Handbook of logic in computer science (vol. 2)
Reasoning about knowledge
Artificial Intelligence
Dynamic Logic
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Automata logics, and infinite games
Coalgebraic modal logic: soundness, completeness and decidability of local consequence
Theoretical Computer Science
A compositional approach to defining logics for coalgebras
Theoretical Computer Science - Selected papers of CMCS'03
Modular construction of complete coalgebraic logics
Theoretical Computer Science
Admissibility of Cut in Coalgebraic Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
TABLEAUX '07 Proceedings of the 16th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
An Experimental Evaluation of Global Caching for $\mathcal {ALC}$ (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
PSPACE bounds for rank-1 modal logics
ACM Transactions on Computational Logic (TOCL)
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Sound Global State Caching for ALC with Inverse Roles
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
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
FaCT++ description logic reasoner: system description
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Modular algorithms for heterogeneous modal logics
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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
Global caching for coalgebraic description logics
IJCAR'10 Proceedings of the 5th international conference on Automated 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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Deciding whether a modal formula is satisfiable with respect to a given set of (global) assumptions is a question of fundamental importance in applications of logic in computer science. Tableau methods have proved extremely versatile for solving this problem for many different individual logics but they typically do not meet the known complexity bounds for the logics in question. Recently, it has been shown that optimality can be obtained for some logics while retaining practicality by using a technique called “global caching”. Here, we show that global caching is applicable to all logics that can be equipped with coalgebraic semantics, for example, classical modal logic, graded modal logic, probabilistic modal logic and coalition logic. In particular, the coalgebraic approach also covers logics that combine these various features. We thus show that global caching is a widely applicable technique and also provide foundations for optimal tableau algorithms that uniformly apply to a large class of modal logics.