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Achieving parametric uniformity for knowledge bases in a relational probabilistic conditional logic with maximum entropy semantics

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Abstract

When extending probabilistic logic to a relational setting, it is desirable to still be able to use efficient computation mechanisms developed for the propositional case. In this paper, we investigate the relational probabilistic conditional logic FO-PCL whose semantics employs the principle of maximum entropy. While in general, this semantics is defined via the ground instances of the rules in an FO-PCL knowledge base \({\cal R}\), the maximum entropy model can be computed on the level of rules rather than on the level of instances of the rules if \({\cal R}\) is parametrically uniform. We elaborate in detail the reasons that cause \({\cal R}\) to be not parametrically uniform. Based on this investigation, we derive a new syntactic criterion for parametric uniformity and develop an algorithm that transforms any FO-PCL knowledge base \({\cal R}\) into an equivalent knowledge base \({\cal R}^{\prime}\) that is parametrically uniform. This provides a basis for a simplified maximum entropy model computation since for this computation, \({\cal R}^{\prime}\) can be used instead of \({\cal R}\).

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Authors and Affiliations

  1. Department of Computer Science, FernUniversität in Hagen, 58084, Hagen, Germany

    Christoph Beierle & Annika Krämer

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  1. Christoph Beierle
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  2. Annika Krämer
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Correspondence to Christoph Beierle.

Additional information

The research reported here was supported by the Deutsche Forschungsgemeinschaft (grant BE 1700/7-2).

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Beierle, C., Krämer, A. Achieving parametric uniformity for knowledge bases in a relational probabilistic conditional logic with maximum entropy semantics. Ann Math Artif Intell 73, 5–45 (2015). https://doi.org/10.1007/s10472-013-9369-3

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