Gabbay / Schlechta Logical Tools for Handling Change in Agent-Based Systems

1. Auflage 2010
ISBN: 978-3-642-04407-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 305 Seiten

Reihe: Cognitive Technologies

Agents act on the basis of their beliefs and these beliefs change as they interact with other agents. In this book the authors propose and explain general logical tools for handling change. These tools include preferential reasoning, theory revision, and reasoning in inheritance systems, and the authors use these tools to examine nonmonotonic logic, deontic logic, counterfactuals, modal logic, intuitionistic logic, and temporal logic. This book will be of benefit to researchers engaged with artificial intelligence, and in particular agents, multiagent systems and nonmonotonic logic.

Autoren/Hrsg.

Gabbay, Dov M.

Schlechta, Karl

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;1 Introduction and Motivation;11
3.1; Programme;11
3.2; Short Overview of the Different Logics;12
3.2.1; Nonmonotonic Logics;12
3.2.2; Theory Revision;13
3.2.3; Theory Update;14
3.2.4; Deontic Logic;16
3.2.5; Counterfactual Conditionals;16
3.2.6; Modal Logic;17
3.2.7; Intuitionistic Logic;18
3.2.8; Inheritance Systems;18
3.2.9; A Summarizing Table for the Semantics;18
3.3; A Discussion of Concepts;20
3.3.1; Basic Semantic Entities, Truth Values, and Operators;20
3.3.2; Algebraic and Structural Semantics;22
3.3.3; Restricted Operators and Relations;25
3.3.4; Copies in Preferential Models;26
3.3.5; Further Remarks on Universality of Representation Proofs;27
3.3.6; in the Object Language?;27
3.3.7; Various Considerations on Abstract Semantics;30
3.3.8; A Comparison with Reiter Defaults;31
3.4; IBRS;31
3.4.1; Definition and Comments;31
3.4.2; The Power of IBRS;35
3.4.3; Abstract Semantics for IBRS and Its Engineering Realization;36
4;2 Basic Definitions and Results ;41
4.1; Algebraic Definitions;41
4.2; Basic Logical Definitions;44
4.3; Basic Definitions and Results for Nonmonotonic Logics;45
5;3 Abstract Semantics by Size;62
5.1; The First-Order Setting;62
5.2; General Size Semantics;63
5.2.1; Introduction;63
5.2.2; Main Table;64
5.2.3; Coherent Systems;73
5.2.4; Size and Principal Filter Logic;78
6;4 Preferential Structures -- Part I ;81
6.1; Introduction;81
6.1.1; Remarks on Nonmonotonic Logics and Preferential Semantics;81
6.1.2; Basic Definitions;85
6.2; Preferential Structures Without Domain Conditions;95
6.2.1; General Discussion;95
6.2.2; Detailed Discussion;102
7;5 Preferential Structures -- Part II;126
7.1; Simplifications by Domain Conditions, Logical Properties;126
7.1.1; Introduction;126
7.1.2; Smooth Structures;126
7.1.3; Ranked Structures;130
7.1.4; The Logical Properties with Definability Preservation;131
7.2; A-Ranked Structures;132
7.2.1; Representation Results for A-Ranked Structures;132
7.3; Two-Sequent Calculi;138
7.3.1; Introduction;138
7.3.2; Plausibility Logic;138
7.3.3; A Comment on the Work by Arieli and Avron;140
7.4; Blurred Observation -- Absence of Definability Preservation;141
7.4.1; Introduction;141
7.4.2; General and Smooth Structures Without Definability Preservation;145
7.4.3; Ranked Structures;150
7.5; The Limit Variant;152
7.5.1; Introduction;152
7.5.2; The Algebraic Limit;154
7.5.3; The Logical Limit;156
8;6 Higher Preferential Structures;163
8.1; Introduction;163
8.2; The General Case;168
8.3; Discussion of the Totally Smooth Case;173
8.4; The Essentially Smooth Case;175
8.5; Translation to Logic;179
9;7 Deontic Logic and Hierarchical Conditionals;180
9.1; Semantics of Deontic Logic;180
9.1.1; Introductory Remarks;180
9.1.2; Basic Definitions;184
9.1.3; Philosophical Discussion of Obligations;191
9.1.4; Examination of the Various Cases;198
9.1.5; What Is An Obligation?;202
9.1.6; Conclusion;203
9.2; A Comment on Work by Aqvist;203
9.2.1; Introduction;203
9.2.2; There Are (At Least) Two Solutions;204
9.2.3; Outline;206
9.2.4; Gm A Implies G A (Outline);210
9.3; Hierarchical Conditionals;210
9.3.1; Introduction;210
9.3.2; Formal Modelling and Summary of Results;214
9.3.3; Overview;216
9.3.4; Connections with Other Concepts;217
9.3.5; Formal Results and Representation for Hierarchical Conditionals;219
10;8 Theory Update and Theory Revision;223
10.1; Update;223
10.1.1; Introduction;223
10.1.2; Hidden Dimensions;223
10.2; Theory Revision;231
10.2.1; Introduction to Theory Revision;231
10.2.2; Booth Revision;240
10.2.3; Revision and Independence;248
10.2.4; Preferential Modelling of Defaults;253
10.2.5; Remarks on Independence;254
11;9 An Analysis of Defeasible Inheritance Systems;255
11.1; Introduction;255
11.1.1; Terminology;255
11.1.2; Inheritance and Reactive Diagrams;255
11.1.3; Conceptual Analysis;261
11.2; Introduction to Nonmonotonic Inheritance;262
11.2.1; Basic Discussion;262
11.2.2; Directly Sceptical Split Validity Upward Chaining Off-Path Inheritance;266
11.2.3; Review of Other Approaches and Problems;273
11.3; Defeasible Inheritance and Reactive Diagrams;274
11.3.1; Summary of Our Algorithm;274
11.3.2; Overview;276
11.3.3; Compilation and Memorization;277
11.3.4; Executing the Algorithm;277
11.3.5; Signposts;278
11.3.6; Beyond Inheritance;278
11.4; Interpretations;279
11.4.1; Introduction;279
11.4.2; Informal Comparison of Inheritance with the Systems P and R;280
11.4.3; Inheritance as Information Transfer;281
11.4.4; Inheritance as Reasoning with Prototypes;285
11.5; Detailed Translation of Inheritance to Modified Systems of Small Sets;288
11.5.1; Normality;288
11.5.2; Small Sets;289
12;Bibliography;298
13;Index;302