Skip to main content
SpringerLink
Log in

Reasoning on \(\textit{DL-Lite}_\mathcal{R}\) with Defeasibility in ASP

  • Conference paper
  • First Online:
Rules and Reasoning (RuleML+RR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11784))

Included in the following conference series:

Abstract

Reasoning on defeasible knowledge is a topic of interest in the area of description logics, as it is related to the need of representing exceptional instances in knowledge bases. In this direction, in our previous works we presented a framework for representing (contextualized) OWL RL knowledge bases with a notion of justified exceptions on defeasible axioms: reasoning in such framework is realized by a translation into ASP programs. The resulting reasoning process for OWL RL, however, introduces a complex encoding in order to capture reasoning on the negative information needed for reasoning on exceptions. In this paper, we apply the justified exception approach to knowledge bases in \(\textit{DL-Lite}_\mathcal{R}\), i.e. the language underlying OWL QL. We provide a definition for \(\textit{DL-Lite}_\mathcal{R}\) knowledge bases with defeasible axioms and study their semantic and computational properties. The limited form of \(\textit{DL-Lite}_\mathcal{R}\) axioms allows us to formulate a simpler encoding into ASP programs, where reasoning on negative information is managed by direct rules. The resulting materialization method gives rise to a complete reasoning procedure for instance checking in \(\textit{DL-Lite}_\mathcal{R}\) with defeasible axioms.

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 EPUB and 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

Notes

  1. 1.

    In the following, we will use C to denote a left-side concept and D as a right-side concept.

  2. 2.

    Strong negation can be easily emulated using fresh atoms and weak negation resp. constraints. While it does not yield higher expressiveness, it is more convenient for presentation.

  3. 3.

    Note that, by the normal form above, this kind of axioms is in the form \(A_{\exists R} \sqsubseteq \exists R\).

  4. 4.

    The models of \( CIRC (F;P,\emptyset ;\{z\})\) are all models M of F such that no model \(M'\) of F exists with \(M'\setminus \{z\} \subset M\setminus \{z\}\).

References

  1. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  2. Bonatti, P.A., Faella, M., Petrova, I., Sauro, L.: A new semantics for overriding in description logics. Artif. Intell. 222, 1–48 (2015)

    Article  MathSciNet  Google Scholar 

  3. Bonatti, P.A., Faella, M., Sauro, L.: Defeasible inclusions in low-complexity DLs. J. Artif. Intell. Research 42, 719–764 (2011)

    MathSciNet  MATH  Google Scholar 

  4. Bonatti, P.A., Lutz, C., Wolter, F.: Description logics with circumscription. In: KR 2006, pp. 400–410. AAAI Press (2006)

    Google Scholar 

  5. Bozzato, L., Eiter, T., Serafini, L.: Contextualized knowledge repositories with justifiable exceptions. In: DL2014. CEUR-WP, vol. 1193, pp. 112–123 (2014). CEUR-WS.org

  6. Bozzato, L., Eiter, T., Serafini, L.: Enhancing context knowledge repositories with justifiable exceptions. Artif. Intell. 257, 72–126 (2018)

    Article  MathSciNet  Google Scholar 

  7. Bozzato, L., Homola, M., Serafini, L.: Towards more effective tableaux reasoning for CKR. In: DL2012, CEUR-WP, vol. 846, pp. 114–124 (2012). CEUR-WS.org

  8. Bozzato, L., Serafini, L.: Materialization calculus for contexts in the semantic web. In: DL2013, CEUR-WP, vol. 1014, pp. 552–572 (2013). CEUR-WS.org

  9. Bozzato, L., Serafini, L., Eiter, T.: Reasoning with justifiable exceptions in contextual hierarchies. In: KR 2018, pp. 329–338. AAAI Press (2018)

    Google Scholar 

  10. Britz, K., Varzinczak, I.: Introducing role defeasibility in description logics. In: Michael, L., Kakas, A. (eds.) JELIA 2016. LNCS (LNAI), vol. 10021, pp. 174–189. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-48758-8_12

    Chapter  MATH  Google Scholar 

  11. de Bruijn, J., Eiter, T., Tompits, H.: Embedding approaches to combining rules and ontologies into autoepistemic logic. In: KR 2008, pp. 485–495. AAAI Press (2008)

    Google Scholar 

  12. Cadoli, M., Lenzerini, M.: The complexity of propositional closed world reasoning and circumscription. J. Comput. Syst. Sci. 48(2), 255–310 (1994)

    Article  MathSciNet  Google Scholar 

  13. Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: the DL-Lite family. J. Autom. Reasoning 39(3), 385–429 (2007)

    Article  MathSciNet  Google Scholar 

  14. Casini, G., Straccia, U.: Rational closure for defeasible description logics. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS (LNAI), vol. 6341, pp. 77–90. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15675-5_9

    Chapter  MATH  Google Scholar 

  15. Eiter, T., Ianni, G., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Combining answer set programming with description logics for the semantic web. Artif. Intell. 172(12–13), 1495–1539 (2008)

    Article  MathSciNet  Google Scholar 

  16. Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Gener. Comput. 9, 365–385 (1991)

    Article  Google Scholar 

  17. Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: Reasoning about typicality in low complexity DLs: the logics \(\cal{EL}^{\bot }T_{min}\) and DL-Lite\(_{c}T_{min}\). In: Walsh, T. (ed.) IJCAI 2011, pp. 894–899. IJCAI/AAAI (2011)

    Google Scholar 

  18. Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: A non-monotonic description logic for reasoning about typicality. Artif. Intell. 195, 165–202 (2013)

    Article  MathSciNet  Google Scholar 

  19. Krötzsch, M.: Efficient inferencing for OWL EL. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS (LNAI), vol. 6341, pp. 234–246. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15675-5_21

    Chapter  Google Scholar 

  20. Lembo, D., Lenzerini, M., Rosati, R., Ruzzi, M., Savo, D.F.: Inconsistency-tolerant semantics for description logics. In: Hitzler, P., Lukasiewicz, T. (eds.) RR 2010. LNCS, vol. 6333, pp. 103–117. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15918-3_9

    Chapter  Google Scholar 

  21. Motik, B., Fokoue, A., Horrocks, I., Wu, Z., Lutz, C., Grau, B.C.: OWL 2 web ontology language profiles. In: W3C Recommendation, W3C, October 2009

    Google Scholar 

  22. Pensel, M., Turhan, A.: Reasoning in the defeasible description logic \(\cal{EL}_{\bot }\) - computing standard inferences under rational and relevant semantics. Int. J. Approx. Reasoning 103, 28–70 (2018)

    Article  MathSciNet  Google Scholar 

  23. Serafini, L., Homola, M.: Contextualized knowledge repositories for the semantic web. J. Web Semant. 12, 64–87 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fondazione Bruno Kessler, Via Sommarive 18, 38123, Trento, Italy

    Loris Bozzato & Luciano Serafini

  2. Institute of Logic and Computation, Technische Universität Wien, Favoritenstraße 9-11, 1040, Vienna, Austria

    Thomas Eiter

Authors
  1. Loris Bozzato
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Eiter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luciano Serafini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Loris Bozzato .

Editor information

Editors and Affiliations

  1. Stony Brook University, Stony Brook, NY, USA

    Paul Fodor

  2. Free University of Bozen-Bolzano, Bolzano, Italy

    Marco Montali

  3. Free University of Bozen-Bolzano, Bolzano, Italy

    Diego Calvanese

  4. SINTEF AS, Oslo, Norway

    Dumitru Roman

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bozzato, L., Eiter, T., Serafini, L. (2019). Reasoning on \(\textit{DL-Lite}_\mathcal{R}\) with Defeasibility in ASP. In: Fodor, P., Montali, M., Calvanese, D., Roman, D. (eds) Rules and Reasoning. RuleML+RR 2019. Lecture Notes in Computer Science(), vol 11784. Springer, Cham. https://doi.org/10.1007/978-3-030-31095-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-31095-0_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-31094-3

  • Online ISBN: 978-3-030-31095-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation