The Modal Logic Programming System MProlog: Theory, Design, and Implementation

We present a general framework for developing fixpoint semantics, the least model semantics, and SLD-resolution calculi for logic programs in normal multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. ∀x ∃y Ri(x, y)) and some classical firstorder Horn formulas. Our approach is direct and no special restriction on occurrences of 2i and 3i is assumed. We prove that under certain expected properties of a concrete instantiation of the framework for a specific multimodal logic, the SLD-resolution calculus is sound and com-