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Satisfiability of formulae with one ∀ is decidable in exponential time

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In first order logic without equality, but with arbitrary relations and functions the ∃*∀∃* class is the unique maximal solvable prefix class. We show that the satisfiability problem for this class is decidable in deterministic exponential time The result is established by a structural analysis of a particular infinite subset of the Herbrand universe and by a polynomial space bounded alternating procedure.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051, Basel, Switzerland

    Erich Grädel

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  1. Erich Grädel
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This work was done while the author was staying at the University of Pisa, Italy, and was supported by the Swiss National Science Foundation

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Grädel, E. Satisfiability of formulae with one ∀ is decidable in exponential time. Arch Math Logic 29, 265–276 (1990). https://doi.org/10.1007/BF01651329

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  • DOI: https://doi.org/10.1007/BF01651329

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