Unification modulo Presburger Arithmetic and other decidable theories

Abstract

We present a general unification algorithm modulo Presburger Arithmetic for a restricted class of modularly specified theories where function symbols of the target theory have non arithmetic codomain sorts. Additionally, we comment on conditions guaranteeing decidability of matching and unification problems modulo more general theories than the arithmetic ones, which appear when automated deduction is implemented by combining conditional rewriting techniques and decision algorithms for built-in predicates.