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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.
Table of contents ......Page 6
Acknowledgments ......Page 8
Part I. Introduction ......Page 10
1.2 Extending modal logic ......Page 12
1.3 A look ahead ......Page 13
2.1 Introduction ......Page 15
2.2 A framework for modal logic ......Page 16
2.3 Examples ......Page 19
2.4 Questions and comments ......Page 21
2.5 Concluding remarks ......Page 24
Part II. Three Case Studies ......Page 26
3.1 Introduction ......Page 28
3.2 Some comparisons ......Page 32
3.3 Axiomatics ......Page 38
3.4 Definability ......Page 51
3.5 Concluding remarks ......Page 55
4.1 Introduction ......Page 57
4.2 Preliminaries ......Page 59
4.3 Using DML ......Page 61
4.4 The expressive power of DML ......Page 63
4.5 Decidability ......Page 69
4.6 Completeness ......Page 73
4.7 Concluding remarks ......Page 77
5.2 Preliminaries ......Page 80
5.3 Modal preliminaries ......Page 85
5.5 Set equations and relation equations ......Page 91
5.6 Expressive power ......Page 110
5.7 Concluding remarks ......Page 113
Part III. Two General Themes ......Page 114
6.1 Introduction ......Page 116
6.2 Preliminaries ......Page 117
6.3 Basic bisimulations ......Page 118
6.4 Modal equivalence and bisimulations ......Page 122
6.5 Definability and characterization ......Page 127
6.6 Preservation ......Page 135
6.7 Beyond the basic pattern ......Page 141
6.8 Concluding remarks ......Page 144
7.1 Introduction ......Page 146
7.2 Preliminaries ......Page 147
7.3 Reducibility ......Page 148
7.4 Finding the right instances ......Page 150
7.5 Reduction algorithms ......Page 161
7.6 Applying the algorithms ......Page 168
7.7 Another perspective: global restrictions ......Page 174
7.8 Concluding remarks ......Page 176
Appendix: Background material ......Page 178
Bibliography ......Page 180
Index ......Page 185
List of symbols ......Page 188
Samenvatting ......Page 190
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 is a PhD Thesis written under supervision of Prof.dr. J.A.G. Groenendijk and Prof.dr. J.F.A.K. van Benthem at the Institute for Logic, Language and Computation.
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.
In this thesis we investigate modal logics from a lattice theoretic point of view. There are essentially two well-known methods of research on lattices of modal logics. The investigation of the lattice of modal logics as a whole, and the local investigation of the lattice of extensions of some stron