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Learning Description Logic Axioms from Discrete Probability Distributions over Description Graphs

  • Francesco KriegelEmail author
Conference paper
  • 267 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11468)

Abstract

Description logics in their standard setting only allow for representing and reasoning with crisp knowledge without any degree of uncertainty. Of course, this is a serious shortcoming for use cases where it is impossible to perfectly determine the truth of a statement. For resolving this expressivity restriction, probabilistic variants of description logics have been introduced. Their model-theoretic semantics is built upon so-called probabilistic interpretations, that is, families of directed graphs the vertices and edges of which are labeled and for which there exists a probability measure on this graph family. Results of scientific experiments, e.g., in medicine, psychology, or biology, that are repeated several times can induce probabilistic interpretations in a natural way. In this document, we shall develop a suitable axiomatization technique for deducing terminological knowledge from the assertional data given in such probabilistic interpretations. More specifically, we consider a probabilistic variant of the description logic \(\mathcal {E\!L}^{\!\bot }\), and provide a method for constructing a set of rules, so-called concept inclusions, from probabilistic interpretations in a sound and complete manner.

Keywords

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

Notes

Acknowledgments

The author gratefully thanks Franz Baader for drawing attention to the issue in [15], and furthermore thanks the reviewers for their constructive remarks.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Theoretical Computer ScienceTechnische Universität DresdenDresdenGermany

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