
Many-Dimensional Modal Logics: Theory and Applications
Description
Readership
Table of Contents
- I Introduction
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.
Product details
- No. of pages: 766
- Language: English
- Copyright: © North Holland 2003
- Published: October 21, 2003
- Imprint: North Holland
- eBook ISBN: 9780080535784
About the Authors
A. Kurucz
Affiliations and Expertise
F. Wolter
Affiliations and Expertise
M. Zakharyaschev
Affiliations and Expertise
Dov M. Gabbay
Affiliations and Expertise
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