REASONING WITH THE FUZZY DESCRIPTION LOGIC fZSI

Jidi Zhao, Harold Boley, Weichang Du

Abstract

While applications in different areas have shown the necessity of dealing with uncertain knowledge, Semantic Web techniques based on standard Description Logics do not have such a capability. Motivated by this discrepancy, we introduce an expressive fuzzy description logic, fZSI , which extends the classic Description Logic SI to deal with uncertain knowledge about concepts and roles as well as instances of concepts and roles. In the family of Fuzzy Logics it is semantically based on Zadeh Logic, which naturally interprets uncertain knowledge about concepts and roles as fuzzy sets and fuzzy relations, and interprets uncertain knowledge about instances as elements with degrees of membership. The paper focuses on several reasoning methods for the main reasoning problems in fZSI, including consistency checking, instance range entailment, and f-retrieval problems.

References

  1. Baader, F., Calvanese, D., McGuinness, D. L., Nardi, D., and Patel-Schneider, P. F. (2003). The Description Logic Handbook: Theory, Implementation and Applications. Cambridge University Press, Cambridge, MA.
  2. Berners-Lee, T., Hendler, J., and Lassila, O. (2001). The semantic web. Scientific American, 284(5):34-44.
  3. Díaz, S., De Baets, B., and Montes, S. (2010). General results on the decomposition of transitive fuzzy relations. Fuzzy Optimization and Decision Making, 9(1):1-29.
  4. GLPK (2008). GNU linear programming kit. Technical Report http://gnuwin32.sourceforge.net/packages/ glpk.htm.
  5. Haase, P. and Völker, J. (2005). Ontology learning and reasoning - dealing with uncertainty and inconsistency. In Proceedings of Uncertainty Reasoning for the Semantic Web, pages 45-55.
  6. Horrocks, I. and Sattler, U. (1999). A description logic with transitive and inverse roles and role hierarchies. J. of Logic and Computation, 9(3):385-410.
  7. Horrocks, I., Sattler, U., and Tobies, S. (1998). A PSPACEalgorithm for deciding A L C I R+ -satisfiability. LTCSReport 98-08, LuFg Theoretical Computer Science, RWTH Aachen, Germany.
  8. Horrocks, I., Sattler, U., and Tobies, S. (2000). Reasoning with individuals for the description logic S H I Q . In McAllester, D., editor, Proc. of the 17th Int. Conf. on Automated Deduction (CADE 2000), volume 1831 of Lecture Notes in Computer Science, pages 482-496. Springer.
  9. Jaeger, M. (1994). Probabilistic reasoning in terminological logics. In Proc. of the 4th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR94), pages 305-316.
  10. Koller, D., Levy, A., and Pfeffer, A. (1997). P-classic: A tractable probabilistic description logic. In Proceedings of the Fourteenth National Conference on Artificial Intelligence (AAAI-97), pages 390-397.
  11. Laskey, K. J., Laskey, K. B., Costa, P. C. G., Kokar, M. M., Martin, T., and Lukasiewicz, T. (05 March, 2008). W3C incubator group report. Technical Report http://www.w3.org/2005/Incubator/urw3, W3C.
  12. Lee, H.-S. (2001). An optimal algorithm for computing the maxmin transitive closure of a fuzzy similarity matrix. Fuzzy Sets and Systems, 123(1):129-136.
  13. Lukasiewicz, T. (2008). Fuzzy description logic programs under the answer set semantics for the semantic web. Fundamenta Informaticae, 82(3):289-310.
  14. Martin-Recuerda, F. and Robertson, D. (2005). Discovery and uncertainty in semantic web services. In Proceedings of Uncertainty Reasoning for the Semantic Web, page 188.
  15. McGuinness, D. L. and van Harmelen, F. (2004). Owl web ontology language overview. http://www.w3.org/TR/owl-features/.
  16. Mitsuishi, T. and Bancerek, G. (2003). Transitive closure of fuzzy relations. Journal of Formalized Mathematics, 15.
  17. Spencer, B. (2006). ALCAS: An ALC Reasoner for CAS. http://www.cs.unb.ca/ bspencer/cs6795swt/alcas.prolog.
  18. Stamou, G., van Ossenbruggen, J., Pan, J. Z., and Schreiber, G. (2006). Multimedia annotations on the semantic web. IEEE MultiMedia, 13:86-90.
  19. Stevens, R., Aranguren, M. E., Wolstencroft, K., Sattlera, U., Drummond, N., Horridge, M., and Rectora, A. (2007). Using owl to model biological knowledge. International Journal of Human-Computer Studies, 65(7):583-594.
  20. Straccia, U. (2001). Reasoning within fuzzy description logics. Journal of Artificial Intelligence Research, 14:137-166.
  21. Yen, J. (1991). Generalizing term subsumption languages to fuzzy logic. In Proc. of the 12th Int. Joint Conf. on Artificial Intelligence (IJCAI'91), pages 472-477.
  22. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3):338-353.
  23. Zhao, J. (2010). Uncertainty and Rule Extensions to Description Logics and Semantic Web Ontologies, chapter 1, pages 1-22. Advances in Semantic Computing. Technomathematics Research Foundation. accepted.
  24. Zhao, J. and Boley, H. (2010). Knowledge Representation and Reasoning in Norm-Parameterized Fuzzy Description Logics. Canadian Semantic Web: Technologies and Applications. Springer.
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Paper Citation


in Harvard Style

Zhao J., Boley H. and Du W. (2010). REASONING WITH THE FUZZY DESCRIPTION LOGIC fZSI . In Proceedings of the International Conference on Fuzzy Computation and 2nd International Conference on Neural Computation - Volume 1: ICFC, (IJCCI 2010) ISBN 978-989-8425-32-4, pages 21-30. DOI: 10.5220/0003054700210030


in Bibtex Style

@conference{icfc10,
author={Jidi Zhao and Harold Boley and Weichang Du},
title={REASONING WITH THE FUZZY DESCRIPTION LOGIC fZSI},
booktitle={Proceedings of the International Conference on Fuzzy Computation and 2nd International Conference on Neural Computation - Volume 1: ICFC, (IJCCI 2010)},
year={2010},
pages={21-30},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003054700210030},
isbn={978-989-8425-32-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Fuzzy Computation and 2nd International Conference on Neural Computation - Volume 1: ICFC, (IJCCI 2010)
TI - REASONING WITH THE FUZZY DESCRIPTION LOGIC fZSI
SN - 978-989-8425-32-4
AU - Zhao J.
AU - Boley H.
AU - Du W.
PY - 2010
SP - 21
EP - 30
DO - 10.5220/0003054700210030