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Uni cation Modulo Presburger Arithmetic and Other Decidable Theories

Summary: Uni cation Modulo Presburger Arithmetic and
Other Decidable Theories
Mauricio Ayala-Rincon ? and Ivan E. Tavares Araujo ??
Departamento de Matematica, Universidade de Braslia, 70910-900 Brasil
ayala@mat.unb.br, ivan@mat.unb.br,ivan.araujo@psy.ox.ac.uk
Abstract. We present a general uni cation algorithm modulo Pres-
burger Arithmetic for a restricted class of modularly speci ed theo-
ries where function symbols of the target theory have non arithmetic
codomain sorts. Additionally, we comment on conditions guaranteeing
decidability of matching and uni cation 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 built-in predicates.
Keywords: Equational uni cation, automated reasoning, algebraic spec-
i cation, conditional rewriting systems
1 Introduction
Uni cation modulo general theories is very important in the context of auto-
mated reasoning and algebraic speci cation. In particular, uni cation modulo
arithmetic theories, such as Presburger Arithmetic (PA) [Pre29], is relevant
since many deductive systems are speci ed so as to contain an arithmetic theory


Source: Ayala-Rincón, Mauricio - Departamento de Matemática, Universidade de Brasília


Collections: Mathematics