Advertisement

Including Quantification in Defeasible Reasoning for the Description Logic \(\mathcal {EL} _{\bot } \)

  • Maximilian Pensel
  • Anni-Yasmin Turhan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10377)

Abstract

Defeasible Description Logics (DDLs) can state defeasible concept inclusions and often use rational closure according to the KLM postulates for reasoning. If in DDLs with quantification a defeasible subsumption relationship holds between concepts, it can also hold if these concepts appear nested in existential restrictions. Earlier reasoning algorithms did not detect this kind of relationships. We devise a new form of canonical models that extend classical ones for \(\mathcal {EL} _{\bot }\) by elements that satisfy increasing amounts of defeasible knowledge and show that reasoning w.r.t. these models yields the missing rational entailments.

References

  1. 1.
    Brandt, S.: Polynomial time reasoning in a description logic with existential restrictions, GCI axioms, and–what else? In: Proceedings of ECAI 2004, pp. 298–302 (2004)Google Scholar
  2. 2.
    Britz, A., Casini, G., Meyer, T., Moodley, K., Varzinczak, I.: Ordered interpretations and entailment for defeasible description logics. CAIR & UKZN, Technical report (2013)Google Scholar
  3. 3.
    Casini, G., Meyer, T., Moodley, K., Nortjé, R.: Relevant closure: a new form of defeasible reasoning for description logics. In: Fermé, E., Leite, J. (eds.) JELIA 2014. LNCS (LNAI), vol. 8761, pp. 92–106. Springer, Cham (2014). doi: 10.1007/978-3-319-11558-0_7 Google Scholar
  4. 4.
    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). doi: 10.1007/978-3-642-15675-5_9 CrossRefGoogle Scholar
  5. 5.
    Casini, G., Straccia, U.: Lexicographic closure for defeasible description logics. In: Proceedings of the 8th Australasian Ontology Workshop, pp. 28–39 (2012)Google Scholar
  6. 6.
    Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: Semantic characterization of rational closure: from propositional logic to description logics. Artif. Intell. 226, 1–33 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kraus, S., Lehmann, D.J., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44(1–2), 167–207 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artif. Intell. 55, 1–60 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Pensel, M., Turhan, A.-Y.: Including quantification in defeasible reasoning for the description logic \(\cal{EL}_{\bot }\). LTCS-Report 17–01, TU Dresden (2017). http://lat.inf.tu-dresden.de/research/reports.html

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute for Theoretical Computer ScienceTechnische Universität DresdenDresdenGermany

Personalised recommendations