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arXiv · 1604.06483

On Stronger Calculi for QBFs

Uwe Egly
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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.

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Uwe Egly. 2016-04-21. On Stronger Calculi for QBFs. https://arxiv.org/abs/1604.06483

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