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Modal logic for belief and preference change [PhD Thesis]

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Author(s): Patrick Girard
Series: ILLC Dissertation Series DS-2008-04
Publisher: University of Amsterdam
Year: 2008

Language: English
Pages: 173
City: Amsterdam

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 Wright’s preference logic: Historical considerations . . . . . . . . 57
4.2 Binary preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3 The ∀∀ 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