Gupta / Pacuit Games, Norms and Reasons

Logic at the Crossroads
1. Auflage 2011
ISBN: 978-94-007-0714-6
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 232 Seiten

Games, Norms, and Reasons: Logic at the Crossroads provides an overview of modern logic focusing on its relationships with other disciplines, including new interfaces with rational choice theory, epistemology, game theory and informatics. This book continues a series called 'Logic at the Crossroads' whose title reflects a view that the deep insights from the classical phase of mathematical logic can form a harmonious mixture with a new, more ambitious research agenda of understanding and enhancing human reasoning and intelligent interaction. The editors have gathered together articles from active authors in this new area that explore dynamic logical aspects of norms, reasons, preferences and beliefs in human agency, human interaction and groups. The book pays a special tribute to Professor Rohit Parikh, a pioneer in this movement.

Autoren/Hrsg.

Gupta, Amitabha

Pacuit, Eric

Inhaltsverzeichnis

1;Preface;6
2;Contents;12
3;List of Contributors;16
4;1 Bounded Rationality: Models for Some Fast and Frugal Heuristics;18
4.1;1.1 Introduction;18
4.2;1.2 Take The Best;20
4.3;1.3 Rational Choice: The Received View;25
4.4;1.4 Choice Functions for Take The Best;29
4.5;1.5 Conclusion and Discussion;34
4.5.1;1.5.1 Future Work;36
4.6;References;37
5;2 Why Do We Need Justification Logic?;39
5.1;2.1 Introduction;39
5.2;2.2 Justifications and Operations;41
5.3;2.3 Basic Logic of Justifications;42
5.4;2.4 Red Barn Example and Tracking Justifications;46
5.4.1;2.4.1 Red Barn in Modal Logic of Belief;46
5.4.2;2.4.2 Red Barn in Modal Logic of Knowledge;47
5.4.3;2.4.3 Red Barn in Justification Logic of Belief;47
5.4.4;2.4.4 Red Barn in Justification Logic of Knowledge;48
5.4.5;2.4.5 Red Barn and Formal Epistemic Models;49
5.5;2.5 Basic Epistemic Semantics;49
5.6;2.6 Adding Factivity;51
5.7;2.7 Conclusions;52
5.8;References;52
6;3 Why Meanings Are Not Normative ;55
7;4 The Realization Theorem for S5 A Simple, Constructive Proof;76
7.1;4.1 Introduction;76
7.2;4.2 Justification Logics;76
7.3;4.3 An S5 Gentzen System;80
7.4;4.4 Annotations and Realizations;82
7.5;4.5 Modifying Realizations;83
7.6;4.6 A Realization Example;89
7.7;References;91
8;5 Merging Information;92
8.1;5.1 Introduction: The Milieu;92
8.2;5.2 The Vast Realm of Approaches;93
8.2.1;5.2.1 Revising vs Merging;94
8.2.2;5.2.2 Different Approaches;94
8.2.2.1;5.2.2.1 Logical Approaches;95
8.2.2.2;5.2.2.2 Connectionist Approaches;96
8.3;5.3 Merging Opinions, Preferences and Beliefs;98
8.3.1;5.3.1 Logic of Opinions;99
8.3.2;5.3.2 Logic of Opinions and Beliefs;103
8.4;5.4 Conclusion;105
8.5;5.5 Completeness for LO;106
8.6;5.6 Completeness for LOB-;108
8.7;References;109
9;6 Modal Logic for Lexicographic Preference Aggregation ;112
9.1;6.1 Basic Preference Logic;113
9.2;6.2 Lexicographic Reordering;115
9.3;6.3 Modal logic for Preference Aggregation;119
9.4;6.4 Applications;123
9.5;6.5 Dynamics;125
9.6;6.6 Conclusion;131
9.7;References;131
10;7 No--Regret: A Connection between Computational Learning Theory and Game Theory;133
10.1;7.1 Introduction;133
10.2;7.2 -Regret ;135
10.2.1;7.2.1 Blackwell's Approachability Theory;135
10.2.2;7.2.2 Action Transformations;137
10.2.3;7.2.3 No -Regret Learning;138
10.3;7.3 Existence of No--Regret Learning Algorithms ;138
10.4;7.4 -Equilibria ;141
10.4.1;7.4.1 Examples of -Equilibria;141
10.4.2;7.4.2 Properties of -Equilibrium;143
10.5;7.5 Convergence of No--Regret Learning Algorithms ;145
10.6;7.6 The Power of No Internal Regret ;146
10.7;7.7 Related Work ;149
10.7.1;7.7.1 On the Existence of No-Regret Algorithms;149
10.7.2;7.7.2 On the Connection Between Learning and Games;151
10.8;7.8 Summary ;152
10.9;7.9 Proof of Lemma 7.4 ;152
10.10;References;153
11;8 Axioms of Distinction in Social Software;155
11.1;8.1 Perspectives, Agents and Axioms;156
11.2;8.2 Setting Up the Matrix;158
11.3;8.3 Negative Introspection of Knowledge;160
11.4;8.4 Negative Introspection in Games;160
11.5;8.5 Negative Introspection in Economics;161
11.6;8.6 Axioms of Distinction;162
11.7;References;163
12;9 Publication/Citation: A Proof-Theoretic Approach to Mathematical Knowledge Management;165
12.1;9.1 Introduction;165
12.2;9.2 A Classical Proof System;166
12.3;9.3 A New System;168
12.4;9.4 An Example;171
12.5;9.5 Related and Future Work;173
12.6;References;174
13;10 Generalizing Parikh's Theorem;176
13.1;10.1 Generalizing Parikh's Theorem;176
13.2;10.2 Monadic Second Order Logic and Its Extension;177
13.3;10.3 Spectra of Sentences of Monadic Second Order Logic;178
13.3.1;10.3.1 Spectra of Sentences with One Unary Function Symbol;178
13.3.2;10.3.2 From One Unary Function to Bounded Tree-Width;178
13.3.3;10.3.3 Many-Sorted Spectra;179
13.4;10.4 Structures of Bounded Width;180
13.4.1;10.4.1 Tree-Width;180
13.4.2;10.4.2 Clique-Width;182
13.4.3;10.4.3 Patch-Width;184
13.5;10.5 Applications of Theorem 10.8;185
13.5.1;10.5.1 Classes of Unbounded Patch-Width;185
13.5.2;10.5.2 The Patch-Width of Incidence Graphs;186
13.5.3;10.5.3 Proof of Theorem 10.9;186
13.6;10.6 Conclusions and Open problems;187
13.7;References;189
14;11 Syllogistic Logic with Complements;191
14.1;11.1 Introduction;191
14.1.1;11.1.1 Syllogistic Logic with Complement;192
14.1.2;11.1.2 The Indirect System: Reductio Ad Absurdum;195
14.1.3;11.1.3 Comparison with Previous Work;195
14.2;11.2 Completeness via Representation of Orthoposets;196
14.2.1;11.2.1 Completeness;198
14.3;11.3 Going Further: Boolean Connectives Inside and Out;200
14.4;11.4 Ex Falso Quodlibet Versus Reductio ad Absurdum;202
14.4.1;11.4.1 Injective Proofs and Normal Forms;203
14.4.2;11.4.2 Proofs with and Without Contradiction;206
14.5;11.5 Further Work in the Area;209
14.6;References;209
15;12 From Unary to Binary Inductive Logic;210
15.1;12.1 Introduction;210
15.2;12.2 Notation and Background;211
15.3;12.3 Principles of Symmetry;214
15.4;12.4 Johnson's Sufficientness Principle;217
15.5;12.5 Representation Theorems for Functions Satisfying Sx;218
15.6;12.6 Instantial Relevance;221
15.7;12.7 Conclusion;223
15.8;Dedication;223
15.9;References;223
16;13 Challenges for Decidable Epistemic Logics from Security Protocols;225
16.1;13.1 Summary;225
16.1.1;13.1.1 Knowledge and Communication;225
16.1.2;13.1.2 Cryptographic Protocols;226
16.1.3;13.1.3 Difficulties;227
16.1.4;13.1.4 Decidability Issues;228
16.1.5;13.1.5 This Paper;229
16.1.6;13.1.6 The Proposal;229
16.1.7;13.1.7 BAN Logic;230
16.2;13.2 Security Protocol Modelling;231
16.3;13.3 The Semantics of the Logic;235
16.4;13.4 Decidability;237
16.5;13.5 Discussion;240
16.6;References;241