The Modal Query Language MDatalog

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.