A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
Reasoning about knowledge and probability
Journal of the ACM (JACM)
On the complexity of integer programming
Journal of the ACM (JACM)
Coalgebraic modal logic: soundness, completeness and decidability of local consequence
Theoretical Computer Science
PSPACE Bounds for Rank-1 Modal Logics
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
A sequent calculus and a theorem prover for standard conditional logics
ACM Transactions on Computational Logic (TOCL)
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Presburger modal logic is PSPACE-Complete
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Ability in a multi-agent context: a model in the situation calculus
CLIMA'05 Proceedings of the 6th international conference on Computational Logic in Multi-Agent Systems
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
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)
Modular algorithms for heterogeneous modal logics via multi-sorted coalgebra
Mathematical Structures in Computer Science
VoCS'08 Proceedings of the 2008 international conference on Visions of Computer Science: BCS International Academic Conference
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Modal logics see a wide variety of applications in artificial intelligence, e.g. in reasoning about knowledge, belief, uncertainty, agency, defaults, and relevance. From the perspective of applications, the attractivity of modal logics stems from a combination of expressive power and comparatively low computational complexity. Compared to the classical treatment of modal logics with relational semantics, the use of modal logics in AI has two characteristic traits: Firstly, a large and growing variety of logics is used, adapted to the concrete situation at hand, and secondly, these logics are often non-normal. Here, we present a shallow model construction that witnesses PSPACE bounds for a broad class of mostly non-normal modal logics. Our approach is uniform and generic: we present general criteria that uniformly apply to and are easily checked in large numbers of examples. Thus, we not only re-prove known complexity bounds for a wide variety of structurally different logics and obtain previously unknown PSPACE-bounds, e.g. for Elgesem's logic of agency, but also lay the foundations upon which the complexity of newly emerging logics can be determined.