# Non-Disjoint Unions of Theories and Combinations of Satisfiability Procedures: First Results

1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In this paper we outline a theoretical framework for the combination of decision procedures for the satisfiability of constraints with respect to a constrainttheory. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory ${\cal T}_1$ and one that decides constraint satisfiability with respect to a constraint theory ${\cal T}_2$, is able to produce a procedure that (semi-)decides constraint satisfiability with respect to the union of ${\cal T}_1$ and ${\cal T}_2$. We also provide some 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 ${\cal T}_1$ and ${\cal T}_2$ are non-disjoint.
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https://hal.inria.fr/inria-00073288
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• HAL Id : inria-00073288, version 1

### Citation

Cesare Tinelli, Christophe Ringeissen. Non-Disjoint Unions of Theories and Combinations of Satisfiability Procedures: First Results. [Research Report] RR-3402, INRIA. 1998, pp.63. ⟨inria-00073288⟩

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