A Gentle Non-Disjoint Combination of Satisfiability Procedures (Extended Version)

Paula Chocron 1, 2 Pascal Fontaine 3 Christophe Ringeissen 2
2 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
3 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
LORIA - FM - Department of Formal Methods , Inria Nancy - Grand Est, MPII - Max-Planck-Institut für Informatik
Abstract : A satisfiability problem is often expressed in a combination of theories, and a natural approach consists in solving the problem by combining the satisfiability procedures available for the component theories. This is the purpose of the combination method introduced by Nelson and Oppen. However, in its initial presentation, the Nelson-Oppen combination method requires the theories to be signature-disjoint and stably infinite (to guarantee the existence of an infinite model). The notion of gentle theory has been introduced in the last few years as one solution to go beyond the restriction of stable infiniteness, but in the case of disjoint theories. In this paper, we adapt the notion of gentle theory to the non-disjoint combination of theories sharing only unary predicates (plus constants and the equality). Like in the disjoint case, combining two theories, one of them being gentle, requires some minor assumptions on the other one. We show that major classes of theories, i.e.\ Löwenheim and Bernays-Schönfinkel-Ramsey, satisfy the appropriate notion of gentleness introduced for this particular non-disjoint combination framework.
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Paula Chocron, Pascal Fontaine, Christophe Ringeissen. A Gentle Non-Disjoint Combination of Satisfiability Procedures (Extended Version). [Research Report] RR-8529, INRIA. 2014. ⟨hal-00985135⟩

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