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Elements for Weighted Answer-Set Programming

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

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  • Theory of computation → Program semantics
Keywords
  • Answer-Set Programming
  • Stable Models
  • Probabilistic Logic Programming

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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) https://doi.org/10.4230/OASIcs.SLATE.2025.3

Author Details

Francisco Coelho
  • NOVA-LINCS, University of Évora, Portugal
Bruno Dinis
  • CIMA, University of Évora, Portugal
Dietmar Seipel
  • Universität Würzburg, Germany
Salvador Abreu
  • NOVA-LINCS, University of Évora, Portugal

Funding

This work is supported by UID/04516/NOVA Laboratory for Computer Science and Informatics (NOVA LINCS) with the financial support of FCT.IP.

Acknowledgements

The authors are grateful to Lígia Henriques-Rodrigues, Matthias Knorr and Ricardo Gonçalves for valuable comments on a preliminary version of this paper, and Alice Martins for contributions on software development.

References

  1. Weronika T Adrian, Mario Alviano, Francesco Calimeri, Bernardo Cuteri, Carmine Dodaro, Wolfgang Faber, Davide Fuscà, Nicola Leone, Marco Manna, Simona Perri, et al. The asp system dlv: advancements and applications. KI-Künstliche Intelligenz, 32:177-179, 2018. URL: https://doi.org/10.1007/S13218-018-0533-0.
  2. Marco Alberti, Elena Bellodi, Giuseppe Cota, Fabrizio Riguzzi, and Riccardo Zese. cplint on swish: Probabilistic logical inference with a web browser. Intelligenza Artificiale, 11(1):47-64, 2017. URL: https://doi.org/10.3233/IA-170106.
  3. Joaquín Arias, Manuel Carro, Zhuo Chen, and Gopal Gupta. Justifications for goal-directed constraint answer set programming. arXiv preprint arXiv:2009.10238, 2020. Google Scholar
  4. Chitta Baral, Michael Gelfond, and Nelson Rushton. Probabilistic reasoning with Answer Sets. Theory and Practice of Logic Programming, 9(1):57-144, 2009. URL: https://doi.org/10.1017/S1471068408003645.
  5. Francesco Calimeri, Wolfgang Faber, Martin Gebser, Giovambattista Ianni, Roland Kaminski, Thomas Krennwallner, Nicola Leone, Marco Maratea, Francesco Ricca, and Torsten Schaub. Asp-core-2 input language format. Theory and Practice of Logic Programming, 20(2):294-309, 2020. URL: https://doi.org/10.1017/S1471068419000450.
  6. Fabio Gagliardi Cozman and Denis Deratani Mauá. The joy of probabilistic answer set programming: semantics, complexity, expressivity, inference. International Journal of Approximate Reasoning, 125:218-239, 2020. URL: https://doi.org/10.1016/J.IJAR.2020.07.004.
  7. Luc De Raedt, Angelika Kimmig, Hannu Toivonen, and M Veloso. Problog: A probabilistic Prolog and its application in link discovery. In IJCAI 2007, Proceedings of the 20th international joint conference on artificial intelligence, pages 2462-2467. IJCAI-INT JOINT CONF ARTIF INTELL, 2007. Google Scholar
  8. Daan Fierens, Guy Van den Broeck, Joris Renkens, Dimitar Shterionov, Bernd Gutmann, Ingo Thon, Gerda Janssens, and Luc De Raedt. Inference and learning in probabilistic logic programs using weighted boolean formulas. Theory and Practice of Logic Programming, 15(3):358-401, 2015. URL: https://doi.org/10.1017/S1471068414000076.
  9. Martin Gebser, Roland Kaminski, Benjamin Kaufmann, and Torsten Schaub. Answer set solving in practice. Springer Nature, 2022. Google Scholar
  10. Martin Gebser, Benjamin Kaufmann, Roland Kaminski, Max Ostrowski, Torsten Schaub, and Marius Schneider. Potassco: The Potsdam answer set solving collection. AI Communications, 24(2):107-124, 2011. URL: https://doi.org/10.3233/AIC-2011-0491.
  11. Michael Gelfond and Vladimir Lifschitz. The stable model semantics for logic programming. In ICLP/SLP, volume 88, pages 1070-1080. Cambridge, MA, 1988. Google Scholar
  12. Werner Kießling, Helmut Thöne, and Ulrich Güntzer. Database support for problematic knowledge. In Advances in Database Technology - EDBT'92: 3rd International Conference on Extending Database Technology Vienna, Austria, March 23-27, 1992 Proceedings 3, pages 421-436. Springer, 1992. URL: https://doi.org/10.1007/BFB0032446.
  13. Michael Kifer and VS Subrahmanian. Theory of generalized annotated logic programming and its applications. The Journal of Logic Programming, 12(4):335-367, 1992. URL: https://doi.org/10.1016/0743-1066(92)90007-P.
  14. Ross Kindermann and J. Laurie Snell. Markov random fields and their applications, volume 1 of Contemporary Mathematics. American Mathematical Society, Providence, RI, 1980. Google Scholar
  15. Joohyung Lee and Yi Wang. Weighted rules under the stable model semantics. In Fifteenth international conference on the principles of knowledge representation and reasoning, 2016. Google Scholar
  16. Joohyung Lee and Zhun Yang. Lpmln, Weak Constraints, and P-log. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 31, 2017. Google Scholar
  17. Vladimir Lifschitz. Twelve definitions of a stable model. In International Conference on Logic Programming, pages 37-51. Springer, 2008. URL: https://doi.org/10.1007/978-3-540-89982-2_8.
  18. Kyle Marple, Elmer Salazar, and Gopal Gupta. Computing stable models of normal logic programs without grounding. arXiv preprint arXiv:1709.00501, 2017. URL: https://arxiv.org/abs/1709.00501.
  19. Ilkka Niemelä and Patrik Simons. Smodels - an implementation of the stable model and well-founded semantics for normal logic programs. In Logic Programming And Nonmonotonic Reasoning: 4th International Conference, LPNMR'97 Dagstuhl Castle, Germany, July 28-31, 1997 Proceedings 4, pages 420-429. Springer, 1997. Google Scholar
  20. Judea Pearl. Probabilistic reasoning in intelligent systems: networks of plausible inference. The Morgan Kaufmann Series in Representation and Reasoning. Morgan Kaufmann, San Mateo, CA, 1988. Google Scholar
  21. Luc De Raedt, Kristian Kersting, Sriraam Natarajan, and David Poole. Statistical relational artificial intelligence: Logic, probability, and computation. Synthesis lectures on artificial intelligence and machine learning, 10(2):1-189, 2016. Google Scholar
  22. Matthew Richardson and Pedro Domingos. Markov logic networks. Machine learning, 62:107-136, 2006. URL: https://doi.org/10.1007/S10994-006-5833-1.
  23. Fabrizio Riguzzi. Foundations of Probabilistic Logic Programming: Languages, Semantics, Inference and Learning. River Publishers, New York, 1 edition, September 2022. URL: https://doi.org/10.1201/9781003338192.
  24. Fabrizio Riguzzi and Terrance Swift. Well-definedness and efficient inference for probabilistic logic programming under the distribution semantics. Theory and practice of logic programming, 13(2):279-302, 2013. URL: https://doi.org/10.1017/S1471068411000664.
  25. Taisuke Sato. A statistical learning method for logic programs with distribution semantics. In International Conference on Logic Programming, 1995. Google Scholar
  26. Helmut Thöne, Ulrich Güntzer, and Werner Kießling. Increased robustness of bayesian networks through probability intervals. International Journal of Approximate Reasoning, 17(1):37-76, 1997. URL: https://doi.org/10.1016/S0888-613X(96)00138-7.
  27. Allen Van Gelder, Kenneth A Ross, and John S Schlipf. The well-founded semantics for general logic programs. Journal of the ACM (JACM), 38(3):619-649, 1991. URL: https://doi.org/10.1145/116825.116838.
  28. Victor Verreet, Vincent Derkinderen, Pedro Zuidberg Dos Martires, and Luc De Raedt. Inference and learning with model uncertainty in probabilistic logic programs. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 36, pages 10060-10069, 2022. URL: https://doi.org/10.1609/AAAI.V36I9.21245.
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