Skip to main content
SpringerLink
Log in

Interpolation Theorems for Some Extended Description Logics

  • Conference paper
Knowlege-Based and Intelligent Information and Engineering Systems (KES 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6882))

  • 1277 Accesses

Abstract

Description logics have been studied as a logical foundation of web ontology languages. Interpolation theorems for description logics are known to be useful for extracting modular ontologies. In this paper, the interpolation theorems for two extended paraconsistent and temporal description logics are proved using some theorems for embedding these logics into a standard description logic.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Almukdad, A., Nelson, D.: Constructible falsity and inexact predicates. Journal of Symbolic Logic 49, 231–233 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  2. Artale, A., Franconi, E.: A survey of temporal extensions of description logics. Annals of Mathematics and Artificial Intelligence 30, 171–210 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baader, F., Bauer, A., Lippmann, M.: Runtime verification using a temporal description logic. In: Ghilardi, S., Sebastiani, R. (eds.) FroCoS 2009. LNCS, vol. 5749, pp. 149–164. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  4. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds.): The description logic handbook: Theory, implementation and applications. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  5. Baader, F., Ghilardi, S., Lutz, C.: LTL over description logic axioms. In: Proceedings of the 11th International Conference on Principles of Knowledge Representation and Reasoning (KR 2008), pp. 684–694. AAAI Press, Menlo Park (2008)

    Google Scholar 

  6. ten Cate, B., Conradie, W., Marx, M., Venema, Y.: Definitorially complete description logics. In: Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning (KR 2006), pp. 79–89. AAAI Press, Menlo Park (2006)

    Google Scholar 

  7. Craig, W.: Three uses of the Herbrand-Gentzen theorems in relating model theory and proof theory. Journal of Symbolic Logic 22(3), 269–285 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  8. Eiter, T., Wang, K.: Semantic forgetting in answer set programming. Artificial Intelligence 172(14), 1644–1672 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gurevich, Y.: Intuitionistic logic with strong negation. Studia Logica 36, 49–59 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kamide, N.: Paraconsistent description logics revisited. In: Proceedings of the 23rd International Workshop on Description Logics (DL 2010), CEUR Workshop Proceedings, vol. 573 (2010)

    Google Scholar 

  11. Kamide, N.: A compatible approach to temporal description logics. In: Proceedings of the 23rd International Workshop on Description Logics (DL 2010), CEUR Workshop Proceedings, vol. 573 (2010)

    Google Scholar 

  12. Knov, B., Walther, D., Wolter, F.: Forgetting and uniform interpolation in large-scale description logic terminologies. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence, pp. 830–835 (2009)

    Google Scholar 

  13. Kontchakov, R., Wolter, F., Zakharyaschev, M.: Can you tell the difference between DL-Lite ontologies? In: Proceedings of the 11th International Conference on Principles of Knowledge Representation and Reasoning (KR 2008), pp. 285–295 (2008)

    Google Scholar 

  14. Lutz, C., Wolter, F., Zakharyashev, M.: Temporal description logics: A survey. In: Proceedings of the 15th International Symposium on Temporal Representation and Reasoning (TIME 2008), pp. 3–14. IEEE Computer Society, Los Alamitos (2008)

    Chapter  Google Scholar 

  15. Ma, Y., Hitzler, P., Lin, Z.: Algorithms for paraconsistent reasoning with OWL. In: Franconi, E., Kifer, M., May, W. (eds.) ESWC 2007. LNCS, vol. 4519, pp. 399–413. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Ma, Y., Hitzler, P., Lin, Z.: Paraconsistent reasoning for expressive and tractable description logics. In: Proceedings of the 21st International Workshop on Description Logic (DL 2008), CEUR Workshop Proceedings, vol. 353 (2008)

    Google Scholar 

  17. Meghini, C., Straccia, U.: A relevance terminological logic for information retrieval. In: Proceedings of the 19th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 197–205 (1996)

    Google Scholar 

  18. Meghini, C., Sebastiani, F., Straccia, U.: Mirlog: A logic for multimedia information retrieval. In: Uncertainty and Logics: Advanced Models for the Representation and Retrieval of Information, pp. 151–185. Kluwer Academic Publishing, Dordrecht (1998)

    Chapter  Google Scholar 

  19. Nelson, D.: Constructible falsity. Journal of Symbolic Logic 14, 16–26 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  20. Odintsov, S.P., Wansing, H.: Inconsistency-tolerant description logic: Motivation and basic systems. In: Hendricks, V.F., Malinowski, J. (eds.) Trends in Logic: 50 Years of Studia Logica, pp. 301–335. Kluwer Academic Publishers, Dordrecht (2003)

    Chapter  Google Scholar 

  21. Odintsov, S.P., Wansing, H.: Inconsistency-tolerant Description Logic. Part II: Tableau Algorithms. Journal of Applied Logic 6, 343–360 (2008)

    MATH  Google Scholar 

  22. Patel-Schneider, P.F.: A four-valued semantics for terminological logics. Artificial Intelligence 38, 319–351 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  23. Prior, A.N.: Time and modality. Clarendon Press, Oxford (1957)

    MATH  Google Scholar 

  24. Prior, A.N.: Past, present and future. Clarendon Press, Oxford (1967)

    Book  MATH  Google Scholar 

  25. Rautenberg, W.: Klassische und nicht-klassische Aussagenlogik, Vieweg, Braunschweig (1979)

    Google Scholar 

  26. Schmidt-Schauss, M., Smolka, G.: Attributive concept descriptions with complements. Artificial Intelligence 48, 1–26 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  27. 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 

  28. Wang, Z., Wang, K., Topor, R.W., Pan, J.Z.: Forgetting concepts in DL-Lite. In: Bechhofer, S., Hauswirth, M., Hoffmann, J., Koubarakis, M. (eds.) ESWC 2008. LNCS, vol. 5021, pp. 245–257. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  29. Wansing, H.: The Logic of Information Structures. LNCS (LNAI), vol. 681, pp. 1–163. Springer, Heidelberg (1993)

    MATH  Google Scholar 

  30. Wansing, H.: Displaying The Modal Logic of Consistency. Journal of Symbolic Logic 64(4), 1573–1590 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  31. Wolter, F., Zakharyashev, M.: Temporalizing description logic. In: Gabbay, D., de Rijke, M. (eds.) Frontiers of Combining Systems, pp. 379–402. Studies Press/Wiley (1999)

    Google Scholar 

  32. Zhang, X., Lin, Z.: Paraconsistent reasoning with quasi-classical semantics in \({\cal ALC}\). In: Calvanese, D., Lausen, G. (eds.) RR 2008. LNCS, vol. 5341, pp. 222–229. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  33. Zhang, X., Qi, G., Ma, Y., Lin, Z.: Quasi-classical semantics for expressive description logics. In: Proceedings of the 22nd International Workshop on Description Logic (DL 2009), CEUR Workshop Proceedings, vol. 477 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Waseda Institute for Advanced Study, Waseda University, 1-6-1 Nishi Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan

    Norihiro Kamide

Authors
  1. Norihiro Kamide
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Integrated Sensor Systems, University of Kaiserslautern, Erwin-Schroedinger-str. 12, 67663, Kaiserslautern, Germany

    Andreas König

  2. Knowledge-Based Systems Group, Department of Computer Science, University of Kaiserslautern, P.O. Box 3049, 67653, Kaiserslautern, Germany

    Andreas Dengel

  3. School of Business, University of Applied Sciences Northwestern Switzerland, Riggenbachstr. 16, 4600, Olten, Switzerland

    Knut Hinkelmann

  4. Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, 599-8531, Sakai,, Osaka, Japan

    Koichi Kise

  5. KES International, P.O. Box 2115, BN43 9AF, Shoreham-by-sea, UK

    Robert J. Howlett

  6. University of South Australia, Adelaide, 5095, Mawson Lakes, SA, Australia

    Lakhmi C. Jain

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kamide, N. (2011). Interpolation Theorems for Some Extended Description Logics. In: König, A., Dengel, A., Hinkelmann, K., Kise, K., Howlett, R.J., Jain, L.C. (eds) Knowlege-Based and Intelligent Information and Engineering Systems. KES 2011. Lecture Notes in Computer Science(), vol 6882. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23863-5_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-23863-5_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23862-8

  • Online ISBN: 978-3-642-23863-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation