TY - GEN
T1 - Optimal tableau algorithms for coalgebraic logics
AU - Goré, Rajeev
AU - Kupke, Clemens
AU - Pattinson, Dirk
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77951617983&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-12002-2_9
DO - 10.1007/978-3-642-12002-2_9
M3 - Conference contribution
SN - 3642120016
SN - 9783642120015
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 114
EP - 128
BT - Tools and Algorithms for the Construction and Analysis of Systems - 16th Int. Conf., TACAS 2010, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2010, Proc.
T2 - 16th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2010, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2010
Y2 - 20 March 2010 through 28 March 2010
ER -