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)
Artificial Intelligence
Modal logic
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Optimal Satisfiability for Propositional Calculi and Constraint Satisfaction Problems
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
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
Mathematical modal logic: a view of its evolution
Journal of Applied Logic
A unifying semantics for time and events
Artificial Intelligence - Special issue on logical formalizations and commonsense reasoning
Foundations of knowledge for distributed systems
TARK '86 Proceedings of the 1986 conference on Theoretical aspects of reasoning about knowledge
The logic of distributed protocols: preliminary report
TARK '86 Proceedings of the 1986 conference on Theoretical aspects of reasoning about knowledge
Knowledge updates: Semantics and complexity issues
Artificial Intelligence
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
Journal of Computer and System Sciences
The tractability of model checking for LTL: The good, the bad, and the ugly fragments
ACM Transactions on Computational Logic (TOCL)
Complexity results for modal dependence logic
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
The Complexity of Reasoning for Fragments of Autoepistemic Logic
ACM Transactions on Computational Logic (TOCL)
On the applicability of Post's lattice
Information Processing Letters
Lewis Dichotomies in Many-Valued Logics
Studia Logica
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It is well-known that modal satisfiability is PSPACE-complete [Lad77]. 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.