Many-Dimensional Modal Logics: Theory and Applications

1 Modal logic basics 1.1 Modal axiomatic systems 1.2 Possible world semantics 1.3 Classical first-order logic and the standard translation 1.4 Multimodal logics 1.5 Algebraic semantics 1.6 Decision, complexity and axiomatizability problems

2 Applied modal logic 2.1 Temporal logic 2.2 Interval temporal logic 2.3 Epistemic logic 2.4 Dynamic logic 2.5 Description logic 2.6 Spatial logic 2.7 Intuitionistic logic 2.8 'Model level' reductions between logics

3 Many-dimensional modal logics 3.1 Fusions 3.2 Spatio-temporal logics 3.3 Products 3.4 Temporal epistemic logics 3.5 Classical first-order logic as a propositional multimodal logic 3.6 First-order modal logics 3.7 First-order temporal logics 3.8 Description logics with modal operators 3.9 HS as a two-dimensional logic 3.10 Modal transition logics 3.11 Intuitionistic modal logics

II Fusions and products

4 Fusions of modal logics 4.1 Preserving Kripke completeness and the finite model property 4.2 Algebraic preliminaries 4.3 Preserving decidability of global consequence 4.4 Preserving decidability 4.5 Preserving interpolation 4.6 On the computational complexity of fusions

5 Products of modal logics: introduction 5.1 Axiomatizing products 5.2 Proving decidability with quasimodels 5.3 The finite model property 5.4 Proving undecidability 5.5 Proving complexity with tilings

6 Decidable products 6.1 Warming up: Kn x Km 6.2 CPDL x K_m 6.3 Products of epistemic logics with Km 6.4 Products of temporal logics with Km 6.5 Products with S5 6.6 Products with multimodal S5

7 Undecidable products 7.1 Products of linear orders with infinite ascending chains 7.2 Products of linear orders with infinite descending chains 7.3 Products of Dedekind complete linear orders 7.4 Products of finite linear orders 7.5 More undecidable products

8 Higher-dimensional products 8.1 S5 x S5 x ... x S5 8.2 Products between K4 x K4 x ... x K4 and S5 x S5 x ... x S5 8.3 Products with the fmp 8.4 Between K x K x ... x K and S5 x S5 x ... x S5 8.5 Finitely axiomatizable and decidable products

9 Variations on products 9.1 Relativized products 9.2 Valuation restrictions

10 Intuitionistic modal logics 10.1 Intuitionistic modal logics with Box 10.2 Intuitionistic modal logics with Box and Diamond 10.3 The finite model property

III First-order modal logics

11 Fragments of first-order temporal logics 11.1 Undecidable fragments 11.2 Monodic formulas, decidable fragments 11.3 Embedding into monadic second-order theories 11.4 Complexity of decidable fragments of QLogSU(N) 11.5 Satisfiability in models over (N,<) with finite domains 11.6 Satisfiability in models over (R,<) with finite domains 11.7 Axiomatizing monodic fragments 11.8 Monodicity and equality

12 Fragments of first-order dynamic and epistemic logics 12.1 Decision problems 12.2 Axiomatizing monodic fragments

IV Applications to knowledge representation

13 Temporal epistemic logics 13.1 Synchronous systems 13.2 Agents who know the time and neither forget nor learn

14 Modal description logics 14.1 Concept satisfiability 14.2 General formula satisfiability 14.3 Restricted formula satisfiability 14.4 Satisfiability in models with finite domains

15 Tableaux for modal description logics 15.1 Tableaux for ALC 15.2 Tableaux for K(ALC) with constant domains 15.3 Adding expressive power to K(ALC)

16 Spatio-temporal logics 16.1 Modal formalisms for spatio-temporal reasoning 16.2 Embedding spatio-temporal logics in first-order temporal logic 16.3 Complexity of spatio-temporal logics 16.4 Models based on Euclidean spaces

Epilogue. Bibliography. List of tables. List of languages and logics. Symbol index. Subject index.