Modalities for Reasoning about Knowledge and Quantities [PhD Thesis]

Cover ......Page 1
Acknowledgements ......Page 6
Table of contents ......Page 7
1 Introduction ......Page 9
2.1 Modalities ......Page 10
2.2 Knowledge ......Page 15
2.3 Quantities ......Page 18
3 Modal logic and this thesis ......Page 21
4 Organisation of the thesis ......Page 25
1 Introduction ......Page 27
2 The system KBCD as a basis for knowledge and belief ......Page 28
3 Kripke semantics for KB ......Page 34
4 Some correspondence results ......Page 41
5 Conscious beliefs and believed consciousness ......Page 45
6 Introspection and extraspection ......Page 48
7 Conclusions and problems ......Page 54
1 Introduction ......Page 55
2 Some correspondence results for intersection and union ......Page 57
3 Splitting worlds ......Page 62
4 Adding special properties ......Page 64
5 Applications to implicit knowledge ......Page 76
6 (Truncated) graded modalities ......Page 81
7 Explicit definitions for intersection ......Page 85
1 Introduction ......Page 89
2 Language and semantics ......Page 90
3 Elementary model theory: preservation ......Page 93
4 Expressive power 1: graded modal equivalence ......Page 97
5 Expressive power 2: correspondence ......Page 104
5.1 Definability of first order properties ......Page 105
5.2 First order definability of modal principles ......Page 109
6 Filtration ......Page 115
1 Introduction ......Page 121
2 The system Gr(S5) ......Page 123
3 Epistemic reading ......Page 126
4 Examples ......Page 129
5 Conclusion ......Page 131
1 Introduction ......Page 133
2.1 Basic definitions and examples ......Page 134
2.2 Normal forms ......Page 137
2.3 Connections with other formalisms ......Page 138
3.1 Prerequisites ......Page 141
3.2 Completeness of QUANTk ......Page 142
3 Complexity ......Page 145
4 Semantic constraints and inferential patterns ......Page 146
4.1 Semantic constraints ......Page 147
4.2 Inferential patterns ......Page 150
5 Beyond the first order boundary ......Page 154
5.1 Axioms and notation ......Page 155
5.2 Completeness ......Page 157
5.3 Normal forms and semantic constraints ......Page 158
5.4 Other higher order quantifiers ......Page 163
6 Further directions; concluding remarks ......Page 165
1 Introduction ......Page 167
2 The System QM ......Page 169
3 Probabilistic Kripke models ......Page 173
4 The scheme B(m) ......Page 177
5 Correspondence and expressiveness ......Page 182
6 Conclusion ......Page 189
1 Introduction ......Page 191
2 The logic PFD ......Page 195
3 A semantics for PFD and some of its properties ......Page 199
4 Conclusion and directions for further research ......Page 207
References ......Page 209
Samenvatting ......Page 217