Solving Query-answering Problems with If-and-Only-If Formulas

Kiyoshi Akama, Ekawit Nantajeewarawat

2014

Abstract

A query-answering problem (QA problem) is concerned with finding all ground instances of a query atomic formula that are logical consequences of a given logical formula describing the background knowledge of the problem. A method for solving QA problems on full first-order logic has been invented based on the equivalent transformation (ET) principle, where a given QA problem on first-order logic is converted into a QA problem on extended clauses and is then further transformed repeatedly and equivalently into simpler forms until its answer set can be readily obtained. In this paper, such a clause-based solution is extended by proposing a new method for effectively utilizing a universally quantified if-and-only-if statement defining a predicate, which is called an iff-formula. The background knowledge of a given QA problem is separated into two parts: (i) a conjunction of iff-formulas and (ii) other types of knowledge. Special ET rules for manipulating iffformulas are introduced. The new solution method deals with both iff-knowledge in first-order logic and a set of extended clauses. Application of this solution method is illustrated.

References

  1. Akama, K. and Nantajeewarawat, E. (2008). MeaningPreserving Skolemization on Logical Structures. In Proceedings of the 9th International Conference on Intelligent Technologies, pages 123-132, Samui, Thailand.
  2. Akama, K. and Nantajeewarawat, E. (2011). MeaningPreserving Skolemization. In Proceedings of the 3rd International Conference on Knowledge Engineering and Ontology Development, pages 322-327, Paris, France.
  3. Akama, K. and Nantajeewarawat, E. (2012a). A Delayed Splitting Bottom-Up Procedure for Model Generation. In Proceedings of 25th Australasian Joint Conference on Artificial Intelligence, LNCS 7691, pages 481- 492, Sydney, Australia.
  4. Akama, K. and Nantajeewarawat, E. (2012b). ConjunctionBased Clauses for Equivalent Transformation of Query-Answering Problems. International Journal of Future Computer and Communication, 1:5-8.
  5. Akama, K. and Nantajeewarawat, E. (2013a). Correctness of Solving Query-Answering Problems Using Satisfiability Solvers. In Proceedings of the 5th Asian Conference on Intelligent Information and Database Systems, LNAI 7802, pages 404-413, Kuala Lumpur, Malaysia.
  6. Akama, K. and Nantajeewarawat, E. (2013b). Embedding Proof Problems into Query-Answering Problems and Problem Solving by Equivalent Transformation. In Proceedings of the 5th International Conference on Knowledge Engineering and Ontology Development, pages 253-260, Vilamoura, Portugal.
  7. Akama, K. and Nantajeewarawat, E. (2013c). UnfoldingBased Simplification of Query-Answering Problems in an Extended Clause Space. International Journal of Innovative Computing, Information and Control, 9:3515-3526.
  8. Akama, K. and Nantajeewarawat, E. (2014). Equivalent Transformation in an Extended Space for Solving Query-Answering Problems. In Proceedings of the 6th Asian Conference on Intelligent Information and Database Systems, LNAI 8397, pages 232-241, Bangkok, Thailand.
  9. 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.
  10. Chang, C.-L. and Lee, R. C.-T. (1973). Symbolic Logic and Mechanical Theorem Proving. Academic Press.
  11. Donini, F. M., Lenzerini, M., Nardi, D., and Schaerf, A. (1998). AL -log: Integrating Datalog and Description Logics. Journal of Intelligent Information Systems, 16:227-252.
  12. 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.
  13. Lloyd, J. W. (1987). Foundations of Logic Programming. Springer-Verlag, second, extended edition.
  14. Minker, J., editor (1988). Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA.
  15. Motik, B. and Rosati, R. (2010). Reconciling Description Logics and Rules. Journal of the ACM, 57(30):1-62.
  16. Motik, B., Sattler, U., and Studer, R. (2005). Query Answering for OWL-DL with Rules. Journal of Web Semantics, 3(1):41-60.
Download


Paper Citation


in Harvard Style

Akama K. and Nantajeewarawat E. (2014). Solving Query-answering Problems with If-and-Only-If Formulas . In Proceedings of the International Conference on Knowledge Engineering and Ontology Development - Volume 1: KEOD, (IC3K 2014) ISBN 978-989-758-049-9, pages 333-344. DOI: 10.5220/0005097903330344


in Bibtex Style

@conference{keod14,
author={Kiyoshi Akama and Ekawit Nantajeewarawat},
title={Solving Query-answering Problems with If-and-Only-If Formulas},
booktitle={Proceedings of the International Conference on Knowledge Engineering and Ontology Development - Volume 1: KEOD, (IC3K 2014)},
year={2014},
pages={333-344},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005097903330344},
isbn={978-989-758-049-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Knowledge Engineering and Ontology Development - Volume 1: KEOD, (IC3K 2014)
TI - Solving Query-answering Problems with If-and-Only-If Formulas
SN - 978-989-758-049-9
AU - Akama K.
AU - Nantajeewarawat E.
PY - 2014
SP - 333
EP - 344
DO - 10.5220/0005097903330344