Modal resolution in clausal form
Theoretical Computer Science
A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
Reasoning about knowledge
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
Why are modal logics so robustly decidable?
Current trends in theoretical computer science
Modal logic
A Multiprocess Network Logic with Temporal and Spatial Modalities
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Fixed-Parameter Hierarchies inside PSPACE
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Counting truth assignments of formulas of bounded tree-width or clique-width
Discrete Applied Mathematics
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Uniform Interpolation by Resolution in Modal Logic
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
A note on the expressibility problem for modal logics and star-free regular expressions
Information Processing Letters
A Note on the Complexity of the Satisfiability Problem for Graded Modal Logics
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Characterizing the NP-PSPACE gap in the satisfiability problem for modal logic
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
On problems without polynomial kernels
Journal of Computer and System Sciences
Constraint satisfaction with bounded treewidth revisited
Journal of Computer and System Sciences
On the complexity of some colorful problems parameterized by treewidth
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Tree-width for first order formulae
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Parameterized modal satisfiability
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
The structure of tractable constraint satisfaction problems
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Parameterized complexity results for 1-safe Petri nets
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
Does Treewidth Help in Modal Satisfiability?
ACM Transactions on Computational Logic (TOCL)
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Many tractable algorithms for solving the Constraint Satisfaction Problem (Csp) have been developed using the notion of the treewidth of some graph derived from the input CSP instance. In particular, the incidence graph of the CSP instance is one such graph. We introduce the notion of an incidence graph for modal logic formulae in a certain normal form. We investigate the parameterized complexity of modal satisfiability with the modal depth of the formula and the treewidth of the incidence graph as parameters. For various combinations of Euclidean, reflexive, symmetric and transitive models, we show either that modal satisfiability is FPT, or that it is W[1]-hard. In particular, modal satisfiability in general models is FPT, while it is W[1]-hard in transitive models. As might be expected, modal satisfiability in transitive and Euclidean models is FPT.