C-tableaux

Calogero G. Zarba 1
1 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 Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The Nelson-Oppen combination method combines decision procedures for first-order theories satisfying certain conditions into a single decision procedure for the union theory. The method is restricted to the combination of stably infinite theories over disjoint signatures. In this report we present C-tableaux, an extension of Smullyan tableaux that generalizes the Nelson-Oppen method to the combination of arbitrary universal theories, not necessarily stably infinite and not necessarily over disjoint signatures. C-tableaux are sound and complete, but not terminating in general. Although C-tableaux do not provide a decidability result in general, in this report we describe two approaches that can be used in order to obtain decidability results using C-tableaux. Using the first approach, we are able to obtain a decidability result when combining theories that share the dense orders. Using the second approach, we are able to obtain a decidability result when combining theories whose union is stably finite.
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https://hal.inria.fr/inria-00070767
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Submitted on : Friday, May 19, 2006 - 9:34:34 PM
Last modification on : Friday, July 6, 2018 - 3:06:10 PM
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  • HAL Id : inria-00070767, version 1

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Calogero G. Zarba. C-tableaux. [Research Report] RR-5229, INRIA. 2004, pp.31. ⟨inria-00070767⟩

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