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Deciding First-Order Satisfiability when Universal and Existential Variables are Separated

Thomas Sturm 1, 2, 3 Marco Voigt 4 Christoph Weidenbach 2, 1
1 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
MPII - Max-Planck-Institut für Informatik, Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
3 MOSEL - Proof-oriented development of computer-based systems
LORIA - FM - Department of Formal Methods
Abstract : We introduce a new decidable fragment of first-order logic with equality, which strictly generalizes two already well-known ones— the Bernays–Schönfinkel–Ramsey (BSR) Fragment and the Mo-nadic Fragment. The defining principle is the syntactic separation of universally quantified variables from existentially quantified ones at the level of atoms. Thus, our classification neither rests on restrictions on quantifier prefixes (as in the BSR case) nor on restrictions on the arity of predicate symbols (as in the monadic case). We demonstrate that the new fragment exhibits the finite model property and derive a non-elementary upper bound on the computing time required for deciding satisfiability in the new fragment. For the subfragment of prenex sentences with the quantifier prefix ∃ * ∀ * ∃ * the satisfiability problem is shown to be complete for NEXPTIME. Finally, we discuss how automated reasoning procedures can take advantage of our results.
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Submitted on : Monday, November 14, 2016 - 5:20:05 PM
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Thomas Sturm, Marco Voigt, Christoph Weidenbach. Deciding First-Order Satisfiability when Universal and Existential Variables are Separated. LICS 2016, Jul 2016, New York, United States. pp.86 - 95, ⟨10.1145/2933575.2934532⟩. ⟨hal-01389744⟩



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