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Counting Strategies for the Probabilistic Description Logic \(\mathcal {ALC}^\mathsf {ME}\) Under the Principle of Maximum Entropy

  • Marco WilhelmEmail author
  • Gabriele Kern-Isberner
  • Andreas Ecke
  • Franz Baader
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11468)

Abstract

We present \(\mathcal {ALC}^\mathsf {ME}\), a probabilistic variant of the Description Logic \(\mathcal {ALC}\) that allows for representing and processing conditional statements of the form “if E holds, then F follows with probability p” under the principle of maximum entropy. Probabilities are understood as degrees of belief and formally interpreted by the aggregating semantics. We prove that both checking consistency and drawing inferences based on approximations of the maximum entropy distribution is possible in \(\mathcal {ALC}^\mathsf {ME}\) in time polynomial in the domain size. A major problem for probabilistic reasoning from such conditional knowledge bases is to count models and individuals. To achieve our complexity results, we develop sophisticated counting strategies on interpretations aggregated with respect to the so-called conditional impacts of types, which refine their conditional structure.

Keywords

Probabilistic description logics Aggregating semantics Principle of maximum entropy Domain-lifted inference 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceTU DortmundDortmundGermany
  2. 2.Department of Computer ScienceTU DresdenDresdenGermany

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