Unions of Non-Disjoint Theories and Combinations of Satisfiability Procedures

Cesare Tinelli , Christophe Ringeissen (1)

1 PROTHEO - Constraints, automatic deduction and software properties proofs

In this paper we outline a theoretical framework for the combination of decision procedures for constraint satisfiability. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory T1 and one that decides constraint satisfiability with respect to a constraint theory T2, produces a procedure that (semi-)decides constraint satisfiability with respect to the union of T1 and T2. We provide a number of model-theoretic conditions on the constraint language and the component constraint theories for the method to be sound and complete, with special emphasis on the case in which the signatures of the component theories are non-disjoint. We also describe some general classes of theories to which our combination results apply, and relate our approach to some of the existing combination methods in the field.

Mots clés: decision problems; constraint-based reasoning; procédures de décision; raisonnement avec contraintes; déduction automatique; automated deduction; combinaison de procédures de satisfaisabilité

Domaines: Autre [cs.OH]

Cesare Tinelli, Christophe Ringeissen. Unions of Non-Disjoint Theories and Combinations of Satisfiability Procedures. Theoretical Computer Science, 2003, 290 (1), pp.291-353. ⟨10.1016/S0304-3975(01)00332-2⟩. ⟨inria-00099668⟩