In Formal Ontology in Conceptual Analysis and Knowledge
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Panel: Large Knowledge Bases
From: AAAI Technical Report SS-02-06. Compilation copyright © 2002, AAAI (www.aaai.org). All rights reserved. Panel: Large KnowledgeBases AdamPease (Teknowledge, chair), Chris Welty (Vassar College), Pat Hayes (U. West Florida), Anthony G. Cohn (U. Leeds), Ken Murray (SRI) Fellbaum, C. (1998). WordNet, An Electronic Lexical Database. MITPress. Abstract Lenat, D., 1995, "Cyc: A Large-Scale Investment in It is estimated that 1-2 exabytes of data is now being KnowledgeInfrastructure". Communicationsof the ACM generated each year, almost all of it in purely digital form 38, no. 1 !, November.See also http://www.c¥c.com (Lymanet. ai. 2000). Properly structured, this information could form a global knowledge base. Currently however, Lyman,P., Varian, H., Dunn, J., Strygin, A., Swearingen, this information exists in manydifferent forms, manyof K., (2000). HowMuch Information?, University California, which are only suitable for humanconsumption, and which Berkeley are largely opaque to computerbased understanding. Majorefforts to build large formal ontologies or address http://www.sims.berkeley.edu/research/project.,ghow-much- issues in their construction have been undertaken funded by info the government in the US such as the DARPAKnowledge Niles, I., & Pease, A., (2001), Towarda Standard Upper Sharing Effort (Patil et al, 1992), High Performance Ontology, in Proceedings of the 2nd International KnowledgeBases (Cohen et. al., 1998), Rapid Knowledge Conference on Formal Ontology in Information Systems Formation (RKF, 2002) and in Europe including Advanced (FOIS-2001). See also http:llonlology.teknowledge.com KnowledgeTechnologies (Shadboit, 2001) and OntoWeb and http:l/suo.ieee.org (OntoWeb,2002), as international standards efforts such the IEEE Standard Upper Ontology (Niles & Pease, 2001) OntoWeb(2002). -
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 . -
A Critique of Pure Reason’
151 A critique of pure reason’ DREWMCDERMOTT Yale University, New Haven, CT 06S20, U.S.A. Cornput. Intell. 3. 151-160 (1987) In 1978, Patrick Hayes promulgated the Naive Physics Man- the knowledge that programs must have before we write the ifesto. (It finally appeared as an “official” publication in programs themselves. We know what this knowledge is; it’s Hobbs and Moore 1985.) In this paper, he proposed that an all- what everybody knows, about physics, about time and space, out effort be mounted to formalize commonsense knowledge, about human relationships and behavior. If we attempt to write using first-order logic as a notation. This effort had its roots in the programs first, experience shows that the knowledge will earlier research, especially the work of John McCarthy, but the be shortchanged. The tendency will be to oversimplify what scope of Hayes’s proposal was new and ambitious. He sug- people actually know in order to get a program that works. On gested that the use of Tarskian seniantics could allow us to the other hand, if we free ourselves from the exigencies of study a large volume of knowledge-representation problems hacking, then we can focus on the actual knowledge in all its free from the confines of computer programs. The suggestion complexity. Once we have a rich theory of the commonsense inspired a small community of people to actually try to write world, we can try to embody it in programs. This theory will down all (or most) of commonsense knowledge in predictate become an indispensable aid to writing those programs. -
First-Order Logic
INF5390 – Kunstig intelligens First-Order Logic Roar Fjellheim Outline Logical commitments First-order logic First-order inference Resolution rule Reasoning systems Summary Extracts from AIMA Chapter 8: First-Order Logic Chapter 9: Inference in First-Order Logic INF5390-AI-05 First-Order Logic 2 From propositonal to first-order logic Features of propositional logic: + Declarative + Compositional + ”Possible-world” semantics - Lacks expressiveness First-order logic: Extends propositional logic Keeps good features Adds expressiveness INF5390-AI-05 First-Order Logic 3 First-order logic First-order logic is based on “common sense” or linguistic concepts: Objects: people, houses, numbers, .. Properties: tall, red, .. Relations: brother, bigger than, .. Functions: father of, roof of, .. Variables: x, y, .. (takes objects as values) First-order logic is the most important and best understood logic in philosophy, mathematics, and AI INF5390-AI-05 First-Order Logic 4 Logic “commitments” Ontological commitment Ontology - in philosophy, the study of “what is” What are the underlying assumptions of the logic with respect to the nature of reality Epistemological commitment Epistemology - in philosophy, the study of “what can be known” What are the underlying assumptions of the logic with respect to the nature of what the agent can know INF5390-AI-05 First-Order Logic 5 Commitments of some logic languages Language Ontological Epistemological Commitment Commitment Propositional logic Facts True/false/unknown First-order logic -
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. -
A Translation Approach to Portable Ontology Specifications
Knowledge Systems Laboratory September 1992 Technical Report KSL 92-71 Revised April 1993 A Translation Approach to Portable Ontology Specifications by Thomas R. Gruber Appeared in Knowledge Acquisition, 5(2):199-220, 1993. KNOWLEDGE SYSTEMS LABORATORY Computer Science Department Stanford University Stanford, California 94305 A Translation Approach to Portable Ontology Specifications Thomas R. Gruber Knowledge System Laboratory Stanford University 701 Welch Road, Building C Palo Alto, CA 94304 [email protected] Abstract To support the sharing and reuse of formally represented knowledge among AI systems, it is useful to define the common vocabulary in which shared knowledge is represented. A specification of a representational vocabulary for a shared domain of discourse — definitions of classes, relations, functions, and other objects — is called an ontology. This paper describes a mechanism for defining ontologies that are portable over representation systems. Definitions written in a standard format for predicate calculus are translated by a system called Ontolingua into specialized representations, including frame-based systems as well as relational languages. This allows researchers to share and reuse ontologies, while retaining the computational benefits of specialized implementations. We discuss how the translation approach to portability addresses several technical problems. One problem is how to accommodate the stylistic and organizational differences among representations while preserving declarative content. Another is how -
Ontological Commitment of Natural Language Semantics
Ontological Commitment of Natural Language Semantics MSc Thesis (Afstudeerscriptie) written by Viktoriia Denisova (born July, 23d 1986 in Kustanay, Kazakhstan) under the supervision of Prof. Dr. Martin Stokhof, and submitted to the Board of Examiners in partial fulfillment of the requirements for the degree of MSc in Logic at the Universiteit van Amsterdam. Date of the public defense: Members of the Thesis Committee: March, 23d 2012 Prof. Dr. Martin Stokhof Prof. Dr. Frank Veltman Dr. Paul Dekker Contents Acknowledgments v Abstract vi Introduction 1 1 Quine's Ontological Criterion 5 1.1 Why do we need to define the criterion of ontological commitment? 5 1.2 Why do we operate on the semantic level when talking about on- tology? . 13 1.3 What does Quine's ontological criterion bring to semantics? . 15 1.4 What is the role of logic in determination of the ontological com- mitment? . 17 1.5 Concluding remarks . 19 2 Critique of the Ontological Criterion 21 2.1 Hodges on the philosophical importance of ontological commitment 21 2.2 Evaluation of Hodges's exposition . 25 2.3 Beyond the semantics of standard first-order logic . 27 2.3.1 The difficulties concerning first-order regimentation . 27 2.3.2 Regimentation of the sentences that contain plurals . 30 2.3.3 Regimentation of modals . 31 2.4 Evaluation of Rayo's exposition . 33 3 Ontological commitment within possible worlds semantics 35 3.1 The reasons to consider ontological commitment in intensional lan- guage . 35 3.2 Ontological commitment for proper names . 37 3.3 Natural kind terms . -
Conceptualization and Visualization of Tagging and Folksonomies
Conceptualization and Visualization of Tagging and Folksonomies Von der Fakultät für Ingenieurwissenschaften, Abteilung Informatik und Angewandte Kognitionswissenschaft der Universität Duisburg-Essen zur Erlangung des akademischen Grades Doktor der Ingenieurwissenschaften (Dr.-Ing.) genehmigte Dissertation von Steffen Lohmann aus Hamburg 1. Gutachter: Prof. Dr. Maria Paloma Díaz Pérez 2. Gutachter: Prof. Dr.-Ing. Jürgen Ziegler Tag der mündlichen Prüfung: 27.11.2013 Hinweis: Diese Dissertation ist im Rahmen eines binationalen Promotionsverfahrens (Cotutelle) in Kooperation mit der Universidad Carlos III de Madrid entstanden. Abstract Tagging has become a popular indexing method for interactive systems in the past decade. It offers a simple yet effective way for users to organize an ever increasing amount of digital information for themselves and/or others. The linked user vocabulary resulting from tagging is known as folksonomy and provides a valuable source for the retrieval and exploration of digital resources. Although several models and representations of tagging have been proposed, there is no coherent conceptualization that provides a comprehensive and pre- cise description of the concepts and relationships in the domain. Furthermore, there is little systematic research in the area of folksonomy visualization, and so folksonomies are still mainly depicted as simple tag clouds. Both problems are related, as a well-defined conceptualization is an important prerequisite for the interoperable use and visualization of folksonomies. The thesis addresses these shortcomings by developing a coherent conceptualiza- tion of tagging and visualizations for the interactive exploration of folksonomies. It gives an overview and comparison of tagging models and defines key concepts of the domain. After a comprehensive review of existing tagging ontologies, a unified and coherent conceptualization is presented that incorporates the best parts of the reviewed ontologies. -
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. -
Inconsistency Robustness for Logic Programs Carl Hewitt
Inconsistency Robustness for Logic Programs Carl Hewitt To cite this version: Carl Hewitt. Inconsistency Robustness for Logic Programs. Inconsistency Robustness, 2015, 978-1- 84890-159. hal-01148496v6 HAL Id: hal-01148496 https://hal.archives-ouvertes.fr/hal-01148496v6 Submitted on 27 Apr 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Copyright Inconsistency Robustness for Logic Programs Carl Hewitt This article is dedicated to Alonzo Church and Stanisław Jaśkowski Abstract This article explores the role of Inconsistency Robustness in the history and theory of Logic Programs. Inconsistency Robustness has been a continually recurring issue in Logic Programs from the beginning including Church's system developed in the early 1930s based on partial functions (defined in the lambda calculus) that he thought would allow development of a general logic without the kind of paradoxes that had plagued earlier efforts by Frege, etc.1 Planner [Hewitt 1969, 1971] was a kind of hybrid between the procedural and logical paradigms in that it featured a procedural embedding of logical sentences in that an implication of the form (p implies q) can be procedurally embedded in the following ways: Forward chaining When asserted p, Assert q When asserted q, Assert p Backward chaining When goal q, SetGoal p When goal p, SetGoal q Developments by different research groups in the fall of 1972 gave rise to a controversy over Logic Programs that persists to this day in the form of following alternatives: 1. -
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. -
IKRIS Scenarios Inter-Theory (ISIT)
IKRIS Scenarios Inter-Theory (ISIT) Jerry Hobbs with the IKRIS Scenarios Working Group Contributions from Danny Bobrow, Chris Deaton, Mike Gruninger, Pat Hayes, Arun Majumdar, David Martin, Drew McDermott, Sheila McIlraith, Karen Myers, David Morley, John Sowa, Marco Valtorta, and Chris Welty. IKRIS Scenarios Fundamentals Events Most ontologies dealing with processes or scenarios will have something corresponding to events. PSL uses the term "activity_occurrence" for events. Cyc uses the term "Event". Other possible terms have drawbacks. "Action" connotes an event that has an agent, so it is only a subclass of events. "Process" and "Procedure" connote complex events that have subevents, and we need a term that will cover primitive events as well. One can argue that "activity" and "activity occurrence" have the same problem. For these reasons, we have chosen the term "Events". Types and Tokens We can refer to both event types and event tokens. PSL uses the terms "activity" and "activity_occurrence" for these two. Cyc uses the terms "EventType" and "Event". Another possible pair of term is "EventClass" and "EventInstance", but this biases one toward interpretation of types as classes, which may not be desirable (see below). It may seem desirable to make the type-token distinction explicit in the terms, and thus use "EventType" and "EventToken". But as Pat Hayes has pointed out, an event token may be a token of many types of events. A specific event may be a token of a running event type, an exercising event type, a winning event type, and numerous other types. Essentially, "token" is a relation between specific events and event types.