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

Domenico Cantone
(Dept. of Mathematics and Computer Science, University of Catania, Italy)
Andrea De Domenico
(Scuola Superiore di Catania, University of Catania, Italy)
Pietro Maugeri
(Dept. of Mathematics and Computer Science, University of Catania, Italy)

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 is convex (that is, any conjunction of its literals can imply a disjunction of equalities only when it implies at least one of the equalities) and decidable in polynomial time, the running time of the combination procedure is guaranteed to be polynomial in the size of the input formula. In this paper, we prove the convexity of a fragment of Zermelo-Fraenkel set theory, called Multi-Level Syllogistic, most of whose polynomially decidable fragments we have recently characterized.

In Pierre Ganty and Davide Bresolin: Proceedings 12th International Symposium on Games, Automata, Logics, and Formal Verification (GandALF 2021), Padua, Italy, 20-22 September 2021, Electronic Proceedings in Theoretical Computer Science 346, pp. 195–210.
Published: 17th September 2021.

ArXived at: http://dx.doi.org/10.4204/EPTCS.346.13 bibtex PDF
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