The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
A knowledge-based analysis of zero knowledge
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Attributive concept descriptions with complements
Artificial Intelligence
The complexity of existential quantification in concept languages
Artificial Intelligence
A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
The complexity of concept languages
Information and Computation
Closure properties of constraints
Journal of the ACM (JACM)
Theories of computability
Modal logic
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
On the model theory of knowledge
On the model theory of knowledge
Belief, information acquisition, and trust in multi-agent systems: a modal logic formulation
Artificial Intelligence
Optimal satisfiability for propositional calculi and constraint satisfaction problems
Information and Computation
On the automated implementation of modal logics used to verify security protocols
ISICT '03 Proceedings of the 1st international symposium on Information and communication technologies
A unifying semantics for time and events
Artificial Intelligence - Special issue on logical formalizations and commonsense reasoning
The logic of distributed protocols: preliminary report
TARK '86 Proceedings of the 1986 conference on Theoretical aspects of reasoning about knowledge
PSPACE Bounds for Rank-1 Modal Logics
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Function Algebras on Finite Sets: Basic Course on Many-Valued Logic and Clone Theory (Springer Monographs in Mathematics)
The Tractability of Model-checking for LTL: The Good, the Bad, and the Ugly Fragments
Electronic Notes in Theoretical Computer Science (ENTCS)
The complexity of generalized satisfiability for linear temporal logic
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Generalized modal satisfiability
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
A universally defined undecidable unimodal logic
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Complexity of model checking for modal dependence logic
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Minimization for generalized Boolean formulas
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Model checking for modal intuitionistic dependence logic
TbiLLC'11 Proceedings of the 9th international conference on Logic, Language, and Computation
Complexity Results for Modal Dependence Logic
Studia Logica
Does Treewidth Help in Modal Satisfiability?
ACM Transactions on Computational Logic (TOCL)
Generalized satisfiability for the description logic ALC
Theoretical Computer Science
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It is well known that modal satisfiability is PSPACE-complete (Ladner (1977) [21]). However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators, since a propositional operator is simply a Boolean function. We completely classify the complexity of modal satisfiability for every finite set of propositional operators, i.e., in contrast to previous work, we classify an infinite number of problems. We show that, depending on the set of propositional operators, modal satisfiability is PSPACE-complete, coNP-complete, or in P. We obtain this trichotomy not only for modal formulas, but also for their more succinct representation using modal circuits. We consider both the uni-modal and the multi-modal cases, and study the dual problem of validity as well.