Implementing Connection Calculi for First-order Modal Logics

This paper presents an implementation of an automated theorem prover for first-order modal logic that works for the constant, cumulative, and varying domain of the modal logics D, T, S4, and S5. It is based on the connection calculus for classical logic and uses prefixes representing 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.

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