If a rewrite-based inference system is guaranteed to terminate on the axioms of a theory T and any set of ground literals, then any theorem-proving strategy based on that inference system is a rewrite-based decision procedure for T-satisfiability. In this paper, we consider the class of theories defining recursive data structures, that might appear out of reach for this approach, because they are defined by an infinite set of axioms. We overcome this obstacle by designing a problem reduction that allows us to prove a general termination result for all these theories. We also show that the theorem-proving strategy decides satisfiability problems in any combination of these theories with other theories decided by the rewrite-based approach.

Rewrite-based satisfiability procedures for recursive data structures

BONACINA, Maria Paola;ECHENIM, Bertrand Mnacho
2007

Abstract

If a rewrite-based inference system is guaranteed to terminate on the axioms of a theory T and any set of ground literals, then any theorem-proving strategy based on that inference system is a rewrite-based decision procedure for T-satisfiability. In this paper, we consider the class of theories defining recursive data structures, that might appear out of reach for this approach, because they are defined by an infinite set of axioms. We overcome this obstacle by designing a problem reduction that allows us to prove a general termination result for all these theories. We also show that the theorem-proving strategy decides satisfiability problems in any combination of these theories with other theories decided by the rewrite-based approach.
Satisfiability modulo theories; rewrite-based theorem proving; superposition
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/30956
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