Reinterpreting Dependency Schemes: Soundness Meets Incompleteness in DQBF

Dependency quantified Boolean formulas (DQBF) and QBF dependency schemes have been treated separately in the literature, even though both treatments extend QBF by replacing the linear order of the quantifier prefix with a partial order. We propose to merge the two, by reinterpreting a dependency sch...

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Veröffentlicht in:Journal of automated reasoning Jg. 63; H. 3; S. 597 - 623
Hauptverfasser: Beyersdorff, Olaf, Blinkhorn, Joshua, Chew, Leroy, Schmidt, Renate, Suda, Martin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht Springer Netherlands 01.10.2019
Springer Nature B.V
Schlagworte:
Artificial Intelligence
Boolean algebra
Computer Science
Dependence
Mapping
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Reduction
Symbolic and Algebraic Manipulation
Quantified Boolean formulas
DQBF
F.2.2 Nonnumerical algorithms and problems
Dependency schemes
ISSN:0168-7433, 1573-0670, 1573-0670
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Zusammenfassung:Dependency quantified Boolean formulas (DQBF) and QBF dependency schemes have been treated separately in the literature, even though both treatments extend QBF by replacing the linear order of the quantifier prefix with a partial order. We propose to merge the two, by reinterpreting a dependency scheme as a mapping from QBF into DQBF. Our approach offers a fresh insight on the nature of soundness in proof systems for QBF with dependency schemes, in which a natural property called ‘full exhibition’ is central. We apply our approach to QBF proof systems from two distinct paradigms, termed ‘universal reduction’ and ‘universal expansion’. We show that full exhibition is sufficient (but not necessary) for soundness in universal reduction systems for QBF with dependency schemes, whereas for expansion systems the same property characterises soundness exactly. We prove our results by investigating DQBF proof systems, and then employing our reinterpretation of dependency schemes. Finally, we show that the reflexive resolution path dependency scheme is fully exhibited, thereby proving a conjecture of Slivovsky.
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ISSN:0168-7433
1573-0670
1573-0670
DOI:10.1007/s10817-018-9482-4