DOCSLIB.ORG

Semantics of Logic Programs with Explicit Negation

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Semantics of Logic Programs with Explicit Negation View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by New University of Lisbon's Repository Jos´eJ´ulioAlves Alferes Semantics of Logic Programs with Explicit Negation Disserta¸c˜aoapresentada para a obten¸c˜aodo Grau de Doutor em Engenharia Inform´atica, especialidade InteligˆenciaArtificial, pela Uni- versidade Nova de Lisboa, Faculdade de Ciˆenciase Tecnologia. Lisboa (1993) Acknowledgements First of all, I would like to thank my parents, Ac´acioand Dion´ısia,for the incentive they gave me to pursue the goal of making the PhD, their encouragement, support and many other reasons. Also special thanks to Cristina for her support, and especially for bearing with me during the period while this thesis was being written. Special thanks to my supervisor, Lu´ısMoniz Pereira, for lots of reasons including but not limited to: his availability for discussions, even when he had lots of other urgent things to do; the valuable comments and advice he gave me about this work; for introducing me to the right researchers at the right time, giving me the chance of learning a lot with those researchers; for providing for the good working conditions I had during the preparation of the PhD thesis; for teaching me how to do scientific research in its many aspects, and for the pleasure of doing it together with him. I would also like to thank my colleagues Joaquim Nunes Apar´ıcioand Carlos Dam´asio,who collaborated with me in many tasks during the three years of preparation of this thesis. For many profitable discussions, thanks are due to, among others, my colleagues Salvador Abreu, Lu´ısCaires, Gabriel David, Lu´ısMonteiro, Ant´onioPorto, and Irene Rodrigues. On the international side, I would like to thank, for valuable comments and discussions, Marc Denecker, Michael Gelfond, Tony Kakas, Vladimir Lifschitz, Paolo Mancarella, David Peirce, Halina Przymusinska, Teodor Przymusinski, and Gerd Wagner. Special thanks to Phan Minh Dung. I’m indebted to Carlos Dam´asioand Lu´ısMonteiro, who kindly accepted to read a prelimi- nary version of this report and give me their comments, and to Salvador Abreu for helping me with the French “sommaire”. I would like to acknowledge JNICT (Junta Nacional de Investiga¸c˜aoCient´ıficae Tecnol´ogica) for giving me the PhD grant (no. 137/90-IA) that paid for my survival during these last three years. I thank Esprit BR projects Compulog (no. 3012) and Compulog 2 (no. 6810) for their support, and for giving me the chance of knowing many european researchers in the area of logic programming, with whom I had many aclarifying discussion. For giving me working conditions, I acknowledge the Departamento de Inform´aticaof Fac- uldade de Ciˆenciase Tecnologia of Universidade Nova de Lisboa, the Centro de Inteligˆencia Artificial (CRIA) of Uninova, and Centro de Inform´aticada Universidade Nova de Lisboa (CIUNL). I’m indebted to Anabela Rodrigues and Filipa Reis, for managing most of my bureaucracy, and arranging my travels, during the period of preparation of this thesis and even before. i ii Abstract After a historical introduction, the bulk of the thesis concerns the study of a declarative seman- tics for logic programs. The main original contributions are: ² WFSX (Well–Founded Semantics with eXplicit negation), a new semantics for logic pro- grams with explicit negation (i.e. extended logic programs), which compares favourably in its properties with other extant semantics. ² A generic characterization schema that facilitates comparisons among a diversity of se- mantics of extended logic programs, including WFSX. ² An autoepistemic and a default logic corresponding to WFSX, which solve existing prob- lems of the classical approaches to autoepistemic and default logics, and clarify the mean- ing of explicit negation in logic programs. ² A framework for defining a spectrum of semantics of extended logic programs based on the abduction of negative hypotheses. This framework allows for the characterization of different levels of scepticism/credulity, consensuality, and argumentation. One of the semantics of abduction coincides with WFSX. ² O–semantics, a semantics that uniquely adds more CWA hypotheses to WFSX. The tech- niques used for doing so are applicable as well to the well–founded semantics of normal logic programs. ² By introducing explicit negation into logic programs contradiction may appear. I present two approaches for dealing with contradiction, and show their equivalence. One of the approaches consists in avoiding contradiction, and is based on restrictions in the adoption of abductive hypotheses. The other approach consists in removing contradiction, and is based in a transformation of contradictory programs into noncontradictory ones, guided by the reasons for contradiction. iii iv Sum´ario Depois de uma breve introdu¸c˜aohist´orica,o grosso da tese consiste no estudo de semˆanticas declarativas de programas em l´ogica. As principais contribui¸c˜oesoriginais s˜ao: ² A WFSX (semˆantica bem–fundada com nega¸c˜aoexpl´ıcita), uma nova semˆantica para programas em l´ogicacom nega¸c˜aoexpl´ıcita(i.e. programas em l´ogicaextendidos), que ´e melhor que outras semˆantica existentes, nas suas propriedades. ² Um esquema gen´ericode caracteriza¸c˜aoque facilita compara¸c˜oesentre uma diversidade de semˆanticas, incluindo a WFSX. ² Uma l´ogicaauto–epist´emicae uma l´ogicade regras por omiss˜aocorrespondentes `a WFSX, que por um lado resolvem problemas das abordagens cl´assicasa l´ogicasauto–epist´emicas e a l´ogicasde regras por omiss˜ao,e por outro clarificam o significado da nega¸c˜aoexpl´ıcita em programas em l´ogica. ² Um enquadramento de semˆanticas para programas em l´ogicaextendidos com base na abdu¸c˜aode hip´otesesnegativas. Este enquadramento permite a caracteriza¸c˜aode difer- entes graus de cepticismo/credulidade, consensualidade e argumenta¸c˜ao. Uma das semˆanticas de abdu¸c˜aocoincide com a WFSX. ² A “semˆantica O”, uma semˆantica que acrescenta `a WFSX hip´otesesn˜aocontradit´aveis. As t´ecnicasusadas para a defini¸c˜aodesta semˆantica s˜aotamb´emaplic´aveis `asemˆantica bem–fundada de programas normais. ² Com a introdu¸c˜aoda nega¸c˜aoexpl´ıcitap˜oe–sea quest˜aodo tratamento da contradi¸c˜ao. Introduzem–se duas abordagens, que se mostram equivalentes, para lidar com a con- tradi¸c˜ao.Uma consiste em evit´a–lae a outra em removˆe–la,e s˜aotratadas respectivamente atrav´esde restri¸c˜oesna adop¸c˜aode hip´otesesabdutivas, e da transforma¸c˜aode programas contradit´oriosem programas n˜aocontradit´orios,guiada pelas raz˜oesda contradi¸c˜ao. v vi Sommaire Apr`esune br`eve introduction historique, le gros de la th`eseconsiste en une ´etudede s´emantiques d´eclaratives de la programmation logique. Les principales contribution originales sont: ² La WFSX (s´emantique bien fond´eeavec de la n´egationexplicite), une nouvelle s´emantique pour les programmes logiques avec la n´egationexplicite (c.a.d. programmes logiques ´etendus),laquelle est meilleure que d’autres s´emantiques existantes, en virtu de ses pro- priet´es. ² Un sch´ema caract´erisant g´en´erique qui permet la comparison entre une vari´et´e de s´emantiques, y compris la WFSX. ² Une logique auto–´epist´emiqueet une logique de r´egles`ad´efautcorrespondantes `ala WFSX, qui d’un cot´er´esoudent quelques probl`emesdes abordages classiques aux logiques ´epist´emiqueset des logiques de r´egles`ad´efaut,et qui d’autre part clarifient la signification de la n´egationexplicite en programmation logique. ² Un cadre pour de s´emantiques de la programmation logique ´etendue,fond´esur l’abduction d’hypoth`esesn´egatives. Ce cadre va permettre la caract´erisationde plusieurs degr´esdes cepticisme/cr´edulit´e,de consensualit´eet d’argumentation. Une de ces s´emantiques de l’abduction coincide avec la WFSX. ² L’O–s´emantique, une s´emantique qui ajoute `a la WFSX des hypoth´eses non– contraditables. Les techniques emploiy´eespour la d´efinitionde cette s´emantique sont aussitˆotvalables pour la s´emantique bien fond´eede programmes normaux. ² Avec l’introduction de la n´egationexplicite il se pose la question du traitement de la con- tradiction. On introduit deux approches, qui se r´evelent tout `afait ´equivalens, pour bien faire face `ala contradiction. L’une l’entre elles consiste `al’´eviteret l’autre `ala d`efaire.Ils sont ateints, resp´ectivement, soit par des restrictions sur l’adoption des hypoth´esesabduc- tives, soit par une transformation de programmes contradictoires en d’autres programmes non contradictoires, qui est guid´eepar les causes mˆemesde la contradiction. vii viii Contents Acknowledgements i Abstract iii Sum´ario v Sommaire vii Preface 1 I Semantics of Logic Programs: A Brief Historical Overview 5 1 Normal logic programs 9 1.1 Language :::::::::::::::::::::::::::::::::::::::: 9 1.1.1 Interpretations and models :::::::::::::::::::::::::: 10 1.2 Semantics :::::::::::::::::::::::::::::::::::::::: 11 1.2.1 Stable model semantics :::::::::::::::::::::::::::: 14 1.2.2 Well–founded semantics :::::::::::::::::::::::::::: 15 2 Extended logic programs 17 2.1 Language :::::::::::::::::::::::::::::::::::::::: 19 2.2 Semantics :::::::::::::::::::::::::::::::::::::::: 20 II A New Semantics for Extended Logic Programs 23 3 Why a new semantics for extended programs? 25 4 The WFSX semantics 29 4.1 Interpretations and models :::::::::::::::::::::::::::::: 29 4.2 The definition of WFSX :::::::::::::::::::::::::::::::: 31 4.3 Existence of the semantics ::::::::::::::::::::::::::::::: 36 5 WFSX and autoepistemic logics 39 5.1 Generic semantics
Load more

Recommended publications
  • Here the Handbook of Abstracts
    Handbook of the 4th World Congress and School on Universal Logic March 29 { April 07, 2013 Rio de Janeiro, Brazil UNILOG'2013 www.uni-log.org Edited by Jean-Yves B´eziau,Arthur Buchsbaum and Alexandre Costa-Leite Revised by Alvaro Altair Contents 1 Organizers of UNILOG'13 5 1.1 Scientific Committee . .5 1.2 Organizing Committee . .5 1.3 Supporting Organizers . .6 2 Aim of the event 6 3 4th World School on Universal Logic 8 3.1 Aim of the School . .8 3.2 Tutorials . .9 3.2.1 Why Study Logic? . .9 3.2.2 How to get your Logic Article or Book published in English9 3.2.3 Non-Deterministic Semantics . 10 3.2.4 Logic for the Blind as a Stimulus for the Design of Inno- vative Teaching Materials . 13 3.2.5 Hybrid Logics . 16 3.2.6 Psychology of Reasoning . 17 3.2.7 Truth-Values . 18 3.2.8 The Origin of Indian Logic and Indian Syllogism . 23 3.2.9 Logical Forms . 24 3.2.10 An Introduction to Arabic Logic . 25 3.2.11 Quantum Cognition . 27 3.2.12 Towards a General Theory of Classifications . 28 3.2.13 Connecting Logics . 30 3.2.14 Relativity of Mathematical Concepts . 32 3.2.15 Undecidability and Incompleteness are Everywhere . 33 3.2.16 Logic, Algebra and Implication . 33 3.2.17 Hypersequents and Applications . 35 3.2.18 Introduction to Modern Mathematics . 36 3.2.19 Erotetic Logics . 37 3.2.20 History of Paraconsistent Logic . 38 3.2.21 Institutions .
    [Show full text]
  • Logic-Based Technologies for Intelligent Systems: State of the Art and Perspectives
    information Article Logic-Based Technologies for Intelligent Systems: State of the Art and Perspectives Roberta Calegari 1,* , Giovanni Ciatto 2 , Enrico Denti 3 and Andrea Omicini 2 1 Alma AI—Alma Mater Research Institute for Human-Centered Artificial Intelligence, Alma Mater Studiorum–Università di Bologna, 40121 Bologna, Italy 2 Dipartimento di Informatica–Scienza e Ingegneria (DISI), Alma Mater Studiorum–Università di Bologna, 47522 Cesena, Italy; [email protected] (G.C.); [email protected] (A.O.) 3 Dipartimento di Informatica–Scienza e Ingegneria (DISI), Alma Mater Studiorum–Università di Bologna, 40136 Bologna, Italy; [email protected] * Correspondence: [email protected] Received: 25 February 2020; Accepted: 18 March 2020; Published: 22 March 2020 Abstract: Together with the disruptive development of modern sub-symbolic approaches to artificial intelligence (AI), symbolic approaches to classical AI are re-gaining momentum, as more and more researchers exploit their potential to make AI more comprehensible, explainable, and therefore trustworthy. Since logic-based approaches lay at the core of symbolic AI, summarizing their state of the art is of paramount importance now more than ever, in order to identify trends, benefits, key features, gaps, and limitations of the techniques proposed so far, as well as to identify promising research perspectives. Along this line, this paper provides an overview of logic-based approaches and technologies by sketching their evolution and pointing out their main application areas. Future perspectives for exploitation of logic-based technologies are discussed as well, in order to identify those research fields that deserve more attention, considering the areas that already exploit logic-based approaches as well as those that are more likely to adopt logic-based approaches in the future.
    [Show full text]
  • Axiomatization of Logic. Truth and Proof. Resolution
    H250: Honors Colloquium – Introduction to Computation Axiomatization of Logic. Truth and Proof. Resolution Marius Minea [email protected] How many do we need? (best: few) Are they enough? Can we prove everything? Axiomatization helps answer these questions Motivation: Determining Truth In CS250, we started with truth table proofs. Propositional formula: can always do truth table (even if large) Predicate formula: can’t do truth tables (infinite possibilities) ⇒ must use other proof rules Motivation: Determining Truth In CS250, we started with truth table proofs. Propositional formula: can always do truth table (even if large) Predicate formula: can’t do truth tables (infinite possibilities) ⇒ must use other proof rules How many do we need? (best: few) Are they enough? Can we prove everything? Axiomatization helps answer these questions Symbols of propositional logic: propositions: p, q, r (usually lowercase letters) operators (logical connectives): negation ¬, implication → parentheses () Formulas of propositional logic: defined by structural induction (how to build complex formulas from simpler ones) A formula (compound proposition) is: any proposition (aka atomic formula or variable) (¬α) where α is a formula (α → β) if α and β are formulas Implication and negation suffice! First, Define Syntax We define a language by its symbols and the rules to correctly combine symbols (the syntax) Formulas of propositional logic: defined by structural induction (how to build complex formulas from simpler ones) A formula (compound proposition) is: any
    [Show full text]
  • A Program for the Semantics of Science
    MARIO BUNGE A PROGRAM FOR THE SEMANTICS OF SCIENCE I. PROBLEM, METHOD AND GOAL So far exact semantics has been successful only in relation to logic and mathematics. It has had little if anything to say about factual or empirical science. Indeed, no semantical theory supplies an exact and adequate elucidation and systematization of the intuitive notions of factual referen- ce and factual representation, or of factual sense and partial truth of fact, which are peculiar to factual science and therefore central to its philosophy. The semantics of first order logic and the semantics of mathematics (i.e., model theory) do not handle those semantical notions, for they are not interested in external reference and in partial satisfaction. On the other hand factual science is not concerned with interpreting a theory in terms of another theory but in interpreting a theory by reference to things in the real world and their properties. Surely there have been attempts to tackle the semantic peculiarities of factual science. However, the results are rather poor. We have either vigorous intuitions that remain half-baked and scattered, or rigorous formalisms that are irrelevant to real science. The failure to pass from intuition to theory suggests that semanticists have not dealt with genuine factual science but with some oversimplified images of it, such as the view that a scientific theory is just a special case of set theory, so that model theory accounts for factual meaning and for truth of fact. If we wish to do justice to the semantic peculiarities of factual science we must not attempt to force it into any preconceived Procrustean bed: we must proceed from within science.
    [Show full text]
  • Towards a Unified Theory of Intensional Logic Programming
    J. LOGIC PROGRAMMING 1992:13:413-440 413 TOWARDS A UNIFIED THEORY OF INTENSIONAL LOGIC PROGRAMMING MEHMET A. ORGUN AND WILLIAM W. WADGE D Intensional Logic Programming is a new form of logic programming based on intensional logic and possible worlds semantics. Intensional logic allows us to use logic programming to specify nonterminating computations and to capture the dynamic aspects of certain problems in a natural and problem-oriented style. The meanings of formulas of an intensional first- order language are given according to intensional interpretations and to elements of a set of possible worlds. Neighborhood semantics is employed as an abstract formulation of the denotations of intensional operators. Then we investigate general properties of intensional operators such as universality, monotonicity, finitariness and conjunctivity. These properties are used as constraints on intensional logic programming systems. The model-theoretic and fixpoint semantics of intensional logic programs are developed in terms of least (minimum) intensional Herbrand models. We show in particular that our results apply to a number of intensional logic programming languages such as Chronolog proposed by Wadge and Tem- plog by Abadi and Manna. We consider some elementary extensions to the theory and show that intensional logic program clauses can be used to define new intensional operators. Intensional logic programs with inten- sional operator definitions are regarded as metatheories. a 1. INTRODUCTION Intensional logic programming (ILP) is a new form of logic programming based on intensional logic and possible world semantics. Intensional logic [20] allows us to describe context-dependent properties of certain problems in a natural and prob- Address correspondence to M.
    [Show full text]
  • Logic for Problem Solving
    LOGIC FOR PROBLEM SOLVING Robert Kowalski Imperial College London 12 October 2014 PREFACE It has been fascinating to reflect and comment on the way the topics addressed in this book have developed over the past 40 years or so, since the first version of the book appeared as lecture notes in 1974. Many of the developments have had an impact, not only in computing, but also more widely in such fields as math- ematical, philosophical and informal logic. But just as interesting (and perhaps more important) some of these developments have taken different directions from the ones that I anticipated at the time. I have organised my comments, chapter by chapter, at the end of the book, leaving the 1979 text intact. This should make it easier to compare the state of the subject in 1979 with the subsequent developments that I refer to in my commentary. Although the main purpose of the commentary is to look back over the past 40 years or so, I hope that these reflections will also help to point the way to future directions of work. In particular, I remain confident that the logic-based approach to knowledge representation and problem solving that is the topic of this book will continue to contribute to the improvement of both computer and human intelligence for a considerable time into the future. SUMMARY When I was writing this book, I was clear about the problem-solving interpretation of Horn clauses, and I knew that Horn clauses needed to be extended. However, I did not know what extensions would be most important.
    [Show full text]
  • Parallel Execution of Logic Programs
    Parallel Execution of Logic Programs John S. Conery University of Oregon Copyright c 1994 by John S. Conery ii For Leslie ♥ iv Contents List of Figures ix Preface xi 1 Introduction 3 2 Logic Programming 7 2.1 Syntax ............................... 8 2.2 Semantics ............................. 12 2.3 Control .............................. 16 2.4 Prolog ............................... 19 2.4.1 Evaluable Predicates and Arithmetic .......... 19 2.4.2 Higher Order Functions ................. 21 2.4.3 The Cut Symbol ..................... 22 2.5 Alternate Control Strategies ................... 26 2.5.1 Selection by Number of Solutions ............ 27 2.5.2 Selection by Number of Uninstantiated Variables . 28 2.5.3 Intelligent Backtracking ................. 29 2.5.4 Coroutines ........................ 30 2.6 Chapter Summary ........................ 33 3 ParallelisminLogicPrograms 35 3.1 Models for OR Parallelism .................... 37 3.1.1 Pure OR Parallelism ................... 39 3.1.2 OR Processes ....................... 42 3.1.3 Distributed Search .................... 45 3.1.4 Summary ......................... 47 3.2 Models for AND Parallelism ................... 48 3.2.1 Stream Parallel Models ................. 48 3.2.2 AND Processes ...................... 52 3.2.3 AND Parallelism in the Goal Tree ........... 56 v vi Contents 3.2.4 Summary ......................... 56 3.3 Low Level Parallelism ...................... 57 3.4 Chapter Summary ........................ 59 4 The AND/OR Process Model 63 4.1 Oracle ..............................
    [Show full text]
  • Argumentation Semantics for Defeasible Logics
    Argumentation Semantics for Defeasible Logic Guido Governatori School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, QLD 4072, Australia email: [email protected] Micheal J. Maher Department of Computer Science, Loyola University Chicago, 6525 N. Sheridan Road, Chicago, IL 60626 USA email: [email protected] Grigoris Antoniou Department of Computer Science, University of Crete, P.O. Box 2208, Heraklion, Crete, GR-71409, Greece, email: [email protected] David Billington School of Computing and Information Technology, Griffith University, Nathan, QLD 4111, Australia, email: [email protected] Abstract Defeasible reasoning is a simple but efficient rule-based approach to nonmonotonic reasoning. It has powerful implementations and shows promise to be applied in the areas of legal reasoning and the modeling of business rules. This paper establishes significant links between defeasible reasoning and argumentation. In particular, Dung-like argumentation semantics is provided for two key defeasible logics, of which one is ambiguity propagating and the other ambiguity blocking. There are several reasons for the significance of this work: (a) establishing links between formal systems leads to a better understanding and cross-fertilization, in particular our work sheds light on the argumentation-theoretic features of defeasible logic; (b) we provide the first ambiguity blocking Dung- like argumentation system; (c) defeasible reasoning may provide an efficient implementation platform for systems of argumentation; and (d) argumentation-based semantics support a deeper understanding of defeasible reasoning, especially in the context of the intended applications. Journal of Logic and Computation, 14 (5): 675–702. c Oxford University Press, 2004 The original publication is available at doi: 10.1093/logcom/14.5.675.
    [Show full text]
  • Mathematical Aspects of Logic Programming Semantics
    MATHEMATICAL ASPECTS OF LOGIC PROGRAMMING SEMANTICS Chapman & Hall/CRC Studies in Informatics Series SERIES EDITOR G. Q. Zhang Department of EECS Case Western Reserve University Cleveland, Ohio, U.S.A. PUBLISHED TITLES Stochastic Relations: Foundations for Markov Transition Systems Ernst-Erich Doberkat Conceptual Structures in Practice Pascal Hitzler and Henrik Schärfe Context-Aware Computing and Self-Managing Systems Waltenegus Dargie Introduction to Mathematics of Satisfiability Victor W. Marek Ubiquitous Multimedia Computing Qing Li and Timothy K. Shih Mathematical Aspects of Logic Programming Semantics Pascal Hitzler and Anthony Seda ChapmanChapman & Hall/CRC & Hall/CRC StudiesStudies in Informatics in Informatics Series Series MATHEMATICALMATHEMATICAL ASPECTS ASPECTS OF OF LOGIC LOGIC PROGRAMMINGPROGRAMMING SEMANTICSSEMANTICS PASCALPASCAL HITZLER HITZLER Kno.e.sisKno.e.sis Center Center at at WrightWright State UniversityState University Dayton,Dayton, Ohio, Ohio,USA USA ANTHONYANTHONY SEDA SEDA UniversityUniversity College College Cork Cork IrelandIreland CRC Press Taylor & Francis Group CRC6000 PressBroken Sound Parkway NW, Suite 300 TaylorBoca Raton, & Francis FL 33487-2742 Group 6000 Broken Sound Parkway NW, Suite 300 Boca© 2011 Raton, by Taylor FL 33487-2742 and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business © 2011 by Taylor and Francis Group, LLC CRCNo claim Press to is original an imprint U.S. of Government Taylor & Francis works Group, an Informa business NoPrinted claim in to the original United U.S. States Government of America works on acid-free paper 10 9 8 7 6 5 4 3 2 1 Printed in the United States of America on acid-free paper 10International 9 8 7 6 5 4 Standard3 2 1 Book Number: 978-1-4398-2961-5 (Hardback) InternationalThis book contains Standard information Book Number: obtained 978-1-4398-2961-5 from authentic (Hardback) and highly regarded sources.
    [Show full text]
  • Introduction to Logic Programming
    INTRODUCTION TO LOGIC PROGRAMMING Agostino Dovier Universita` di Udine CLPLAB Udine, November 20, 2018 AGOSTINO DOVIER (CLPLAB) INTRODUCTION TO LOGIC PROGRAMMING UDINE,NOVEMBER 20,2018 1/52 WHERE DID LOGIC PROGRAMMING COME FROM? Logic Programming was born 1972 (circa), presaged by related work by Ted Elcock (left), Cordell Green, Pat Hayes and Carl Hewitt (right) on applying theorem proving to problem solving (planning) and to question-answering systems. AGOSTINO DOVIER (CLPLAB) INTRODUCTION TO LOGIC PROGRAMMING UDINE,NOVEMBER 20,2018 2/52 WHERE DID LOGIC PROGRAMMING COME FROM? It blossomed from Alan Robinson’s (left) seminal contribution, including the Resolution Principle, all the way into a practical, declarative, programming language with automated deduction at its core, through the vision and efforts of Alain Colmerauer and Bob Kowalski (right). AGOSTINO DOVIER (CLPLAB) INTRODUCTION TO LOGIC PROGRAMMING UDINE,NOVEMBER 20,2018 3/52 WHERE DID LOGIC PROGRAMMING COME FROM? DEDUCTIVE REASONING AND FORMAL LOGIC Two basic ingredients: Modus Ponens (if p implies q is true and p is true, then q is true) and Generalization (if something is true of a class of things in general, this truth applies to all legitimate members of that class) allows to state the syllogism by Aristotele: All human beings are mortal. Socrates is human. Therefore, Socrates is mortal. Formal Logic is a formal version of human deductive logic. It provides a formal language with an unambiguous syntax and a precise meaning, and it provides rules for manipulating expressions in a way that respects this meaning. AGOSTINO DOVIER (CLPLAB) INTRODUCTION TO LOGIC PROGRAMMING UDINE,NOVEMBER 20,2018 4/52 WHERE DID LOGIC PROGRAMMING COME FROM? COMPUTATIONAL LOGIC The existence of a formal language for representing information and the existence of a corresponding set of mechanical manipulation rules together make automated reasoning using computers possible.
    [Show full text]
  • Arxiv:Cs/0003013V1 [Cs.AI] 7 Mar 2000 Oe Fdfeetlgc Spolmtc T.I Em Un- Seems It Etc
    A Flexible Framework for Defeasible Logics G. Antoniou and D. Billington and G. Governatori and M.J. Maher School of Computing and Information Technology, Griffith University Nathan, QLD 4111, Australia {ga,db,guido,mjm}@cit.gu.edu.au Abstract likely then that these logics are practically useful for knowl- edge representation. Logics for knowledge representation suffer from over- specialization: while each logic may provide an ideal repre- One way to address this problem is to develop logics that sentation formalism for some problems, it is less than optimal are “tunable” to the situation. That is, to develop a frame- for others. A solution to this problem is to choose from sev- work of logics in which an appropriate logic can be de- eral logics and, when necessary, combine the representations. signed. However, such a framework is not sufficient. Also In general, such an approach results in a very difficult prob- needed is a methodology for designing logics, and the capa- lem of combination. However, if we can choose the logics bility of employing more than one such logic in a represen- from a uniform framework then the problem of combining tation. them is greatly simplified. In this paper, we develop such In this paper we develop such a framework for defeasi- a framework for defeasible logics. It supports all defeasible ble logics. This is a first step towards addressing the above logics that satisfy a strong negation principle. We use logic meta-programs as the basis for the framework. problem for knowledge representation logics more gener- ally. We make some contributions to the methodology by demonstrating how certain properties can be ensured for a Introduction logic.
    [Show full text]
  • Propositional Logic
    CS 441 Discrete Mathematics for CS Lecture 2 Propositional logic Milos Hauskrecht [email protected] 5329 Sennott Square CS 441 Discrete mathematics for CS M. Hauskrecht Course administration Homework 1 • First homework assignment is out today will be posted on the course web page • Due next week on Thurday Recitations: • today at 4:00pm SENSQ 5313 • tomorrow at 11:00 SENSQ 5313 Course web page: http://www.cs.pitt.edu/~milos/courses/cs441/ CS 441 Discrete mathematics for CS M. Hauskrecht 1 Propositional logic: review • Propositional logic: a formal language for representing knowledge and for making logical inferences • A proposition is a statement that is either true or false. • A compound proposition can be created from other propositions using logical connectives • The truth of a compound proposition is defined by truth values of elementary propositions and the meaning of connectives. • The truth table for a compound proposition: table with entries (rows) for all possible combinations of truth values of elementary propositions. CS 441 Discrete mathematics for CS M. Hauskrecht Compound propositions • Let p: 2 is a prime ….. T q: 6 is a prime ….. F • Determine the truth value of the following statements: ¬ p: F p q : F p ¬q: T p q : T p q: T p q: F q p: T CS 441 Discrete mathematics for CS M. Hauskrecht 2 Constructing the truth table • Example: Construct the truth table for (p q) (¬p q) CS 441 Discrete mathematics for CS M. Hauskrecht Constructing the truth table • Example: Construct the truth table for (p q) (¬p q) Rows: all possible combinations of values pq¬pforp elementaryq¬p q(pq) propositions: (¬pq) TT 2n values TF FT FF CS 441 Discrete mathematics for CS M.
    [Show full text]