Labelled Model Modal Logic

1 Introduction There is no agreement among researchers in the area of automated deduction about which features (besides computational efficiency) a suitable theorem proving system for non-classical (in particular modal) logics should have. In our opinion, such a system should (A) avoid ad hoc manipulation of the modal formulas; (B) provide a simple and uniform treatment of a wide variety of modal (and other non-classical) logics; (C) form an adequate basis for developing efficient proof search methods; (D) yield proofs according to familiar, natural inference patterns; (E) provide an explicit model construction. In this paper we describe a modal theorem proving system, that we call KEM , which appears to satisfy all this requirements: it treats the full modal language; it works for a wide class of normal modal logics (and it can be extended to other non-classical logics, e.g. temporal or conditional logics); and it forms a basis for combining both efficiency and naturalness. Moreover it automatically generates models using a label formalism to bookkeep " world " paths. KEM results from the combination of two kinds of rules: rules for processing the propositional part (which are the same for all modal logics), and rules for manipulating labels according to the accessibility relations for the given logics. The key features of KEM are outlined as follows.