Quantitative relativizations of complexity classes
SIAM Journal on Computing
Decision procedures and expressiveness in the temporal logic of branching time
Journal of Computer and System Sciences
Theory of linear and integer programming
Theory of linear and integer programming
Modal resolution in clausal form
Theoretical Computer Science
On the complexity of epistemic reasoning
Proceedings of the Fourth Annual Symposium on Logic in computer science
Bisimulation through probabilistic testing
Information and Computation
A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
Terminal coalgebras in well-founded set theory
Theoretical Computer Science
Reasoning about knowledge and probability
Journal of the ACM (JACM)
Basic proof theory
Modal logics, description logics and arithmetic reasoning
Artificial Intelligence
Journal of the ACM (JACM)
Specifying coalgebras with modal logic
Theoretical Computer Science
Modal logic
Graded Modalities in Epistemic Logic
TVER '92 Proceedings of the Second International Symposium on Logical Foundations of Computer Science
Towards a Mathematical Operational Semantics
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Coalgebraic modal logic: soundness, completeness and decidability of local consequence
Theoretical Computer Science
Mathematical Structures in Computer Science
A hierarchy of probabilistic system types
Theoretical Computer Science - Selected papers of CMCS'03
Automata and fixed point logic: a coalgebraic perspective
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
PSPACE Bounds for Rank-1 Modal Logics
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Modular construction of complete coalgebraic logics
Theoretical Computer Science
Expressivity of coalgebraic modal logic: The limits and beyond
Theoretical 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
A Coalgebraic Perspective on Monotone Modal Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Presburger modal logic is PSPACE-Complete
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Ultrafilter extensions for coalgebras
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Modular algorithms for heterogeneous modal logics
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Generic Modal Cut Elimination Applied to Conditional Logics
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Optimizing Conditional Logic Reasoning within CoLoSS
Electronic Notes in Theoretical Computer Science (ENTCS)
EXPTIME tableaux for the coalgebraic µ-calculus
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Logic of infons: The propositional case
ACM Transactions on Computational Logic (TOCL)
Cut elimination in coalgebraic logics
Information and Computation
Automata for coalgebras: an approach using predicate liftings
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Flat coalgebraic fixed point logics
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
Modular algorithms for heterogeneous modal logics via multi-sorted coalgebra
Mathematical Structures in Computer Science
Cut elimination for shallow modal logics
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Optimal tableau algorithms for coalgebraic logics
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Global caching for coalgebraic description logics
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Solving graded/probabilistic modal logic via linear inequalities (system description)
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Narcissists are easy, stepmothers are hard
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
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For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal logics. Our main result is that all rank-1 logics enjoy a shallow model property and thus are, under mild assumptions on the format of their axiomatisation, in PSPACE. This leads to a unified derivation of tight PSPACE-bounds for a number of logics, including K, KD, coalition logic, graded modal logic, majority logic, and probabilistic modal logic. Our generic algorithm moreover finds tableau proofs that witness pleasant proof-theoretic properties including a weak subformula property. This generality is made possible by a coalgebraic semantics, which conveniently abstracts from the details of a given model class and thus allows covering a broad range of logics in a uniform way.