Skip to main content
SpringerLink
Log in
Book cover

Transactions on Computational Collective Intelligence VI pp 36–55Cite as

Paraconsistent Reasoning for Semantic Web Agents

  • Chapter

Part of the book series: Lecture Notes in Computer Science ((TCCI,volume 7190))

Abstract

Description logics refer to a family of formalisms concentrated around concepts, roles and individuals. They are used in many multiagent and Semantic Web applications as a foundation for specifying knowledge bases and reasoning about them. Among them, one of the most important logics is \(\mathcal{SROIQ}\), providing the logical foundation for the OWL 2 Web Ontology Language recommended by W3C in October 2009.

In the current paper we address the problem of inconsistent knowledge. Inconsistencies may naturally appear in the considered application domains, for example as a result of fusing knowledge from distributed sources. We introduce a number of paraconsistent semantics for \(\mathcal{SROIQ}\), including three-valued and four-valued semantics. The four-valued semantics reflects the well-known approach introduced in [5,4] and is considered here for comparison reasons only. We also study the relationship between the semantics and paraconsistent reasoning in \(\mathcal{SROIQ}\) through a translation into the traditional two-valued semantics. Such a translation allows one to use existing tools and reasoners to deal with inconsistent knowledge.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amo, S., Pais, M.S.: A paraconsistent logic approach for querying inconsistent databases. International Journal of Approximate Reasoning 46, 366–386 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): Description Logic Handbook. Cambridge University Press (2002)

    Google Scholar 

  3. Baader, F., Nutt, W.: Basic description logics. In: Baader, et al. (eds.) [2], pp. 47–100

    Google Scholar 

  4. Belnap, N.D.: How a computer should think. In: Ryle, G. (ed.) Contemporary Aspects of Philosophy, pp. 30–55. Oriel Press, Stocksfield (1977)

    Google Scholar 

  5. Belnap, N.D.: A useful four-valued logic. In: Eptein, G., Dunn, J.M. (eds.) Modern Uses of Many Valued Logic, pp. 8–37. Reidel (1977)

    Google Scholar 

  6. Besnard, P., Hunter, A.: Quasi-Classical Logic: Non-Trivializable Classical Reasoning from Incosistent Information. In: Froidevaux, C., Kohlas, J. (eds.) ECSQARU 1995. LNCS, vol. 946, pp. 44–51. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  7. Béziau, J.-Y., Carnielli, W., Gabbay, D.M. (eds.): Handbook of Paraconsistency. Logic and Cognitive Systems, vol. 9. College Publications (2007)

    Google Scholar 

  8. Bloesch, A.: A tableau style proof system for two paraconsistent logics. Notre Dame Journal of Formal Logic 34(2), 295–301 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  9. Doherty, P., Łukaszewicz, W., Skowron, A., Szałas, A.: Knowledge Representation Techniques. A Rough Set Approach. Studies in Fuziness and Soft Computing, vol. 202. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  10. Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible \(\mathcal{SROIQ}\). In: Doherty, P., Mylopoulos, J., Welty, C.A. (eds.) Proceedings of KR 2006, pp. 57–67. AAAI Press (2006)

    Google Scholar 

  11. Hunter, A.: Paraconsistent logics. In: Gabbay, D., Smets, P. (eds.) Handbook of Defeasible Reasoning and Uncertain Information, pp. 11–36. Kluwer (1998)

    Google Scholar 

  12. Hunter, A.: Reasoning with contradictory information using quasi-classical logic. J. Log. Comput. 10(5), 677–703 (2000)

    Article  MATH  Google Scholar 

  13. Kleene, S.C.: Introduction to Metamathematics. D. Van Nostrand, Princeton (1952)

    Google Scholar 

  14. Ma, Y., Hitzler, P.: Paraconsistent Reasoning for OWL 2. In: Polleres, A., Swift, T. (eds.) RR 2009. LNCS, vol. 5837, pp. 197–211. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  15. Ma, Y., Hitzler, P., Lin, Z.: Paraconsistent reasoning for expressive and tractable description logics. In: Proceedings of Description Logics (2008)

    Google Scholar 

  16. Małuszyński, J., Szałas, A.: Computational aspects of paraconsistent query language 4QL. Journal of Applied Non-classical Logics 21(2), 211–232 (2011)

    Article  MathSciNet  Google Scholar 

  17. Małuszyński, J., Szałas, A.: Living with Inconsistency and Taming Nonmonotonicity. In: Furche, T. (ed.) Datalog 2010. LNCS, vol. 6702, pp. 384–398. Springer, Heidelberg (2011)

    Google Scholar 

  18. Małuszyński, J., Szałas, A., Vitória, A.: Paraconsistent Logic Programs with Four-Valued Rough Sets. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 41–51. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Meghini, C., Straccia, U.: A relevance terminological logic for information retrieval. In: Proceedings of SIGIR 1996, pp. 197–205. ACM (1996)

    Google Scholar 

  20. Nardi, D., Brachman, R.J.: An introduction to description logics. In: Baader, et al. (eds.) [2], pp. 5–44

    Google Scholar 

  21. Nguyen, L.A.: Paraconsistent and Approximate Semantics for the OWL 2 Web Ontology Language. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds.) RSCTC 2010. LNCS (LNAI), vol. 6086, pp. 710–720. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  22. Nguyen, L.A., Szałas, A.: Three-Valued Paraconsistent Reasoning for Semantic Web Agents. In: Jędrzejowicz, P., Nguyen, N.T., Howlet, R.J., Jain, L.C. (eds.) KES-AMSTA 2010, Part I. LNCS, vol. 6070, pp. 152–162. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  23. Nguyen, N.T.: Using distance functions to solve representation choice problems. Fundam. Inform. 48(4), 295–314 (2001)

    Google Scholar 

  24. Nguyen, N.T.: Consensus system for solving conflicts in distributed systems. Inf. Sci. 147(1-4), 91–122 (2002)

    Article  MATH  Google Scholar 

  25. Nguyen, N.T.: Inconsistency of knowledge and collective intelligence. Cybernetics and Systems 39(6), 542–562 (2008)

    Article  MATH  Google Scholar 

  26. Nguyen, N.T., Truong, H.B.: A Consensus-Based Method for Fuzzy Ontology Integration. In: Pan, J.-S., Chen, S.-M., Nguyen, N.T. (eds.) ICCCI 2010, Part II. LNCS, vol. 6422, pp. 480–489. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  27. Odintsov, S.P., Wansing, H.: Inconsistency-tolerant description logic. part II: A tableau algorithm for CACLc. Journal of Applied Logic 6(3), 343–360 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  28. Straccia, U.: A Sequent Calculus for Reasoning in Four-Valued Description Logics. In: Galmiche, D. (ed.) TABLEAUX 1997. LNCS, vol. 1227, pp. 343–357. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  29. Vitória, A., Maluszyński, J., Szałas, A.: Modeling and reasoning in paraconsistent rough sets. Fundamenta Informaticae 97(4), 405–438 (2009)

    MATH  MathSciNet  Google Scholar 

  30. Zhang, X., Lin, Z., Wang, K.: Towards a Paradoxical Description Logic for the Semantic Web. In: Link, S., Prade, H. (eds.) FoIKS 2010. LNCS, vol. 5956, pp. 306–325. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  31. Zhang, X., Qi, G., Ma, Y., Lin, Z.: Quasi-classical semantics for expressive description logics. In: Proceedings of Description Logics (2009)

    Google Scholar 

  32. Zhang, X., Zhang, Z., Lin, Z.: An argumentative semantics for paraconsistent reasoning in description logic ALC. In: Proceedings of Description Logics (2009)

    Google Scholar 

  33. Zhang, X., Zhang, Z., Xu, D., Lin, Z.: Argumentation-Based Reasoning with Inconsistent Knowledge Bases. In: Farzindar, A., Kešelj, V. (eds.) Canadian AI 2010. LNCS, vol. 6085, pp. 87–99. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Linh Anh Nguyen & Andrzej Szałas

  2. Dept. of Computer and Information Science, Linköping University, SE-581 83, Linköping, Sweden

    Andrzej Szałas

Authors
  1. Linh Anh Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrzej Szałas
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Wroclaw University of Technology, Poland

    Ngoc Thanh Nguyen

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Nguyen, L.A., Szałas, A. (2012). Paraconsistent Reasoning for Semantic Web Agents. In: Nguyen, N.T. (eds) Transactions on Computational Collective Intelligence VI. Lecture Notes in Computer Science, vol 7190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29356-6_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29356-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29355-9

  • Online ISBN: 978-3-642-29356-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation