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An Asymptotic Analysis of Probabilistic Logic Programming, with Implications for Expressing Projective Families of Distributions

Published online by Cambridge University Press:  02 November 2021

FELIX Q. WEITKÄMPER Open the ORCID record for FELIX Q. WEITKÄMPER [Opens in a new window]
FELIX Q. WEITKÄMPER*
Affiliation:
Institut für Informatik, LMU München, Oettingenstr. 67, 80538 München (e-mail: felix.weitkaemper@lmu.de)
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Abstract

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Probabilistic logic programming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in a setting of uncertainty. However, the behaviour of statistical relational representations across variable domain sizes is complex, and scaling inference and learning to large domains remains a significant challenge. In recent years, connections have emerged between domain size dependence, lifted inference and learning from sampled subpopulations. The asymptotic behaviour of statistical relational representations has come under scrutiny, and projectivity was investigated as the strongest form of domain size dependence, in which query marginals are completely independent of the domain size. In this contribution we show that every probabilistic logic program under the distribution semantics is asymptotically equivalent to an acyclic probabilistic logic program consisting only of determinate clauses over probabilistic facts. We conclude that every probabilistic logic program inducing a projective family of distributions is in fact everywhere equivalent to a program from this fragment, and we investigate the consequences for the projective families of distributions expressible by probabilistic logic programs.

Keywords

probabilistic logic programmingasymptotic quantifier eliminationdeterminate logic programsprojective families of distributionsfinite model theorydistribution semantics
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 21 , Special Issue 6: 37th International Conference on Logic Programming Special Issue II , November 2021 , pp. 802 - 817
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

*

We would like to thank Manfred Jaeger for his encouragement and for helpful conversations about the subject of this paper, and the anonymous reviewers for facilitating a clearer exposition of the material.

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