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Satisfiability of formulae with one ∀ is decidable in exponential time

Satisfiability of formulae with one ∀ is decidable in exponential time 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Satisfiability of formulae with one ∀ is decidable in exponential time

Archive for Mathematical Logic , Volume 29 (4) – Apr 22, 2005

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References (17)

Publisher
Springer Journals
Copyright
Copyright © 1990 by Springer-Verlag
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/BF01651329
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Archive for Mathematical LogicSpringer Journals

Published: Apr 22, 2005

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