Optimised Modal Translation and Resolution

This thesis studies the optimised functional translation of propositional modal logics to first-order logic, and first-order resolution as a means for realising modal reasoning. The optimised functional translation maps modal logics to a lattice of clausal logics, called path logics. The general apparatus of inference for path logics is theory resolution. We show that satisfiability in basic path logic and certain extensions can be decided by resolution and condensing without requiring additional refinement strategies. We propose an improved theory unification algorithm for \textit{S4}, and we present a calculus of ordered $E$-resolution with normalisation. We show also that some essentially second-order modal logics convert to path logics, which can be exploited for accomodating inference for modal logics with numerical quantifiers in a calculus of resolution and simple arithmetic