Games, Norms and Reasons (eBook)

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