β Scribed by Patrick Girard
No coin nor oath required. For personal study only.
1 Introduction 1
1.1 Case example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Modeling and Modal Logic . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Preorders, statics and dynamics . . . . . . . . . . . . . . . . . . . . . 8
1.4 Overview of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Setting the stage: Order Logic 15
2.1 Order Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 Relational Belief Revision 33
3.1 Doxastic Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Generalized selection functions . . . . . . . . . . . . . . . . . . . . . . 42
3.3 Broccoli logic and Order Logic . . . . . . . . . . . . . . . . . . . . . . 43
3.4 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4 Binary Preference Logic 55
4.1 Von Wrightβs preference logic: Historical considerations . . . . . . . . 57
4.2 Binary preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3 The ββ fragment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.4 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5 Ceteris Paribus Logic 71
5.1 Different senses of ceteris paribus . . . . . . . . . . . . . . . . . . . . 72
5.2 Equality-based ceteris paribus Order Logic . . . . . . . . . . . . . . . 74
5.3 Coming back to von Wright; Ceteris paribus counterparts of binary preference statements . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.4 Mathematical perspective . . . . . . . . . . . . . . . . . . . . . . . . 85
5.5 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.6 Agenda expansion: a new kind of dynamics . . . . . . . . . . . . . . . 91
5.7 A challenge: agenda contraction . . . . . . . . . . . . . . . . . . . . . 95
6 Group Order Logic 99
6.1 Lexicographic reordering . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.2 Modal logic for order aggregation . . . . . . . . . . . . . . . . . . . . 104
6.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.4 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7 Conclusion 119
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.2 Open questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
A Minimal Relational Logic 131
A.1 Minimal relational logic . . . . . . . . . . . . . . . . . . . . . . . . . 131
B CPL and Nash Equilibrium 139
C Some Algebra 143
Bibliography 149
π SIMILAR VOLUMES
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.
This is a doctoral dissertation of Edith Spaan under the supervision of prof. Johan van Benthem.
This is a doctoral dissertation of Yde Venema under the supervision of prof. Johan van Benthem.