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On Stronger Calculi for QBFs

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Theory and Applications of Satisfiability Testing – SAT 2016 (SAT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9710))

Abstract

Quantified Boolean formulas (QBFs) generalize propositional formulas by admitting quantifications over propositional variables. QBFs can be viewed as (restricted) formulas of first-order predicate logic and easy translations of QBFs into first-order formulas exist. We analyze different translations and show that first-order resolution combined with such translations can polynomially simulate well-known deduction concepts for QBFs. Furthermore, we extend QBF calculi by the possibility to instantiate a universal variable by an existential variable of smaller level. Combining such an enhanced calculus with the propositional extension rule results in a calculus with a universal quantifier rule which essentially introduces propositional formulas for universal variables. In this way, one can mimic a very general quantifier rule known from sequent systems.

This work was supported by the Austrian Science Fund (FWF) under grant S11409-N23. Partial results have been announced at the QBF Workshop 2014 (http://www.easychair.org/smart-program/VSL2014/QBF-program.html). We thank the reviewers for valuable comments. An extended version with proofs is available [10].

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Authors and Affiliations

  1. Institut für Informationssysteme 184/3, Technische Universität Wien, Favoritenstrasse 9–11, 1040, Vienna, Austria

    Uwe Egly

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  1. Uwe Egly
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Correspondence to Uwe Egly .

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Editors and Affiliations

  1. Aix-Marseille Université, Marseille, France

    Nadia Creignou

  2. Université d'Artois, Lens, France

    Daniel Le Berre

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Egly, U. (2016). On Stronger Calculi for QBFs. In: Creignou, N., Le Berre, D. (eds) Theory and Applications of Satisfiability Testing – SAT 2016. SAT 2016. Lecture Notes in Computer Science(), vol 9710. Springer, Cham. https://doi.org/10.1007/978-3-319-40970-2_26

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  • DOI: https://doi.org/10.1007/978-3-319-40970-2_26

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