Logical Tools for Handling Change in Agent-Based Systems (eBook)

Preface 5
Contents 7
1 Introduction and Motivation 11
Programme 11
Short Overview of the Different Logics 12
Nonmonotonic Logics 12
Theory Revision 13
Theory Update 14
Deontic Logic 16
Counterfactual Conditionals 16
Modal Logic 17
Intuitionistic Logic 18
Inheritance Systems 18
A Summarizing Table for the Semantics 18
A Discussion of Concepts 20
Basic Semantic Entities, Truth Values, and Operators 20
Algebraic and Structural Semantics 22
Restricted Operators and Relations 25
Copies in Preferential Models 26
Further Remarks on Universality of Representation Proofs 27
in the Object Language? 27
Various Considerations on Abstract Semantics 30
A Comparison with Reiter Defaults 31
IBRS 31
Definition and Comments 31
The Power of IBRS 35
Abstract Semantics for IBRS and Its Engineering Realization 36
2 Basic Definitions and Results 41
Algebraic Definitions 41
Basic Logical Definitions 44
Basic Definitions and Results for Nonmonotonic Logics 45
3 Abstract Semantics by Size 62
The First-Order Setting 62
General Size Semantics 63
Introduction 63
Main Table 64
Coherent Systems 73
Size and Principal Filter Logic 78
4 Preferential Structures -- Part I 81
Introduction 81
Remarks on Nonmonotonic Logics and Preferential Semantics 81
Basic Definitions 85
Preferential Structures Without Domain Conditions 95
General Discussion 95
Detailed Discussion 102
5 Preferential Structures -- Part II 126
Simplifications by Domain Conditions, Logical Properties 126
Introduction 126
Smooth Structures 126
Ranked Structures 130
The Logical Properties with Definability Preservation 131
A-Ranked Structures 132
Representation Results for A-Ranked Structures 132
Two-Sequent Calculi 138
Introduction 138
Plausibility Logic 138
A Comment on the Work by Arieli and Avron 140
Blurred Observation -- Absence of Definability Preservation 141
Introduction 141
General and Smooth Structures Without Definability Preservation 145
Ranked Structures 150
The Limit Variant 152
Introduction 152
The Algebraic Limit 154
The Logical Limit 156
6 Higher Preferential Structures 163
Introduction 163
The General Case 168
Discussion of the Totally Smooth Case 173
The Essentially Smooth Case 175
Translation to Logic 179
7 Deontic Logic and Hierarchical Conditionals 180
Semantics of Deontic Logic 180
Introductory Remarks 180
Basic Definitions 184
Philosophical Discussion of Obligations 191
Examination of the Various Cases 198
What Is An Obligation? 202
Conclusion 203
A Comment on Work by Aqvist 203
Introduction 203
There Are (At Least) Two Solutions 204
Outline 206
Gm A Implies G A (Outline) 210
Hierarchical Conditionals 210
Introduction 210
Formal Modelling and Summary of Results 214
Overview 216
Connections with Other Concepts 217
Formal Results and Representation for Hierarchical Conditionals 219
8 Theory Update and Theory Revision 223
Update 223
Introduction 223
Hidden Dimensions 223
Theory Revision 231
Introduction to Theory Revision 231
Booth Revision 240
Revision and Independence 248
Preferential Modelling of Defaults 253
Remarks on Independence 254
9 An Analysis of Defeasible Inheritance Systems 255
Introduction 255
Terminology 255
Inheritance and Reactive Diagrams 255
Conceptual Analysis 261
Introduction to Nonmonotonic Inheritance 262
Basic Discussion 262
Directly Sceptical Split Validity Upward Chaining Off-Path Inheritance 266
Review of Other Approaches and Problems 273
Defeasible Inheritance and Reactive Diagrams 274
Summary of Our Algorithm 274
Overview 276
Compilation and Memorization 277
Executing the Algorithm 277
Signposts 278
Beyond Inheritance 278
Interpretations 279
Introduction 279
Informal Comparison of Inheritance with the Systems P and R 280
Inheritance as Information Transfer 281
Inheritance as Reasoning with Prototypes 285
Detailed Translation of Inheritance to Modified Systems of Small Sets 288
Normality 288
Small Sets 289
Bibliography 298
Index 302