Axiomatization of General Concept Inclusions in Probabilistic Description Logics

  • Francesco Kriegel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9324)


Probabilistic interpretations consist of a set of interpretations with a shared domain and a measure assigning a probability to each interpretation. Such structures can be obtained as results of repeated experiments, e.g., in biology, psychology, medicine, etc. A translation between probabilistic and crisp description logics is introduced and then utilized to reduce the construction of a base of general concept inclusions of a probabilistic interpretation to the crisp case for which a method for the axiomatization of a base of GCIs is well-known.


Probabilistic description logics Machine learning  Knowledge base General concept inclusion 


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  1. 1.
    Baader, F., Distel, F.: A finite basis for the set of EL-implications holding in a finite model. Tech. rep. 07–02. Dresden, Germany: Inst. für Theoretische Informatik. TU, Dresden (2007)Google Scholar
  2. 2.
    Baader, F., Distel, F.: A finite basis for the set of 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) CrossRefGoogle Scholar
  3. 3.
    Borchmann, D., Distel, F., Kriegel, F.: Axiomatization of General Concept Inclusions from Finite Interpretations. LTCS-Report 15–13. Dresden, Germany: Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universität Dresden (2015)Google Scholar
  4. 4.
    Distel, F.: Learning Description Logic Knowledge Bases from Data using Methods from Formal Concept Analysis. PhD thesis. Dresden University of Technology, Dresden (2011)Google Scholar
  5. 5.
    Ecke, A., Peñaloza, R., Turhan, A.-Y.: Completion-based Generalization Inferences for the Description Logic \(\cal ELOR\) with Subjective Probabilities. International Journal of Approximate Reasoning 55(9), 1939–1970 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ecke, A., Peñaloza, R., Turhan, A.-Y.: Role-depth bounded least common subsumer in prob-\(\cal EL\) with nominals. In: Eiter, T., et al. (eds.) Proceedings of the 26th International Workshop on Description Logics, DL 2013, vol. 1014, pp. 670–688. CEUR-WS. Germany (2013)Google Scholar
  7. 7.
    Kriegel, F.: Extracting ALEQR(Self)-knowledge bases from graphs. In: Proceedings of the International Workshop on Social Network Analysis using Formal Concept Analysis, SNAFCA 2015. CEUR Workshop Proceedings. (2015)Google Scholar
  8. 8.
    Lutz, C., Schröder, L.: Probabilistic description logics for subjective uncertainty. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Twelfth International Conference, KR 2010, Toronto, Ontario, Canada (May 9–13, 2010)Google Scholar
  9. 9.
    Peñaloza, R., Turhan, A.-Y.: Instance-Based non-standard inferences in \(\cal EL\) with subjective probabilities. In: Bobillo, F., Costa, P.C.G., d’Amato, C., Fanizzi, N., Laskey, K.B., Laskey, K.J., Lukasiewicz, T., Nickles, M., Pool, M. (eds.) URSW 2008-2010/UniDL 2010. LNCS, vol. 7123, pp. 80–98. Springer, Heidelberg (2013)Google Scholar
  10. 10.
    Peñaloza, R., Turhan, A.-Y.: Role-depth bounded least common subsumers by completion for \(\cal EL\)- and prob-\(\cal EL\)-TBoxes. In: Haarslev, V., Toman, D., Weddell, G. (eds.) Proc. of the 2010 Description Logic Workshop, DL 2010, vol. 573. CEUR-WS (2010)Google Scholar
  11. 11.
    Peñaloza, R., Turhan, A.-Y.: Towards Approximative Most Specific Concepts by Completion for EL with Subjective Probabilities. In: Lukasiewicz, T., Peñaloza, R., Turhan, A.-Y. (eds.) Proceedings of the First International Workshop on Uncertainty in Description Logics, UniDL 2010, vol. 613. CEUR-WS (2010)Google Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute for Theoretical Computer ScienceTU DresdenDresdenGermany

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