in his Theatrum philosophicum. The first occurrence in English recorded by the OED appears in Bailey’s dictionary of 1721, which defines ontology as ‘an Account of being in the Abstract’. Methods and Goals of Philosophical Ontology The methods of philosophical ontology are the methods of philosophy in general. They include the development of theories of wider or narrower scope and the testing and refinement of such theories by measuring them up, either against difficult 1 This paper is based upon work supported by the National Science Foundation under Grant No. BCS-9975557 (“Ontology and Geographic Categories”) and by the Alexander von Humboldt Foundation under the auspices of its Wolfgang Paul Program. Thanks go to Thomas Bittner, Olivier Bodenreider, Anita Burgun, Charles Dement, Andrew Frank, Angelika Franzke, Wolfgang Grassl, Pierre Grenon, Nicola Guarino, Patrick Hayes, Kathleen Hornsby, Ingvar Johansson, Fritz Lehmann, Chris Menzel, Kevin Mulligan, Chris Partridge, David W. Smith, William Rapaport, Daniel von Wachter, Chris Welty and Graham White for helpful comments. -
First-Order Logic in a Nutshell Syntax
First-Order Logic in a Nutshell 27 numbers is empty, and hence cannot be a member of itself (otherwise, it would not be empty). Now, call a set x good if x is not a member of itself and let C be the col- lection of all sets which are good. Is C, as a set, good or not? If C is good, then C is not a member of itself, but since C contains all sets which are good, C is a member of C, a contradiction. Otherwise, if C is a member of itself, then C must be good, again a contradiction. In order to avoid this paradox we have to exclude the collec- tion C from being a set, but then, we have to give reasons why certain collections are sets and others are not. The axiomatic way to do this is described by Zermelo as follows: Starting with the historically grown Set Theory, one has to search for the principles required for the foundations of this mathematical discipline. In solving the problem we must, on the one hand, restrict these principles sufficiently to ex- clude all contradictions and, on the other hand, take them sufficiently wide to retain all the features of this theory. The principles, which are called axioms, will tell us how to get new sets from already existing ones. In fact, most of the axioms of Set Theory are constructive to some extent, i.e., they tell us how new sets are constructed from already existing ones and what elements they contain. However, before we state the axioms of Set Theory we would like to introduce informally the formal language in which these axioms will be formulated. -
Leibniz's Theory of Propositional Terms: a Reply to Massimo
Leibniz’s Theory of Propositional Terms: A Reply to Massimo Mugnai Marko Malink, New York University Anubav Vasudevan, University of Chicago n his contribution to this volume of the Leibniz Review, Massimo Mugnai provides a very helpful review of our paper “The Logic of Leibniz’s Generales IInquisitiones de Analysi Notionum et Veritatum.” Mugnai’s review, which contains many insightful comments and criticisms, raises a number of issues that are of central importance for a proper understanding of Leibniz’s logical theory. We are grateful for the opportunity to explain our position on these issues in greater depth than we did in the paper. In his review, Mugnai puts forward two main criticisms of our reconstruction of the logical calculus developed by Leibniz in the Generales Inquisitiones. Both of these criticisms relate to Leibniz’s theory of propositional terms. The first concerns certain extensional features that we ascribe to the relation of conceptual containment as it applies to propositional terms. The second concerns the syntactic distinction we draw between propositions and propositional terms in the language of Leibniz’s calculus. In what follows, we address each of these criticisms in turn, beginning with the second. Propositions and Propositional Terms One of the most innovative aspects of the Generales Inquisitiones is Leibniz’s in- troduction into his logical theory of the device of propositional terms. By means of this device, Leibniz proposed to represent propositions of the form A is B by terms such as A’s being B. Leibniz regarded these propositional terms as abstract terms (abstracti termini, A VI 4 987), with the important qualification that they are merely “logical” or “notional” abstracts (A VI 4 740; cf.