Dynamic Formal Epistemology (eBook)

P. Girard: PhD. Stanford University, 2009. Publications in Journal of Applied Non-Classical Logic and Journal of Philosophical Logic.O. Roy: PhD. Institute for Logic, Language and Computation, Amsterdam, 2008. Publications in Journal of Philosophical Logic, Synthese, Economics and Philosophy.M. Marion: PhD. Oxford, 1991. Publications in Philosophiques, Synthese, Philosophia Scientiae.

Acknowledgements 6
Contents 7
Contributors 9
1 Introduction 11
Patrick Girard, Mathieu Marion, and Olivier Roy 11
2 Logics of Rational Interaction 15
Barteld Kooi and Eric Pacuit 15
2.1 Introduction 15
2.2 Reasoning About Rational Interaction 16
2.2.1 Epistemic Temporal Logic 18
2.2.2 Dynamic Epistemic Logic 22
2.2.3 Comparing DEL and ETL 25
2.3 Extensions, Connections and Applications 29
2.3.1 Propositional Dynamic Logic 30
2.3.2 Belief Revision 30
2.3.3 Probability Logic 31
2.3.4 Situation Calculus 31
2.3.5 Factual Change 32
2.3.6 Logics of Rational Agency 32
2.3.7 Inference Logic 33
2.3.8 Justification Logic 33
2.3.9 Puzzles and Paradoxes 34
2.3.10 Game Theory 35
2.3.11 Security 36
2.4 Conclusion: Towards a Unified Account of Rational Interaction 36
References 37
3 Dynamic Epistemic Logic and Temporal Modality 43
Audrey Yap 43
3.1 Dynamic Epistemic Logic 43
3.1.1 Language and Models 43
3.2 Dynamic Epistemic Logic with History 45
3.2.1 Language and Models 46
3.2.2 About the Logic 47
3.3 Expressive Power and Variations 57
3.3.1 Bisimulation 57
3.3.2 Common Knowledge and Unsuccessful Updates 57
3.3.3 Axiom Variants 58
References 60
4 Exploring the Power of Converse Events 61
Guillaume Aucher and Andreas Herzig 61
4.1 Introduction 61
4.1.1 Aim: Reason About Perception of Events 61
4.1.2 Semantics of Events: Products vs. Accessibility Relations 62
4.1.3 Translating BMS into EDL 62
4.1.4 Organization of the Chapter 63
4.2 EDL: Epistemic Dynamic Logic with Converse 63
4.2.1 The Language LEDL of EDL 63
4.2.2 Semantics of EDL 64
4.2.3 Completeness 67
4.3 BMS: Static Models, Event Models, and Their Products 67
4.3.1 Semantics 68
4.3.2 Completeness 69
4.4 From BMS to EDL 69
4.4.1 A ``Semantic'' Embedding 70
4.4.2 A ``Syntactic'' Embedding 73
4.4.3 A Representation Theorem 76
4.5 Comparison with ETL and Other Related Work 77
4.5.1 Basics of ETL 77
4.5.2 ETL and EDL 78
4.5.3 Other Related Work 81
4.6 Conclusion 82
References 82
5 Modal Logic for Qualitative Dynamics 85
Darko Sarenac 85
5.1 Introduction 85
5.1.1 Modal View of Dynamics 86
5.2 Iterated Function Systems and Some General Notes on Dynamical Systems 87
5.2.1 Time and Space as Dynamical Control Variables 88
5.2.2 Time, Change, and Dynamics 91
5.2.3 CFS: Time as Continuum 92
5.2.4 Dynamic Topological Logic, DTL 94
5.2.5 Modalities and Their Semantics 95
5.2.6 Some Computational Properties of DTL and Its Fragments 95
5.2.7 Poincare and Topology of Dynamical Systems 96
5.3 A Case Study: IFS=(R*, x3) via Some Qualitative Modal Languages 99
5.3.1 RC and the Local Language of DTL 100
5.3.2 Qualitative Modal Operators 102
5.3.3 Modal Languages for Higher Dimensional Dynamical Systems 104
5.3.4 Dynamic Epistemic Logic and the IFS Perspective 106
5.3.5 DEL vs. IFS 107
5.4 Conclusion 110
References 111
6 Knowing One's Limits: An Analysis in Centered Dynamic Epistemic Logic 112
Denis Bonnay and Paul Égré 112
6.1 Dynamic Logic and Epistemic Paradoxes 112
6.2 Centered Semantics with an Update Operator 114
6.2.1 Centered Semantics 115
6.2.2 Centered Dynamic Epistemic Logic 116
6.3 The Margin of Error Paradox 117
6.3.1 The Paradox 117
6.3.2 Knowing and Realizing 119
6.3.3 Reanalyzing the Paradox with Epistemic Updates 120
6.3.4 CDEL does it better 123
6.4 Keeping on Reflecting 125
6.4.1 Once Versus More Than Once 125
6.4.2 Discounted Margins 128
6.4.3 The Surprise Examination 130
6.5 Conclusion 131
References 135
7 Simple Evidence Elimination in Justification Logic 136
Bryan Renne 136
7.1 Introduction 136
7.2 Syntax 137
7.3 Semantics 139
7.4 Axiomatics 145
7.5 The Courtroom Evidence Example Formalized 156
7.6 Conclusion 157
References 158
8 Belief Update as Social Choice 159
Johan van Benthem 159
8.1 Introduction 159
8.2 Dynamic-Doxastic Belief Change 159
8.3 ``Social Choice'' as Preference Merge for Groups 161
8.4 Belief Change as Social Choice: The Motivating Analogy 161
8.5 Finding Intuitive Conditions on Plausibility Update 162
8.6 Characterizing Priority Update 164
8.7 Weaker Conditions: Additional Update Rules 165
8.8 Further Questions, and Conclusion 166
References 167
9 Revision with Conditional Probability Functions: Two Impossibility Results 169
François Lepage and Charles Morgan 169
9.1 Context and Background 169
9.1.1 Conditional Probability Functions 170
9.2 First Result 171
9.3 Second Result 173
9.4 Closing Remarks 174
References 179
10 Indeterminacy and Belief Change 181
Horacio Arló-Costa 181
10.1 Introduction 181
10.1.1 The Received View and Why It Does Not Work 182
10.2 Technical Preliminaries 184
10.3 Some Results from the Theory of Choice 185
10.3.1 Pseudo-rationality 188
10.4 Belief Revision 189
10.4.1 Postulates for Belief Revision 189
10.4.2 Selection Functions in Belief Revision 190
10.5 Rott's Correspondence Results 191
10.6 Choosing What to Believe 195
10.7 Admissibility 195
10.7.1 Admissibility by a Two-Tier Rule 196
10.8 Applications: Philosophy of Science 197
10.8.1 An Interesting Challenge: Theories-of and Theories-for 201
References 203
11 Perspectival Act Utilitarianism 204
John F. Horty 204
11.1 Introduction 204
11.2 Background 205
11.2.1 Individual Actions 205
11.2.2 Group Actions 207
11.3 The Dominance Account 209
11.3.1 Our Question 209
11.3.2 Dominance Act Utilitarianism 211
11.4 The Orthodox Account 214
11.4.1 An Example 214
11.4.2 Orthodox Act Utilitarianism 216
11.5 The Perspectival Account 219
11.5.1 A Problem 219
11.5.2 Perspectival Act Utilitarianism 221
11.6 Conclusion 223
References 227
12 Real Change, Deontic Action 229
Krister Segerberg 229
12.1 Real Change 229
12.2 Pure Deontic Actions 230
12.3 Mixed Deontic Actions 231
References 232
13 Neither Logically Omniscient nor Completely Irrational Agents: Principles for a Fine-Grained Analysis of Propositional Attitudes and Attitude Revision 233
Daniel Vanderveken 233
13.1 Introduction 233
13.2 Compositional Analysis of Propositional Attitudes 234
13.3 Neither Logically Omniscient nor Completely Irrational Agents 236
13.4 Agency, Time and Indeterminism 237
13.5 Satisfaction as a Generalization of Truth 238
13.6 A Closer Look at the Basic Categories of Cognition and Volition 240
13.7 Attitudes Revisions 241
13.8 Conclusion 242
References 243
Index 244