Combination of Disjoint Theories: Beyond Decidability

  • Pascal Fontaine
  • Stephan Merz
  • Christoph Weidenbach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7364)

Abstract

Combination of theories underlies the design of satisfiability modulo theories (SMT) solvers. The Nelson-Oppen framework can be used to build a decision procedure for the combination of two disjoint decidable stably infinite theories.

We here study combinations involving an arbitrary first-order theory. Decidability is lost, but refutational completeness is preserved. We consider two cases and provide complete (semi-)algorithms for them. First, we show that it is possible under minor technical conditions to combine a decidable (not necessarily stably infinite) theory and a disjoint finitely axiomatized theory, obtaining a refutationally complete procedure. Second, we provide a refutationally complete procedure for the union of two disjoint finitely axiomatized theories, that uses the assumed procedures for the underlying theories without modifying them.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Pascal Fontaine
    • 1
  • Stephan Merz
    • 2
  • Christoph Weidenbach
    • 3
  1. 1.Université de Lorraine & LORIANancyFrance
  2. 2.INRIA Nancy & LORIANancyFrance
  3. 3.Max-Planck-Institut für InformatikSaarbrückenGermany

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