Proximity-Based Unification and Matching for Fully Fuzzy Signatures

Abstract

We consider the problem of solving approximate equations between logic terms. The approximation is expressed by proximity relations. They are reflexive and symmetric (but not necessarily transitive) fuzzy binary relations. The equations are solved by variable substitutions that bring the sides of equations “close” to each other with respect to a predefined degree. We consider unification and matching equations in which mismatches in function symbol names, arity, and in the argument order are tolerated (i.e., the approximate equations are formulated over so called fully fuzzy signatures). This work generalizes on the one hand, class-based proximity unification to fully fuzzy signatures, and on the other hand, unification with similarity relations over a fully fuzzy signature by extending similarity to proximity.