โ Scribed by Olivier Roy
No coin nor oath required. For personal study only.
1 Introduction 1
1.1 Instrumental rationality, decision and game theory . . . . . . . . . 3
1.1.1 Decision theory: rational decision making under uncertainty 3
1.1.2 Game theory: reasoning with mutual expectations . . . . . 5
1.2 Intentions and planning agency . . . . . . . . . . . . . . . . . . . 7
1.3 Dynamic epistemic logic . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Intentions and individual decision making 17
2.1 Extensive decision problems . . . . . . . . . . . . . . . . . . . . . 18
2.2 Actions- and outcomes-intentions in extensive decision problems . 21
2.3 Intentions with counterfactual consequences . . . . . . . . . . . . 26
2.4 Ideal and resources-bounded agents . . . . . . . . . . . . . . . . . 29
2.5 From extensive to strategic representations . . . . . . . . . . . . . 31
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 Intentions and coordination in strategic games 35
3.1 Intentions in strategic interactions . . . . . . . . . . . . . . . . . . 36
3.2 Coordination in Hi-Lo games . . . . . . . . . . . . . . . . . . . . . 39
3.3 Intentions and rational expectations . . . . . . . . . . . . . . . . . 42
3.4 Epistemic models for games with intentions . . . . . . . . . . . . 45
3.5 Coordination with payoff-compatible intentions . . . . . . . . . . 48
3.6 Stackelberg heuristic and intention-based coordination . . . . . . 54
3.7 Limits of payoff-compatibility of intentions . . . . . . . . . . . . . 56
3.8 A general account of intention-based coordination . . . . . . . . . 57
3.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.10 Appendix - Solution concepts . . . . . . . . . . . . . . . . . . . . 62
4 Intentions and transformations of strategic games 63
4.1 Ruling out options . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2 Grouping redundant options . . . . . . . . . . . . . . . . . . . . . 71
4.3 Grouping and ruling out options . . . . . . . . . . . . . . . . . . . 76
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5 Logics for practical reasoning with intentions 83
5.1 Preliminaries: modal logic for preferences . . . . . . . . . . . . . . 83
5.1.1 Preference models and language . . . . . . . . . . . . . . . 84
5.1.2 Expressive power . . . . . . . . . . . . . . . . . . . . . . . 86
5.1.3 Axiomatization . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2 Logic for games with intentions . . . . . . . . . . . . . . . . . . . 89
5.2.1 Language for epistemic game models with intentions . . . 89
5.2.2 Expressive power . . . . . . . . . . . . . . . . . . . . . . . 93
5.2.3 Axiomatization . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3 Transformations of games with intentions . . . . . . . . . . . . . . 102
5.3.1 Dynamic language . . . . . . . . . . . . . . . . . . . . . . 104
5.3.2 Axiomatization . . . . . . . . . . . . . . . . . . . . . . . . 106
5.3.3 Expressive power . . . . . . . . . . . . . . . . . . . . . . . 108
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.5.1 Bisimulation and modal equivalence for LP . . . . . . . . . 125
5.5.2 More on lifted relations in LP . . . . . . . . . . . . . . . . 126
5.5.3 More on the expressive power of LGF . . . . . . . . . . . . 127
5.5.4 Proof of Theorem 5.2.13 . . . . . . . . . . . . . . . . . . . 128
5.5.5 Complete axiom system for DLGF . . . . . . . . . . . . . . 133
5.5.6 Dynamic characterization of Nash equilibrium. . . . . . . . 134
6 Hybrid pragmatism, acceptances and norms on intentions 137
6.1 Constraints on rational intentions . . . . . . . . . . . . . . . . . . 138
6.2 Cognitivism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.2.1 The functionalist view on beliefs . . . . . . . . . . . . . . . 142
6.2.2 Constraints on rational beliefs . . . . . . . . . . . . . . . . 143
6.2.3 Weak, intermediate and strong cognitivism . . . . . . . . . 145
6.2.4 Rational intentions from rational beliefs . . . . . . . . . . 146
6.2.5 A general concern against cognitivism . . . . . . . . . . . . 150
6.3 Acceptances in deliberation . . . . . . . . . . . . . . . . . . . . . 152
6.3.1 Accepting or taking for granted in deliberation . . . . . . . 152
6.3.2 The adjusted background of deliberation . . . . . . . . . . 155
6.3.3 Requirements on the background of deliberation . . . . . . 155
6.4 Hybrid Pragmatism . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.4.1 Intentions and acceptances . . . . . . . . . . . . . . . . . . 158
6.4.2 The absent-minded cyclist revisited . . . . . . . . . . . . . 159
6.4.3 Relevance for a deliberation . . . . . . . . . . . . . . . . . 159
6.4.4 Rational intentions from rational acceptances . . . . . . . 160
6.4.5 Acceptances and intentions in deliberation . . . . . . . . . 165
6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
7 Conclusion 171
7.1 Review of the chapters . . . . . . . . . . . . . . . . . . . . . . . . 171
7.2 Open questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Index 185
Samenvatting 191
Resume 193
Abstract 195
๐ SIMILAR VOLUMES
This is a PhD Thesis written under supervision of Dr. Peter van Emde Boas.
To those who believe that there is such a thing as the logic of conditionals this dissertation may appear to be yet another attempt to unravel its secrets - which it is not. As a logician, you can do no more than devise a logic for conditionals and try to persuade your readers to adopt it. You may s
To those who believe that there is such a thing as the logic of conditionals this dissertation may appear to be yet another attempt to unravel its secrets - which it is not. As a logician, you can do no more than devise a logic for conditionals and try to persuade your readers to adopt it. You may s
This dissertation is about extending modal logic. It tells you what a system of extended modal logic is, it gives you three case studies of systems of modal logic, and it gives you very general approaches to two important themes in modal logic.
This dissertation is about extending modal logic. It tells you what a system of extended modal logic is, it gives you three case studies of systems of modal logic, and it gives you very general approaches to two important themes in modal logic.