 
Summary: Unication Modulo Presburger Arithmetic and
Other Decidable Theories
Mauricio AyalaRincon ? and Ivan E. Tavares Araujo ??
Departamento de Matematica, Universidade de Braslia, 70910900 Brasil
ayala@mat.unb.br, ivan@mat.unb.br,ivan.araujo@psy.ox.ac.uk
Abstract. We present a general unication algorithm modulo Pres
burger Arithmetic for a restricted class of modularly specied theo
ries where function symbols of the target theory have non arithmetic
codomain sorts. Additionally, we comment on conditions guaranteeing
decidability of matching and unication problems modulo more general
theories than the arithmetic ones, which appear when automated deduc
tion is implemented by combining conditional rewriting techniques and
decision algorithms for builtin predicates.
Keywords: Equational unication, automated reasoning, algebraic spec
ication, conditional rewriting systems
1 Introduction
Unication modulo general theories is very important in the context of auto
mated reasoning and algebraic specication. In particular, unication modulo
arithmetic theories, such as Presburger Arithmetic (PA) [Pre29], is relevant
since many deductive systems are specied so as to contain an arithmetic theory
