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Reports (Research Report) Year : 2004

C-tableaux

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.

Domains

Other [cs.OH]
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Dates and versions

inria-00070767 , version 1 (19-05-2006)

Identifiers

  • HAL Id : inria-00070767 , version 1

Cite

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