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Tables of Contents for Modal Logic
Chapter/Section Title
Page #
Page Count
Preface
xi
Basic Concepts
1
49
Relational Structures
2
7
Modal Languages
9
7
Models and Frames
16
12
General Frames
28
3
Modal Consequence Relations
31
2
Normal Modal Logics
33
4
Historical Overview
37
11
Summary of Chapter 1
48
2
Models
50
73
Invariance Results
51
13
Bisimulations
64
9
Finite Models
73
10
The Standard Translation
83
8
Modal Saturation via Ultrafilter Extensions
91
9
Characterization and Definability
100
10
Simulation and Safety
110
7
Summary of Chapter 2
117
6
Notes
118
5
Frames
123
65
Frame Definability
124
6
Frame Definability and Second-Order Logic
130
8
Definable and Undefinable Properties
138
5
Finite Frames
143
5
Automatic First-Order Correspondence
148
8
Sahlqvist Formulas
156
11
More about Sahlqvist Formulas
167
11
Advanced Frame Theory
178
5
Summary of Chapter 3
183
5
Notes
185
3
Completeness
188
73
Preliminaries
189
7
Canonical Models
196
5
Applications
201
10
Limitative Results
211
6
Transforming the Canonical Model
217
6
Step by Step
223
6
Rules for the Undefinable
229
10
Finitary Methods I
239
8
Finitary Methods II
247
9
Summary of Chapter 4
256
5
Notes
258
3
Algebras and General Frames
261
71
Logic as Algebra
262
13
Algebraizing Modal Logic
275
8
The Jonsson-Tarski Theorem
283
11
Duality Theory
294
9
General Frames
303
15
Persistence
318
8
Summary of Chapter 5
326
6
Notes
327
5
Computability and Complexity
332
81
Computing Satisfiability
333
5
Decidability via Finite Models
338
9
Decidability via Interpretations
347
9
Decidability via Quasi-models and Mosaics
356
8
Undecidability via Tiling
364
9
NP
373
8
PSPACE
381
12
EXPTIME
393
13
Summary of Chapter 6
406
7
Notes
407
6
Extended Modal Logic
413
72
Logical Modalities
414
12
Since and Until
426
8
Hybrid Logic
434
12
The Guarded Fragment
446
12
Multi-Dimensional Modal Logic
458
12
A Lindstrom Theorem for Modal Logic
470
6
Summary of Chapter 7
476
9
Notes
477
8
Appendix A A Logical Toolkit
485
12
Appendix B An Algebraic Toolkit
497
7
Appendix C A Computational Toolkit
504
12
Appendix D A Guide to the Literature
516
8
Bibliography
524
20
List of Notation
544
3
Index
547