DOCSLIB.ORG

Towards More Flexible and Common-Sense Reasoning About

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Towards More Flexible and Common-Sense Reasoning About From: AAAI Technical Report SS-95-05. Compilation copyright © 1995, AAAI (www.aaai.org). All rights reserved. TowardsMore Flexible and Common-SensicalReasoning about Beliefs Gees C. Stein John A. Barnden Computing Research Lab Computing Research Lab & Computer Science Dept. & Computer Science Dept. NewMexico State University NewMexico State University Las Cruces, NM88003-8001 Las Cruces, NM88003-8001 gstein@crl, nmsu. edu j barnden@cri. nmsu. edu Abstract in the future. Someimportant research problemswithin reasoning about beliefs are howto deal withincomplete, inaccurate or uncertain Belief-Reasoning Issues Addressed beliefs, whento ascribe beliefs and howto makereasoning In this section we discuss aspects of several of the crucial about beliefs morecommon-sensical. We present two systems issues mentioned in the call for papers for the workshop. that attack such problems.The first, called CaseMent,uses These aspects are addressed by one or both of the systems we case-basedreasoning to reason about beliefs. It appears will be describing. that using cases as opposedto roles has advantageswith respectto reusability, context-sensitivityof reasoning,belief Kinds of Reasoning Done by People ascriptionand introspection. Although the programis still in an initial stage, the first results fromthe existingimplementation Classical logics rely on deductive inferences and most systems look promising. The second system, ATI’-Meta,addresses that reason about beliefs do the same (Creary, 1979; Haas, the fact that metaphoricaldescriptions of mentalstates play 1986; Hadley, 1988; Lakemeyer, 1991; Levesque, 1984; an important role in the coherence of mundanediscourse Maidaet al., 1991). In particular, believers are implicitly or (including stories). ATI’-Meta’sreasoning modulehas explicitly cast as performing deduction. However,people do advancedprototype implementation. It incorporates powerful not only use deductionbut also induction, abduction, analogy- facilities for defeasibleand uncertain reasoning. Both systems based reasoning and other forms of plausible reasoning. They use simulative reasoning and thereby reduce the amountof havethe ability to infer general rules to explain someparticular explicit self-knowledgethey needin ascribing,to other agents, beliefs and reasoningssimilar to their own. examples(induction) or generate plausible explanations for observedfacts (abduction --- see, for example,Hobbs et al., 1993). While deduction produces logically sound results, Introduction induction and abduction produce plausible results, which do The call for papers addressed the issues of what is needed not necessarily have to be true. Ideally, systems that reason for story understanding, the way mental states should be about beliefs should be able to ascribe abduction, deduction, represented, the reusability of representations, introspection, induction, analogy-basedreasoning etc. to people. and the type/amountof explicit self-knowledge.In this paper two systems will be discussed that reason about beliefs and Incomplete, Incorrect or Uncertain Information address certain aspects of these issues. The two systems are Ideally, reasoning happenswith all the relevant information based on different reasoning techniques and focus on different available, and with all the information being correct and problems of reasoning about beliefs. The first system uses free of uncertainties. In reality people often have to reason case-based reasoning in order to grapple with somecommon- with incomplete, incorrect and uncertain information. They sensical aspects of reasoning about beliefs. The secondsystem generate defeasible conclusions, conclusions that seemlikely focuses on other common-sensicalaspects in concentrating to be true but later mightturn out to be false. A systemthat on discourse contexts that contain metaphorical descriptions reasons about beliefs has to deal with these issues at both the of mentalstates. system level and within a belief space. Becauseagents might Althoughboth systems are currently confined to reasoning have incompleteor uncertain beliefs it is not enoughfor the about beliefs as opposedto other mental states, we plan to system itself to knowhow to reason with its ownincomplete, expandto other mental states in the future. uncertain beliefs; it has to ascribe such reasoning to other Section 2 discusses those issues from the workshop’s agents as well. Only a minority of research on belief has call for papers that our systems address to a significant endowedsystems with this sort of capability. Oneexample is extent. Section 3 discusses the general technique of case- the work of Cravo & Martins (1993), on a version of SNePS based reasoning, which is the basis of our first system, that uses default reasoning. CaseMent.Section 4 sketches CaseMentitself, and section 5 shows why case-based reasoning helps with some of the Shades of Belief issues of section 2. Section 6 sketches our ATT-Metasystem, Most systems do not deal with different kinds of beliefs. and then section 7 discusses its benefits with regard to the However,beliefs can be of different varieties or "shades". issues of section 2. Section 8 concludes, and briefly points For example, they can be held with different degrees of out how CaseMentand ATT-Metacould be brought together consciousness, they can be more or less active (i.e., more 127 or less capable of affecting reasoning and action), and they (ii) if other people similar to P believe B, then ascribing B can be momentaryor long-lasting. The particular shade of a P is reasonable. belief can be implied by its context. Take for instance "Helga (iii) if other people similar to P believe somethingsimilar believes that Werner is intelligent," in a context where subject matter to B, then ascribing B to P is reasonable. Helga is not just in love with Werner, but really worships Thus, analogy might be a good way for a system to improve him, and where Werner is not in fact intelligent. Then, its belief ascription. Of course, a suitable notion of similarity plausibly, Helga’s belief is a kind of "wishful thinking" would need to be developed. belief: something halfway between wishing and believing. Contrast this with "Marybelieves olive oil is very healthy," Introspection: Knowledge of Own Mental given that Mary has done a lot of research on howolive Processes oil affects health and that Maryis a well-respectedscientist. It is useful for an intelligent systemto be able to view other Mary’s belief is presumably not wishful thinking. Other agents as reasoning in muchthe sameway as it itself reasons. mental states also come in various shades. For instance, This view is a useful default, in the absence of specific hoping involves a context-sensitive mixture of expectation evidence about how another agent is reasoning. Now, a and desire. particularly effective way of embodyingthis strategy in a Levesque(1984) and Lakemeyer(1991) makea distinction system is simulative reasoning. This technique has often been between "explicit" and "implicit" beliefs, mainly to solve suggested in AI, under various names(see, e.g., Attardi the logical omniscienceproblem. It is commonin philosophy Simi, 1994; Ballim & Wilks, 1991; Chalupsky, 1993; Creary, to distinguish "tacit" beliefs as a special case (see Richard 1979; Dinsmore, 1991; Haas, 1986; Konolige, 1986; Moore, (1990) for discussion). However,these distinctions only 1973); it is also closely related to the Simulation Theory scratch the surface of the issue of shadesof belief (or of other in philosophy and psychology (Davies & Stone, in press). mentalstates). Simulative reasoning works as follows. Whenreasoning about another agent X, the system in effect pretends it is Ascribing Beliefs agent X by using X’s beliefs as if they were its own, and Tobe able to reason about other agents’ beliefs a systemhas to applying its own reasoning mechanism to them. Results makeassumptions about what the agents believe. Normally, of such pretences are then wrappedinside an "X believes relatively few if any of the beliefs of an agent are knownwith that" layer. Simulative reasoning has various advantages over the alternative methodsthat would otherwise be needed certainty, and the system has to "ascribe" beliefs: assume (such as reasoning explicitly about inference steps taken that the agent has particular beliefs. by X). Onesalient benefit is that it does not require the Peopledo a similar thing: they can interact even with some- system to have explicit information about its own reasoning one totally unknownby assumingthat this person has certain abilities in order to to be able to ascribe themto other agents. beliefs. People appear often to make a default assumption This advantage is especially strong in a system that has a that other people have beliefs similar to their own.By default variety of reasoning methods--- e.g., induction, abduction, everybodyis expectedto believe that the earth is round. At the analogy-based reasoning, as well as deduction --- or where sametime a person might have certain beliefs that he or she an individual methodis procedurally very complex--- e.g., does not ascribe to others: an astronomer will not generally analogy-based reasoning. (See Haas, 1986, and Barnden, in assumethat non-astronomershave the same beliefs as (s)he press, for further discussion and other advantages.) Under aboutstars. simulative reasoning, the system’s reasoning methods are A system has to knowwhich of its beliefs it can ascribe to automatically and implicitly ascribed to other agents. other agents and
Load more

Recommended publications
  • Graph-Based Reasoning in Collaborative Knowledge Management for Industrial Maintenance Bernard Kamsu-Foguem, Daniel Noyes
    Graph-based reasoning in collaborative knowledge management for industrial maintenance Bernard Kamsu-Foguem, Daniel Noyes To cite this version: Bernard Kamsu-Foguem, Daniel Noyes. Graph-based reasoning in collaborative knowledge manage- ment for industrial maintenance. Computers in Industry, Elsevier, 2013, Vol. 64, pp. 998-1013. 10.1016/j.compind.2013.06.013. hal-00881052 HAL Id: hal-00881052 https://hal.archives-ouvertes.fr/hal-00881052 Submitted on 7 Nov 2013 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. Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID: 9587 To link to this article: doi.org/10.1016/j.compind.2013.06.013 http://www.sciencedirect.com/science/article/pii/S0166361513001279 To cite this version: Kamsu Foguem, Bernard and Noyes, Daniel Graph-based reasoning in collaborative knowledge management for industrial
    [Show full text]
  • Next Generation Logic Programming Systems Gopal Gupta
    Next Generation Logic Programming Systems Gopal Gupta In the last 30 years logic programming (LP), with Prolog as the most representative logic programming language, has emerged as a powerful paradigm for intelligent reasoning and deductive problem solving. In the last 15 years several powerful and highly successful extensions of logic programming have been proposed and researched. These include constraint logic programming (CLP), tabled logic programming, inductive logic programming, concurrent/parallel logic programming, Andorra Prolog and adaptations for non- monotonic reasoning such as answer set programming. These extensions have led to very powerful applications in reasoning, for example, CLP has been used in industry for intelligently and efficiently solving large scale scheduling and resource allocation problems, tabled logic programming has been used for intelligently solving large verification problems as well as non- monotonic reasoning problems, inductive logic programming for new drug discoveries, and answer set programming for practical planning problems, etc. However, all these powerful extensions of logic programming have been developed by extending standard logic programming (Prolog) systems, and each one has been developed in isolation from others. While each extension has resulted in very powerful applications in reasoning, considerably more powerful applications will become possible if all these extensions were combined into a single system. This power will come about due to search space being dramatically pruned, reducing the time taken to find a solution given a reasoning problem coded as a logic program. Given the current state-of-the-art, even two extensions are not available together in a single system. Realizing multiple or all extensions in a single framework has been rendered difficult by the enormous complexity of implementing reasoning systems in general and logic programming systems in particular.
    [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]
  • Compiling a Default Reasoning System Into Prolog
    Compiling A Default Reasoning System into Prolog David Poole Department of Computer Science University of British Columbia Vancouver BC Canada VT W p o olecsub cca July Abstract Articial intelligence researchers have b een designing representa tion systems for default and ab ductive reasoning Logic Programming researchers have b een working on techniques to improve the eciency of Horn Clause deduction systems This pap er describ es how one such default and ab ductive reasoning system namely Theorist can b e translated into Horn clauses with negation as failure so that we can use the clarity of ab ductive reasoning systems and the eciency of Horn clause deduction systems Wethus showhowadvances in expressivepower that articial intelligence workers are working on can directly utilise advances in eciency that logic programming re searchers are working on Actual co de from a running system is given Intro duction Many p eople in Articial Intelligence have b een working on default reasoning and ab ductive diagnosis systems The systems implemented so far eg are only prototyp es or have b een develop ed in A Theorist to Prolog Compiler ways that cannot take full advantage in the advances of logic programming implementation technology Many p eople are working on making logic programming systems more ecient These systems however usually assume that the input is in the form of Horn clauses with negation as failure This pap er shows howto implement the default reasoning system Theorist by compiling its input into Horn clauses
    [Show full text]
  • Mathematical Reasoning with Diagrams Mateja Jamnik
    Mathematical Reasoning with Diagrams Mateja Jamnik ISBN: 1-57586-324-3 Copyright notice: Excerpted from Mathematical Reasoning with Diagrams by Mateja Jamnik, published by CSLI Publications. ©2001 by CSLI Publications. All rights reserved. This text may be used and shared in accordance with the fair-use provisions of U.S. copyright law, and it may be archived and redistributed in electronic form, provided that this entire notice, including copyright information, is carried and provided that CSLI Publications is notified and no fee is charged for access. Archiving, redistribution, or republication of this text on other terms, in any medium, requires the consent of CSLI Publications. Contents Foreword vii Preface xi 1 Introduction 1 2 The History of Diagrammatic Systems 11 3 Diagrammatic Theorems and the Problem Domain 27 4 The Constructive ω-Rule and Schematic Proofs 49 5 Designing a Diagrammatic Reasoning System 71 6 Diagrammatic Operations 89 7 The Construction of Schematic Proofs 103 8 The Verification of Schematic Proofs 123 9 Diamond in Action 149 10 Complete Automation 163 Appendix A: More Examples of Diagrammatic Theorems 175 Appendix B: The ω-Rule 181 Glossary 185 References 190 Index 199 v Foreword The advent of the modern computer in the nineteen-fifties immediately suggested a new research challenge: to seek ways of programming these versatile machines which would make them behave as much like intel- ligent human beings as possible. After fifty years or so, this quest has produced some intriguing results, but until now progress has been dis- appointingly slow. This book is a welcome and encouraging sign that things may at last be about to change.
    [Show full text]
  • 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.
    [Show full text]
  • The Logic Reasoning System a Brief Introduction   Franz Wotawa
    The Logic Reasoning System A Brief Introduction Franz Wotawa Technische Universität Graz Institute for Software Technology Inffeldgasse 16b/2, 8010 Graz, Austria [email protected] http://www.ist.tugraz.at/ The Logic Reasoning System – A brief introduction Franz Wotawa1 Graz University of Technology Institute for Software Technology Inffeldgasse 16b/2, A-8010 Graz, Austria [email protected] Abstract. In this article we describe how to use the Logic Reason- ing System that is based on an Assumption-Based Truth Maintenance system. In particular we show by example how models following the consistency-based reasoning and the abductive reasoning methodology can be formulated. We use one example from the boolean circuit domain and give the two different models for the circuit, which can be used for diagnosis. Moreover, we show how the system can be used to compute diagnoses using consistency-based diagnosis and abductive diagnosis re- spectively. Keywords: Logic-based reasoning systems, ATMS, Diagnosis 1 Introduction The Logic Reasoning System (LRS) can be obtained from the author of this article. The system is implemented in Java 1.5 and ships out as an executable JAR file. To install the system the JAR file and the example models should be copied to a directory on your computer. You can open LRS by simple executing the JAR file if the Java runtime engine 1.5 or higher is installed. The system comes with no warranty. Before discussing modeling we briefly recall the related literature behind LRS. The implementation is based on DeKleer’s Assumption-based Truth Main- tenance System (ATMS) [1, 2].
    [Show full text]
  • A Classification Approach for Automated Reasoning Systems--A Case Study in Graph Theory Rong Lin Old Dominion University
    Old Dominion University ODU Digital Commons Computer Science Theses & Dissertations Computer Science Spring 1989 A Classification Approach for Automated Reasoning Systems--A Case Study in Graph Theory Rong Lin Old Dominion University Follow this and additional works at: https://digitalcommons.odu.edu/computerscience_etds Part of the Artificial Intelligence and Robotics Commons Recommended Citation Lin, Rong. "A Classification Approach for Automated Reasoning Systems--A Case Study in Graph Theory" (1989). Doctor of Philosophy (PhD), dissertation, Computer Science, Old Dominion University, DOI: 10.25777/5qk4-1w09 https://digitalcommons.odu.edu/computerscience_etds/115 This Dissertation is brought to you for free and open access by the Computer Science at ODU Digital Commons. It has been accepted for inclusion in Computer Science Theses & Dissertations by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. A CLASSIFICATION APPROACH FOR AUTOMATED REASONING SYSTEMS - A CASE STUDY IN GRAPH THEORY By Rong Lin A THESIS SUBMITTED TO THE FACULTY OF OLD DOMINION UNIVERSITY N PARTIAL FULFILLMENT OF TIIE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY COMPUTER SCIENCE Norfolk, Virginia April, 1989 Approved by: Shunichi Toida (Director) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT Reasoning systems which create classifications of structured objects face the problem of how object descriptions can be used to reflect their components as well as relations among these com­ ponents. Current reasoning sysLcms on grapli theory do not adequately provide models to discover complex relations among mathematical concepts (eg: relations involving subgraphs) mainly due to the inability to solve this problem.
    [Show full text]
  • The Fragmentation of Reasoning
    PUBLISHED IN: Pablo Quintanilla, Carla Mantilla, Paola Cépeda (eds.), Cognición social y lenguaje. La intersubjetividad en la evolución de la especie y en el desarrollo del niño, Lima: Pontificia Universidad Católica del Perú, 2014. ISBN: 978-612-4146-80-0 THE FRAGMENTATION OF REASONING Peter Carruthers University of Maryland 1. INTRODUCTION Scientists who study human reasoning across a range of cognitive domains have increasingly converged on the idea that there are two distinct systems (or types of system) involved. These domains include learning (Berry & Dienes, 1993; Reber, 1993), conditional and probabilistic reasoning (Evans & Over, 1996; Sloman, 1996 and 2002; Stanovich, 1999), decision making (Kahneman & Frederick, 2002; Kahneman, 2003), and social cognition of various sorts (Petty & Cacioppo, 1986; Chaike, and others, 1989; Wilson, and others, 2000). Although terminology has differed, many now use the labels «System 1» and «System 2» to mark the intended distinction. System 1 is supposed to be fast and unconscious in its operations, issuing in intuitively compelling answers to learning or reasoning problems in ways that subjects themselves have no access to. System 2, in contrast, is supposed to be slow and conscious in its operations, and is engaged whenever we are induced to tackle reasoning tasks in a reflective manner. Many theorists now accept that System 1 is really a set of systems, arranged in parallel, while believing that System 2 is a single serially-operating ability. Moreover, System 1 is generally thought to be unchangeable in its basic operations, to be universal amongst humans, and to be shared (at least in significant part) with other species of animal.
    [Show full text]
  • Case-Based Reasoning Is a Methodology Not a Technologyଝ
    Knowledge-Based Systems 12 (1999) 303–308 Case-based reasoning is a methodology not a technologyq I. Watson AI-CBR, University of Salford, Salford M5 4WT, UK Received 1 December 1998; accepted 17 March 1999 Abstract This paper asks whether case-based reasoning is an artificial intelligence (AI) technology like rule-based reasoning, neural networks or genetic algorithms or whether it is better described as a methodology for problem solving, that may use any appropriate technology. By describing four applications of case-based reasoning (CBR), that variously use: nearest neighbour, induction, fuzzy logic and SQL, the author shows that CBR is a methodology and not a technology. The implications of this are discussed. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Case-based reasoning; Artificial intelligence technology; Problem solving methodolgy 1. Introduction 2. Case-based reasoning Artificial intelligence (AI) is often described in terms of CBR arose out of research into cognitive science, most the various technologies developed over the last three or prominently that of Roger Schank and his students at Yale four decades. Technologies such as logic programming, University [1–4]. It is relevant to the argument presented in rule-based reasoning, neural networks, genetic algorithms, this paper that CBR’s origins were stimulated by a desire to fuzzy logic, constraint-based programming and others. understand how people remember information and are in These technologies are characterised by specific program- turn reminded of information; and that subsequently it ming languages or environments (e.g. Prolog or rule-based was recognised that people commonly solve problems by shells) or by specific algorithms and techniques (e.g.
    [Show full text]
  • Logic Programming and Knowledge Representation—The A-Prolog Perspective ✩
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Artificial Intelligence 138 (2002) 3–38 www.elsevier.com/locate/artint Logic programming and knowledge representation—The A-Prolog perspective ✩ Michael Gelfond a,∗, Nicola Leone b a Department of Computer Science, Texas Tech University, Lubbock, TX 79409-3104, USA b Department of Mathematics, University of Calabria, 87030 Rende (CS), Italy Abstract In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a ‘feel’ for the field’s history and some of its recent developments. The discussion is mainly limited to logic programs under the answer set semantics. For understanding of approaches to logic programming built on well-founded semantics, general theories of argumentation, abductive reasoning, etc., the reader is referred to other publications. 2002 Elsevier Science B.V. All rights reserved. Keywords: Logic programming; Nonmonotonic reasoning; Default reasoning; Answer set programming 1. Introduction If we want to design an entity (a machine or a program) capable of behaving intelligently in some environment, then we need to supply this entity with sufficient knowledge about this environment. To do that, we need an unambiguous language capable of expressing this knowledge, together with some precise and well understood way of manipulating sets of sentences of the language which will allow us to draw inferences, answer queries, and update both the knowledge base and the desired program behavior. A good knowledge representation language should allow construction of elaboration tolerant knowledge bases, i.e., bases in which small modifications of the informal body of knowledge correspond to small modifications of the formal base representing this knowledge.
    [Show full text]
  • 4 Combinatorics and Probability
    CHAPTER 4 Combinatorics ✦ ✦ ✦ ✦ and Probability In computer science we frequently need to count things and measure the likelihood of events. The science of counting is captured by a branch of mathematics called combinatorics. The concepts that surround attempts to measure the likelihood of events are embodied in a field called probability theory. This chapter introduces the rudiments of these two fields. We shall learn how to answer questions such as how many execution paths are there in a program, or what is the likelihood of occurrence of a given path? ✦ ✦ ✦ ✦ 4.1 What This Chapter Is About We shall study combinatorics, or “counting,” by presenting a sequence of increas- ingly more complex situations, each of which is represented by a simple paradigm problem. For each problem, we derive a formula that lets us determine the number of possible outcomes. The problems we study are: ✦ Counting assignments (Section 4.2). The paradigm problem is how many ways can we paint a row of n houses, each in any of k colors. ✦ Counting permutations (Section 4.3). The paradigm problem here is to deter- mine the number of different orderings for n distinct items. ✦ Counting ordered selections (Section 4.4), that is, the number of ways to pick k things out of n and arrange the k things in order. The paradigm problem is counting the number of ways different horses can win, place, and show in a horse race. ✦ Counting the combinations of m things out of n (Section 4.5), that is, the selection of m from n distinct objects, without regard to the order of the selected objects.
    [Show full text]