Minimal and Complete Prefix Unification for Non-Classical Theorem Proving

For theorem proving in non-classical logics two similar approaches have been established: a matrix characterization of Wallen and Ohlbach’s resolution calculus. In both cases the essential extension of the classical calculi is a need for unifying the so-called prefixes of atomic formulae or so-called world-paths respectively. We present a specialized string-unification algorithm which computes a minimal set of most general unifiers. By transforming systems of equations we obtain an elegant and efficient procedure which applies to intuitionistic logic and the modal logic S4. With some modifications it also applies to the modal logics D, K, D4, K4, S5, and T. We explain our method by an intuitive graphical illustration, prove termination, correctness, completeness, and minimality, and investigate its complexity.