Integrating Belief Domains into Probabilistic Logic Programs

Damiano Azzolini, Fabrizio Riguzzi, Theresa Swift
7/23/2025
cs.LOcs.AI

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Abstract

Probabilistic Logic Programming (PLP) under the Distribution Semantics is a leading approach to practical reasoning under uncertainty. An advantage of the Distribution Semantics is its suitability for implementation as a Prolog or Python library, available through two well-maintained implementations, namely ProbLog and cplint/PITA. However, current formulations of the Distribution Semantics use point-probabilities, making it difficult to express epistemic uncertainty, such as arises from, for example, hierarchical classifications from computer vision models. Belief functions generalize probability measures as non-additive capacities, and address epistemic uncertainty via interval probabilities. This paper introduces interval-based Capacity Logic Programs based on an extension of the Distribution Semantics to include belief functions, and describes properties of the new framework that make it amenable to practical applications.

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Cite this paper

@article{azzolini2025integrating,
  title  = {Integrating Belief Domains into Probabilistic Logic Programs},
  author = {Damiano Azzolini and Fabrizio Riguzzi and Theresa Swift},
  year   = {2025},
  eprint = {2507.17291},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2507.17291v2}
}

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