MEANING-PRESERVING SKOLEMIZATION

Kiyoshi Akama, Ekawit Nantajeewarawat

2011

Abstract

Skolemization is a well-known method for removing existential quantifiers from a logical formula. Although it always yields a satisfiability-preserving transformation step, classical Skolemization in general does not preserve the logical meaning of a source formula. We develop in this paper a theory for extending a space of logical formulas by incorporation of function variables and show how meaning-preserving Skolemization can be achieved in an obtained extended space. A procedure for converting a logical formula into an equivalent one in an extended conjunctive normal form on the extended space is described. This work lays a theoretical foundation for solving logical problems involving existential quantifications based on meaning-preserving formula transformation.

References

  1. Akama, K. and Nantajeewarawat, E. (2006). Formalization of the Equivalent Transformation Computation Model. Journal of Advanced Computational Intelligence and Intelligent Informatics, 10(3):245-259.
  2. Akama, K. and Nantajeewarawat, E. (2011). MeaningPreserving Skolemization. Technical report, Hokkaido University, Sapporo, Japan.
  3. Baader, F., Calvanese, D., McGuinness, D. L., Nardi, D., and Patel-Schneider, P. F., editors (2007). The Description Logic Handbook. Cambridge University Press, second edition.
  4. Chang, C.-L. and Lee, R. C.-T. (1973). Symbolic Logic and Mechanical Theorem Proving. Academic Press.
  5. Donini, F. M., Lenzerini, M., Nardi, D., and Schaerf, A. (1998). A L -log: Integrating Datalog and Description Logics. Journal of Intelligent Information Systems, 16:227-252.
  6. Horrocks, I., Patel-schneider, P. F., Bechhofer, S., and Tsarkov, D. (2005). OWL Rules: A Proposal and Prototype Implementation. Journal of Web Semantics, 3(1):23-40.
  7. Levy, A. Y. and Rousset, M.-C. (1998). Combining Horn Rules and Description Logics in CARIN. Artificial Intelligence, 104(1-2):165-209.
  8. Lloyd, J. W. (1987). Foundations of Logic Programming. Springer-Verlag, second, extended edition.
  9. Motik, B., Sattler, U., and Studer, R. (2005). Query Answering for OWL-DL with Rules. Journal of Web Semantics, 3(1):41-60.
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Paper Citation


in Harvard Style

Akama K. and Nantajeewarawat E. (2011). MEANING-PRESERVING SKOLEMIZATION . In Proceedings of the International Conference on Knowledge Engineering and Ontology Development - Volume 1: KEOD, (IC3K 2011) ISBN 978-989-8425-80-5, pages 322-327. DOI: 10.5220/0003692003220327


in Bibtex Style

@conference{keod11,
author={Kiyoshi Akama and Ekawit Nantajeewarawat},
title={MEANING-PRESERVING SKOLEMIZATION},
booktitle={Proceedings of the International Conference on Knowledge Engineering and Ontology Development - Volume 1: KEOD, (IC3K 2011)},
year={2011},
pages={322-327},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003692003220327},
isbn={978-989-8425-80-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Knowledge Engineering and Ontology Development - Volume 1: KEOD, (IC3K 2011)
TI - MEANING-PRESERVING SKOLEMIZATION
SN - 978-989-8425-80-5
AU - Akama K.
AU - Nantajeewarawat E.
PY - 2011
SP - 322
EP - 327
DO - 10.5220/0003692003220327