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A Fixpoint Semantics and an SLD-Resolution Calculus for Modal Logic Programs

Nguyen L.A.

Fundamenta Informaticae

2003

Vol. 55, nr 1

63-100

We propose a modal logic programming language called MProlog, which is as expressive as the general modal Horn fragment. We give a fixpoint semantics and an SLD-resolution calculus for MProlog in all of the basic serial modal logics KD, T, KDB, B, KD4, S4, KD5, KD45, and S5. For an MProlog program P and for L being one of the mentioned logics, we define an operator T_L,P, which has the least fixpoint I_L,P. This fixpoint is a set of formulae, which may contain labeled forms of the modal operator , and is called the leasta-model generator of P. The standard model of I_L,P is shown to be a least L-model of P. The SLD-resolution calculus for MProlog is designed with a similar style as for classical logic programming. It is sound and complete. We also extend the calculus for MProlog in the almost serial modal logics KB, K5, K45, and KB5.