A Resolution Proof System for Dependency Stochastic Boolean Satisfiability

Dependency stochastic Boolean satisfiability (DSSAT), which generalizes stochastic Boolean satisfiability (SSAT) and dependency quantified Boolean formula (DQBF), is a new logical formalism that allows compact encoding of NEXPTIME decision problems under uncertainty. Despite potentially broad applic...

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Bibliographic Details
Published inJournal of automated reasoning Vol. 67; no. 3; p. 26
Main Authors Luo, Yun-Rong, Cheng, Che, Jiang, Jie-Hong R.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.09.2023
Springer Nature B.V
Subjects
Artificial Intelligence
Automation
Boolean
Calculus
Computer Science
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Probability
Symbolic and Algebraic Manipulation
Variables
Proof system
Resolution calculus
Dependency stochastic Boolean satisfiability
Satisfying probability
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Summary:Dependency stochastic Boolean satisfiability (DSSAT), which generalizes stochastic Boolean satisfiability (SSAT) and dependency quantified Boolean formula (DQBF), is a new logical formalism that allows compact encoding of NEXPTIME decision problems under uncertainty. Despite potentially broad applications, a decision procedure for DSSAT remains lacking. In this work, we present the first sound and complete resolution calculus for DSSAT. The resolution system deduces the maximum satisfying probability of a DSSAT formula and provides a witnessing certificate. We also show that when the special case of SSAT formulas is considered, the DSSAT resolution calculus p-simulates a known SSAT resolution scheme. Our result may pave a theoretical foundation for further development and certification of DSSAT solvers.
ISSN:0168-7433
1573-0670
DOI:10.1007/s10817-023-09670-6