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A Coalgebraic Perspective on Probabilistic Logic Programming

Authors Tao Gu, Fabio Zanasi

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Author Details

Tao Gu
  • University College London, London, UK
Fabio Zanasi
  • University College London, London, UK

Funding

  • Zanasi, Fabio: partial support from epsrc grant n. EP/R020604/1.

Acknowledgements

Fabio Zanasi acknowledges support from epsrc grant n. EP/R020604/1. The authors thank Alessandro Facchini for useful pointers to the literature, and the anonymous reviewers for the useful comments and feedback.

Cite As Get BibTex

Tao Gu and Fabio Zanasi. A Coalgebraic Perspective on Probabilistic Logic Programming. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.CALCO.2019.10

Abstract

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic perspective on probabilistic logic programming. Programs are modelled as coalgebras for a certain functor F, and two semantics are given in terms of cofree coalgebras. First, the cofree F-coalgebra yields a semantics in terms of derivation trees. Second, by embedding F into another type G, as cofree G-coalgebra we obtain a "possible worlds" interpretation of programs, from which one may recover the usual distribution semantics of probabilistic logic programming.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Theory of computation → Logic
Keywords
  • probabilistic logic programming
  • coalgebraic semantics
  • distribution semantics

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References

  1. Falk Bartels, Ana Sokolova, and Erik P. de Vink. A hierarchy of probabilistic system types. Theor. Comput. Sci., 327(1-2):3-22, 2004. URL: https://doi.org/10.1016/j.tcs.2004.07.019.
  2. Filippo Bonchi and Fabio Zanasi. Saturated semantics for coalgebraic logic programming. In Algebra and Coalgebra in Computer Science - 5th International Conference, CALCO 2013, Warsaw, Poland, September 3-6, 2013. Proceedings, pages 80-94, 2013. URL: https://doi.org/10.1007/978-3-642-40206-7_8.
  3. Filippo Bonchi and Fabio Zanasi. Bialgebraic semantics for logic programming. Logical Methods in Computer Science, 11(1), 2015. URL: https://doi.org/10.2168/LMCS-11(1:14)2015.
  4. Fredrik Dahlqvist, Vincent Danos, Ilias Garnier, and Ohad Kammar. Bayesian inversion by ω-complete cone duality. In 27th International Conference on Concurrency Theory, CONCUR 2016, August 23-26, 2016, Québec City, Canada, pages 1:1-1:15, 2016. URL: https://doi.org/10.4230/LIPIcs.CONCUR.2016.1.
  5. Eugene Dantsin. Probabilistic logic programs and their semantics. In A. Voronkov, editor, Logic Programming, pages 152-164, Berlin, Heidelberg, 1992. Springer Berlin Heidelberg. Google Scholar
  6. Luc De Raedt, Angelika Kimmig, and Hannu Toivonen. Problog: A probabilistic prolog and its application in link discovery. In Proceedings of the 20th International Joint Conference on Artifical Intelligence, IJCAI'07, pages 2468-2473, San Francisco, CA, USA, 2007. Morgan Kaufmann Publishers Inc. URL: http://dl.acm.org/citation.cfm?id=1625275.1625673.
  7. Luc De Raedt, Angelika Kimmig, and Hannu Toivonen. Problog: A probabilistic prolog and its application in link discovery. In Proceedings of the 20th International Joint Conference on Artifical Intelligence, IJCAI'07, pages 2468-2473, San Francisco, CA, USA, 2007. Morgan Kaufmann Publishers Inc. URL: http://dl.acm.org/citation.cfm?id=1625275.1625673.
  8. Didier Dubois, Lluas Godo, and Henri Prade. Weighted logics for artificial intelligence : an introductory discussion. International Journal of Approximate Reasoning, 55(9):1819-1829, 2014. Weighted Logics for Artificial Intelligence. URL: https://doi.org/10.1016/j.ijar.2014.08.002.
  9. Gopal Gupta, Ajay Bansal, Richard Min, Luke Simon, and Ajay Mallya. Coinductive logic programming and its applications. In Véronica Dahl and Ilkka Niemelä, editors, Logic Programming, pages 27-44, Berlin, Heidelberg, 2007. Springer Berlin Heidelberg. Google Scholar
  10. Gopal Gupta and Vítor Santos Costa. Optimal implementation of and-or parallel prolog. Future Generation Computer Systems, 10(1):71-92, 1994. PARLE '92. URL: https://doi.org/10.1016/0167-739X(94)90052-3.
  11. Bart Jacobs, Aleks Kissinger, and Fabio Zanasi. Causal inference by string diagram surgery. In Foundations of Software Science and Computation Structures - 22nd International Conference, FOSSACS 2019, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019, Proceedings, 2019. URL: http://arxiv.org/abs/1811.08338.
  12. Bart Jacobs and Fabio Zanasi. The logical essentials of bayesian reasoning. In Joost-Peter Katoen Gilles Barthe and Alexandra Silva, editors, Probabilistic Programming. Cambridge University Press, Cambridge, 2019. URL: http://arxiv.org/abs/1804.01193.
  13. Kristian Kersting and Luc De Raedt. Bayesian logic programming: Theory and tool. In Introduction to Statistical Relational Learning, pages 291-322. MIT Press; Cambridge, 2007. URL: https://lirias.kuleuven.be/retrieve/86539.
  14. Ekaterina Komendantskaya and Yue Li. Productive corecursion in logic programming. TPLP, 17(5-6):906-923, 2017. URL: https://doi.org/10.1017/S147106841700028X.
  15. Ekaterina Komendantskaya and Yue Li. Towards coinductive theory exploration in horn clause logic: Position paper. In Proceedings 5th Workshop on Horn Clauses for Verification and Synthesis, HCVS 2018, Oxford, UK, 13th July 2018., pages 27-33, 2018. URL: https://doi.org/10.4204/EPTCS.278.5.
  16. Ekaterina Komendantskaya, Guy McCusker, and John Power. Coalgebraic semantics for parallel derivation strategies in logic programming. In Algebraic Methodology and Software Technology - 13th International Conference, AMAST 2010, Lac-Beauport, QC, Canada, June 23-25, 2010. Revised Selected Papers, pages 111-127, 2010. URL: https://doi.org/10.1007/978-3-642-17796-5_7.
  17. Ekaterina Komendantskaya and John Power. Coalgebraic semantics for derivations in logic programming. In Algebra and Coalgebra in Computer Science - 4th International Conference, CALCO 2011, Winchester, UK, August 30 - September 2, 2011. Proceedings, pages 268-282, 2011. URL: https://doi.org/10.1007/978-3-642-22944-2_19.
  18. Ekaterina Komendantskaya and John Power. Logic programming: Laxness and saturation. J. Log. Algebr. Meth. Program., 101:1-21, 2018. URL: https://doi.org/10.1016/j.jlamp.2018.07.004.
  19. Ekaterina Komendantskaya, John Power, and Martin Schmidt. Coalgebraic logic programming: from semantics to implementation. J. Log. Comput., 26(2):745-783, 2016. URL: https://doi.org/10.1093/logcom/exu026.
  20. John W. Lloyd. Foundations of Logic Programming, 2nd Edition. Springer, 1987. URL: https://doi.org/10.1007/978-3-642-83189-8.
  21. Saunders MacLane. Categories for the Working Mathematician. Springer-Verlag, 1971. Graduate Texts in Mathematics, Vol. 5. Google Scholar
  22. Søren Mørk and Ian Holmes. Evaluating bacterial gene-finding hmm structures as probabilistic logic programs. Bioinformatics, 28(5):636-642, 2012. URL: https://doi.org/10.1093/bioinformatics/btr698.
  23. Raymond Ng and V.S. Subrahmanian. Probabilistic logic programming. Information and Computation, 101(2):150-201, 1992. URL: https://doi.org/10.1016/0890-5401(92)90061-J.
  24. Fabrizio Riguzzi and Terrance Swift. Probabilistic logic programming under the distribution semantics, 2014. Google Scholar
  25. Taisuke Sato. A statistical learning method for logic programs with distribution semantics. In Logic Programming, Proceedings of the Twelfth International Conference on Logic Programming, Tokyo, Japan, June 13-16, 1995, pages 715-729, 1995. Google Scholar
  26. Alexandra Silva. Kleene coalgebra. Phd thesis, CWI, Amsterdam, The Netherlands, 2010. Google Scholar
  27. Sebastian Thrun, Wolfram Burgard, and Dieter Fox. Probabilistic robotics. MIT Press, Cambridge, Mass., 2005. Google Scholar
  28. James Worrell. Terminal sequences for accessible endofunctors. Electronic Notes in Theoretical Computer Science, 19:24-38, 1999. CMCS'99, Coalgebraic Methods in Computer Science. URL: https://doi.org/10.1016/S1571-0661(05)80267-1.
  29. Riccardo Zese. Probabilistic Semantic Web: Reasoning and Learning. IOS Press, Amsterdam, The Netherlands, The Netherlands, 2017. Google Scholar
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