Implementing Connection Calculi for First-order Modal Logics

Abstract

An implementation of an automated theorem prover for first-order modal logic is presented that works for the constant, cumulative and varying domains of the modal logics D, T, S4 and S5. It is based on the (classical) connection calculus and uses prefixes (or world paths) and a prefix unification algorithm to capture the restrictions given by the Kripke semantics of the standard modal logics. This permits a modular and elegant treatment of the considered modal logics and yields an efficient implementation. Details of the calculus, the implementation and performance results on the QMLTP problem library are presented.