Finite Model Reasoning in DL-Lite

  • Riccardo Rosati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5021)


The semantics of OWL-DL and its subclasses are based on the classical semantics of first-order logic, in which the interpretation domain may be an infinite set. This constitutes a serious expressive limitation for such ontology languages, since, in many real application scenarios for the Semantic Web, the domain of interest is actually finite, although the exact cardinality of the domain is unknown. Hence, in these cases the formal semantics of the OWL-DL ontology does not coincide with its intended semantics. In this paper we start filling this gap, by considering the subclasses of OWL-DL which correspond to the logics of the DL-Lite family, and studying reasoning over finite models in such logics. In particular, we mainly consider two reasoning problems: deciding satisfiability of an ontology, and answering unions of conjunctive queries (UCQs) over an ontology. We first consider the description logic \({\textit{DL-Lite}_R}\) and show that, for the two above mentioned problems, finite model reasoning coincides with classical reasoning, i.e., reasoning over arbitrary, unrestricted models. Then, we analyze the description logics \({\textit{DL-Lite}_F}\) and \({\textit{DL-Lite}_A}\). Differently from \({\textit{DL-Lite}_R}\), in such logics finite model reasoning does not coincide with classical reasoning. To solve satisfiability and query answering over finite models in these logics, we define techniques which reduce polynomially both the above reasoning problems over finite models to the corresponding problem over arbitrary models. Thus, for all the DL-Lite languages considered, the good computational properties of satisfiability and query answering under the classical semantics also hold under the finite model semantics. Moreover, we have effectively and easily implemented the above techniques, extending the DL-Lite reasoner QuOnto with support for finite model reasoning.


Knowledge Base Description Logic Model Reasoning Conjunctive Query Classical Semantic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
  2. 2.
    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)MATHGoogle Scholar
  3. 3.
    Bechhofer, S., van Harmelen, F., Hendler, J., Horrocks, I., McGuinness, D.L., Patel-Schneider, P.F., Stein, L.A.: OWL Web Ontology Language reference. W3C Recommendation (February 2004), available at
  4. 4.
    Calvanese, D.: Finite model reasoning in description logics. In: Proc. of KR 1996, pp. 292–303 (1996)Google Scholar
  5. 5.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Poggi, A., Rosati, R.: MASTRO-I: Efficient integration of relational data through dl ontologies. In: Proceedings of the 2007 International Workshop on Description Logic (DL 2007). CEUR Electronic Workshop Proceedings (2007)Google Scholar
  6. 6.
    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. of Automated Reasoning 39, 385–429 (2007)MATHCrossRefGoogle Scholar
  7. 7.
    Cosmadakis, S.S., Kanellakis, P.C., Vardi, M.: Polynomial-time implication problems for unary inclusion dependencies. J. of the ACM 37(1), 15–46 (1990)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Cuenca Grau, B.: Tractable fragments of the OWL 1.1 Web Ontology Language,
  9. 9.
    Glimm, B., Horrocks, I., Lutz, C., Sattler, U.: Conjunctive query answering for the description logic SHIQ. In: Proc. of the 20th Int. Joint Conf. on Artificial Intelligence (IJCAI 2007), pp. 399–404 (2007)Google Scholar
  10. 10.
    Lutz, C., Sattler, U., Tendera, L.: The complexity of finite model reasoning in description logics. Information and Computation 199, 132–171 (2005)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Rosati, R.: On the decidability and finite controllability of query processing in databases with incomplete information. In: Proc. of PODS 2006, pp. 356–365 (2006)Google Scholar
  12. 12.
    Shadbolt, N., Hall, W., Berners-Lee, T.: The semantic web revisited. IEEE Intelligent Systems, 96–101 (May-June 2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Riccardo Rosati
    • 1
  1. 1.Dipartimento di Informatica e SistemisticaSapienza Università di RomaRomaItaly

Personalised recommendations