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Acquisition of Terminological Knowledge in Probabilistic Description Logic

  • Francesco Kriegel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11117)

Abstract

For a probabilistic extension of the description logic \({\mathcal {\mathcal {E\!L}}}^{\!\bot }\), we consider the task of automatic acquisition of terminological knowledge from a given probabilistic interpretation. Basically, such a probabilistic interpretation is a family of directed graphs the vertices and edges of which are labeled, and where a discrete probability measure on this graph family is present. The goal is to derive so-called concept inclusions which are expressible in the considered probabilistic description logic and which hold true in the given probabilistic interpretation. A procedure for an appropriate axiomatization of such graph families is proposed and its soundness and completeness is justified.

Keywords

Data mining Knowledge acquisition Probabilistic description logic Knowledge base Probabilistic interpretation Concept inclusion 

Notes

Acknowledgements

The author gratefully thanks Franz Baader for drawing attention to the issue in [6], and furthermore thanks the anonymous reviewers for their constructive hints and helpful remarks.

References

  1. 1.
    Baader, F., Distel, F.: A finite basis for the set of \(\cal{EL}\)-implications holding in a finite model. In: Medina, R., Obiedkov, S. (eds.) ICFCA 2008. LNCS (LNAI), vol. 4933, pp. 46–61. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-78137-0_4CrossRefGoogle Scholar
  2. 2.
    Baader, F., Horrocks, I., Lutz, C., Sattler, U.: An Introduction to Description Logic. Cambridge University Press, Cambridge (2017)CrossRefGoogle Scholar
  3. 3.
    Borchmann, D., Distel, F., Kriegel, F.: Axiomatisation of general concept inclusions from finite interpretations. J. Appl. Non-Class. Logics 26(1), 1–46 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Distel, F.: Learning description logic knowledge bases from data using methods from formal concept analysis. Doctoral thesis, Technische Universität Dresden (2011)Google Scholar
  5. 5.
    Gutiérrez-Basulto, V., Jung, J.C., Lutz, C., Schröder, L.: Probabilistic description logics for subjective uncertainty. J. Artif. Intell. Res. 58, 1–66 (2017)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kriegel, F.: Axiomatization of general concept inclusions in probabilistic description logics. In: Hölldobler, S., Krötzsch, M., Peñaloza, R., Rudolph, S. (eds.) KI 2015. LNCS (LNAI), vol. 9324, pp. 124–136. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-24489-1_10CrossRefGoogle Scholar
  7. 7.
    Kriegel, F.: Incremental learning of TBoxes from interpretation sequences with methods of formal concept analysis. In: Calvanese, D., Konev, B. (eds.) Proceedings of the 28th International Workshop on Description Logics, Athens, Greece, 7–10 June 2015. CEUR Workshop Proceedings, vol. 1350. CEUR-WS.org (2015)Google Scholar
  8. 8.
    Kriegel, F.: Acquisition of terminological knowledge from social networks in description logic. In: Missaoui, R., Kuznetsov, S.O., Obiedkov, S. (eds.) Formal Concept Analysis of Social Networks. LNSN, pp. 97–142. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-64167-6_5CrossRefGoogle Scholar
  9. 9.
    Kriegel, F.: Terminological knowledge acquisition in probabilistic description logic. LTCS-Report 18–03, Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute of Theoretical Computer ScienceTechnische Universität DresdenDresdenGermany

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