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Axiomatization of General Concept Inclusions in Probabilistic Description Logics

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KI 2015: Advances in Artificial Intelligence (KI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9324))

Abstract

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.

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References

  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. 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)

    Chapter  Google Scholar 

  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. 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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. CEUR-WS.org (2015)

    Google Scholar 

  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. 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. 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. 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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Correspondence to Francesco Kriegel .

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Kriegel, F. (2015). Axiomatization of General Concept Inclusions in Probabilistic Description Logics. In: Hölldobler, S., , Peñaloza, R., Rudolph, S. (eds) KI 2015: Advances in Artificial Intelligence. KI 2015. Lecture Notes in Computer Science(), vol 9324. Springer, Cham. https://doi.org/10.1007/978-3-319-24489-1_10

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  • DOI: https://doi.org/10.1007/978-3-319-24489-1_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24488-4

  • Online ISBN: 978-3-319-24489-1

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