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.