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DOI: 10.4230/OASIcs.SLATE.2025.3

Elements for Weighted Answer-Set Programming

Authors: Francisco Coelho, Bruno Dinis, Dietmar Seipel, and Salvador Abreu

Published in: OASIcs, Volume 135, 14th Symposium on Languages, Applications and Technologies (SLATE 2025)

Abstract

Logic programs, more specifically, answer-set programs, can be annotated with probabilities on facts to express uncertainty. We address the problem of propagating weight annotations on facts (e.g. probabilities) of an answer-set program to its stable models, and from there to events (defined as sets of atoms) in a dataset over the program’s domain. We propose a novel approach which is algebraic in the sense that it relies on an equivalence relation over the set of events. Uncertainty is then described as polynomial expressions over variables. We propagate the weight function in the space of models and events, rather than doing so within the syntax of the program. As evidence that our approach is sound, we show that certain facts behave as expected. Our approach allows us to investigate weight annotated programs and to determine how suitable a given one is for modeling a given dataset containing events. It’s core is illustrated by a running example and the encoding of a Bayesian network.

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Francisco Coelho, Bruno Dinis, Dietmar Seipel, and Salvador Abreu. Elements for Weighted Answer-Set Programming. In 14th Symposium on Languages, Applications and Technologies (SLATE 2025). Open Access Series in Informatics (OASIcs), Volume 135, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{coelho_et_al:OASIcs.SLATE.2025.3,
  author =	{Coelho, Francisco and Dinis, Bruno and Seipel, Dietmar and Abreu, Salvador},
  title =	{{Elements for Weighted Answer-Set Programming}},
  booktitle =	{14th Symposium on Languages, Applications and Technologies (SLATE 2025)},
  pages =	{3:1--3:16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-387-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{135},
  editor =	{Baptista, Jorge and Barateiro, Jos\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SLATE.2025.3},
  URN =		{urn:nbn:de:0030-drops-236836},
  doi =		{10.4230/OASIcs.SLATE.2025.3},
  annote =	{Keywords: Answer-Set Programming, Stable Models, Probabilistic Logic Programming}
}

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Elements for Weighted Answer-Set Programming

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