On the Convexity of a Fragment of Pure Set Theory with Applications within a Nelson-Oppen Framework

  title={On the Convexity of a Fragment of Pure Set Theory with Applications within a Nelson-Oppen Framework},
  author={Domenico Cantone and Andrea De Domenico and Pietro Maugeri},
The Satisfiability Modulo Theories (SMT) issue concerns the satisfiability of formulae from multiple background theories, usually expressed in the language of first-order predicate logic with equality. SMT solvers are often based on variants of the Nelson-Oppen combination method, a solver for the quantifier-free fragment of the combination of theories with disjoint signatures, via cooperation among their decision procedures. When each of the theories to be combined by the Nelson-Oppen method… 



Decidability and Undecidability Results for Nelson-Oppen and Rewrite-Based Decision Procedures

The Nelson-Oppen decidability transfer result is strengthened, by showing that it applies to theories over disjoint signatures, whose satisfiability problem, in either arbitrary or infinite models, is decidable.

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Decision procedures for elementary sublanguages of set theory

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Combining Sets with Cardinals

  • C. G. Zarba
  • Mathematics, Computer Science
    Journal of Automated Reasoning
  • 2005
We introduce a quantifier-free set-theoretic language for combining sets with elements in the presence of the cardinality operator. We prove that the language is decidable by providing a combination

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