A note on the complexity of the satisfiability of modal Horn clauses
Journal of Logic Programming
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Theoretical Computer Science
Constructing the least models for positive modal logic programs
Fundamenta Informaticae
Foundations of Databases: The Logical Level
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LID '96 Proceedings of the International Workshop on Logic in Databases
On temporal logic versus datalog
Theoretical Computer Science - Logic and complexity in computer science
Foundations of Modal Deductive Databases
Fundamenta Informaticae
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The data complexity of MDatalog in basic modal logics
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
ADBIS'05 Proceedings of the 9th East European conference on Advances in Databases and Information Systems
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We propose a modal query language called MDatalog. A rule of an MDatalog program is a universally quantified modal Horn clause. This language is interpreted in fixed-domain first-order modal logics over signatures without functions. We give algorithms to construct the least models for MDatalog programs. We show PTIME complexity of computing queries for a given MDatalog program in the logics KD, T, KB, KDB, B, K5, KD5, K45, KD45, KB5, and S5, provided that the quantifier depths of queries and the program are finitely bounded, and that the modal depth of the program is finitely bounded in the case when the considered logic is not an extension of K5. Some examples are given to illustrate application of the techniques to reason about belief and knowledge.