Functional Semantics for Non-prenex QBF

Igor Stéphan

2014

Abstract

Quantified Boolean Formulae (or QBF) are suitable to represent finite two-player games. Current techniques to solve QBF are for prenex QBF and knowledge representation is rarely in this form. We propose in this article a functional semantics for non-prenex QBF. The proposed formalism is symmetrical for validity and non-validity and allows to give different interpretations to the quantifiers. With our formalism, the solution of a non-prenex QBF is consistent with the specification, directly readable by the designer of the QBF and the locality of the knolewge is preserved.

References

  1. Benedetti, M. (2005a). Extracting Certificates from Quantified Boolean Formulas. In Proceedings of 9th International Joint Conference on Artificial Intelligence (IJCAI'05), pages 47-53.
  2. Benedetti, M. (2005b). Quantifier trees for QBFs. In Poster of the 8th International Conference on Theory and Applications of Satisfiability Testing (SAT'05).
  3. Bordeaux, L. and Monfroy, E. (2002). Beyond NP: ArcConsistency for Quantified Constraints. In Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming (CP'02), pages 371-386.
  4. Coste-Marquis, S., Fargier, H., Lang, J., Le Berre, D., and Marquis, P. (2006). Representing Policies for Quantified Boolean Formulae. In Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning (KR'06), pages 286- 296.
  5. Da Mota, B., Stéphan, I., and Nicolas, P. (2009). Une nouvelle stratégie de mise sous forme prénexe pour des formules booléennes quantifiées avec bi-implications. Revue internationale I3 (Information - Interaction - Intelligence), 9:9-29.
  6. Egly, U., Seidl, M., Tompits, H., Woltran, S., and Zolda, M. (2003). Comparing Different Prenexing Strategies for Quantified Boolean Formulas. In Proceedings of the 6th International Conference on Theory and Applications of Satisfiability Testing (SAT'03), pages 214- 228.
  7. Giunchiglia, E., Narizzano, M., and Tacchella, A. (2006). Quantifier structure in search based procedures for QBFs. In Proceedings of the conference on Design, Automation and Test in Europe (DATE'06), pages 812-817.
  8. Kleine Büning, H., Subramani, K., and Zhao, X. (2007). Boolean Functions as Models for Quantified Boolean Formulas. Journal of Automated Reasoning, 39(1):49-75.
  9. Lonsing, F. and Biere, A. (2010). Integrating Dependency Schemes in Search-Based QBF Solvers. In Proceedings of the 13th International Conference on Theory and Applications of Satisfiability Testing (SAT'10), pages 158-171.
  10. Plaisted, D. and Greenbaum, S. (1986). A StructurePreserving Clause Form Translation. Journal of Symbolic Computation, 2(3):293-304.
  11. Stockmeyer, L. (1977). The polynomial-time hierarchy. Theoretical Computer Science, 3:1-22.
Download


Paper Citation


in Harvard Style

Stéphan I. (2014). Functional Semantics for Non-prenex QBF . In Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-758-015-4, pages 358-365. DOI: 10.5220/0004760303580365


in Bibtex Style

@conference{icaart14,
author={Igor Stéphan},
title={Functional Semantics for Non-prenex QBF},
booktitle={Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2014},
pages={358-365},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004760303580365},
isbn={978-989-758-015-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - Functional Semantics for Non-prenex QBF
SN - 978-989-758-015-4
AU - Stéphan I.
PY - 2014
SP - 358
EP - 365
DO - 10.5220/0004760303580365