Advanced Modal Logic [pp. 83-266]

✍ Scribed by Michael Zakharyaschev, Frank Wolter, Alexander Chagrov

• Publisher: Kluwer
• Year: 2001
• Tongue: English
• Leaves: 184
• Series: Handbook of Philosophical Logic, 2nd Edition, Volume 3
• Category: Library

✦ Table of Contents

Advanced Modal Logic ......Page 1
1.1 The lattice NExtK ......Page 4
1.2 Semantics ......Page 8
Table 1. List of standard normal modal logics ......Page 9
1.3 Persistence ......Page 18
1.4 The degree of Kripke incompleteness ......Page 26
1.5 Stronger forms of Kripke completeness ......Page 30
1.6 Canonical formulas ......Page 33
1.7 Decidability via the finite model property ......Page 38
Table 2. Canonical axioms of standard modal logics ......Page 39
1.8 Subframe and cofinal subframe logics ......Page 43
1.9 More sufficient conditions of FMP ......Page 47
1.10 The reduction method ......Page 52
1.11 Logics containing K4.3 ......Page 54
1.12 Quasi-normal modal logics ......Page 56
1.13 Tabular logics ......Page 63
1.14 Interpolation ......Page 66
2 Polymodal logics ......Page 75
2.1 From unimodal to polymodal ......Page 77
Splittings and the degree of Kripke incompleteness ......Page 78
Some FMP results ......Page 79
2.2 Fusions ......Page 80
2.3 Simulation ......Page 86
2.4 Minimal tense extensions ......Page 89
2.5 Tense logics of linear frames ......Page 94
Table 3. Axiomatizations of standard tense logics ......Page 97
2.6 Bimodal provability logics ......Page 101
Table 4. Axiomatizations of provability logics ......Page 104
2.7 Cartesian products of modal logics ......Page 107
3 Superintuitionistic logics ......Page 110
3.1 Intuitionistic frames ......Page 111
Table 5. List of standard superintuitionistic logics ......Page 112
3.2 Canonical formulas ......Page 115
3.3 Modal companions and preservation theorems ......Page 118
Table 6. Canonical axioms of standard superintuitionistic logics ......Page 119
Kripke completeness ......Page 124
The finite model property ......Page 126
3.5 Disjunction property ......Page 129
3.6 Intuitionistic modal logics ......Page 135
4.1 Undecidable calculi ......Page 144
4.2 Admissibility and derivability of inference rules ......Page 149
4.3 Properties of recursively axiomatizable logics ......Page 155
4.4 Undecidable properties of calculi ......Page 156
4.5 Semantical consequence ......Page 160
Complexity function ......Page 161
Relation to complexity classes ......Page 164
Bisimulations ......Page 167
Acknowledgements ......Page 168
Bibliography ......Page 169