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Computing LPMLN using ASP and MLN solvers*

Published online by Cambridge University Press:  30 August 2017

JOOHYUNG LEE ,
SAMIDH TALSANIA  and
YI WANG
JOOHYUNG LEE
Affiliation:
School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA (e-mail: joolee@asu.edu, stalsani@asu.edu, ywang485@asu.edu)
SAMIDH TALSANIA
Affiliation:
School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA (e-mail: joolee@asu.edu, stalsani@asu.edu, ywang485@asu.edu)
YI WANG
Affiliation:
School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA (e-mail: joolee@asu.edu, stalsani@asu.edu, ywang485@asu.edu)
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Abstract

LPMLN is a recent addition to probabilistic logic programming languages. Its main idea is to overcome the rigid nature of the stable model semantics by assigning a weight to each rule in a way similar to Markov Logic is defined. We present two implementations of LPMLN, lpmln2asp and lpmln2mln. System lpmln2asp translates LPMLN programs into the input language of answer set solver clingo, and using weak constraints and stable model enumeration, it can compute most probable stable models as well as exact conditional and marginal probabilities. System lpmln2mln translates LPMLN programs into the input language of Markov Logic solvers, such as alchemy, tuffy, and rockit, and allows for performing approximate probabilistic inference on LPMLN programs. We also demonstrate the usefulness of the LPMLN systems for computing other languages, such as ProbLog and Pearl's Causal Models, that are shown to be translatable into LPMLN.

Keywords

Answer Set ProgrammingMarkov LogicLPMLN
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 17 , Special Issue 5-6: 33rd International Conference on Logic Programming , September 2017 , pp. 942 - 960
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

*

This work was partially supported by the National Science Foundation under Grants IIS-1319794 and IIS-1526301.

References

Balai, E. and Gelfond, M. 2016. On the relationship between P-log and LPMLN. In Proc. of International Joint Conference on Artificial Intelligence (IJCAI), 915–921.Google Scholar
Baral, C., Gelfond, M. and Rushton, J. N. 2009. Probabilistic reasoning with answer sets. Theory and Practice of Logic Programming 9, 1, 57–144.CrossRefGoogle Scholar
Buccafurri, F., Leone, N. and Rullo, P. 2000. Enhancing disjunctive datalog by constraints. IEEE Transactions on Knowledge and Data Engineering 12, 5, 845–860.CrossRefGoogle Scholar
Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Ricca, F. and Schaub, T. 2012. ASP-Core-2: Input language format. ASP Standardization Working Group, Technical Report.Google Scholar
De Raedt, L., Kimmig, A. and Toivonen, H. 2007. ProbLog: A probabilistic prolog and its application in link discovery. In Proc. of IJCAI, vol. 7. 2462–2467.Google Scholar
Fierens, D., Van den Broeck, G., Renkens, J., Shterionov, D., Gutmann, B., Thon, I., Janssens, G. and De Raedt, L. 2015. Inference and learning in probabilistic logic programs using weighted boolean formulas. Theory and Practice of Logic Programming 15, 3, 358–401.CrossRefGoogle Scholar
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2011. Multi-criteria optimization in answer set programming. In LIPIcs-Leibniz International Proceedings in Informatics, vol. 11. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 1–10.Google Scholar
Lee, J., Meng, Y. and Wang, Y. 2015. Markov logic style weighted rules under the stable model semantics. In Technical Communications of the 31st International Conference on Logic Programming.Google Scholar
Lee, J., Talsania, S. and Wang, Y. 2017. Online appendix for the paper “Computing LPMLN using ASP and MLN solvers”. TPLP Archive. https://doi.org/10.1017/S1471068417000400 CrossRefGoogle Scholar
Lee, J. and Wang, Y. 2016. Weighted rules under the stable model semantics. In Proc. of International Conference on Principles of Knowledge Representation and Reasoning (KR), 145–154.Google Scholar
Lee, J. and Yang, Z. 2017. LPMLN, weak constraints, and P-log. In Proc. of the AAAI Conference on Artificial Intelligence (AAAI), 1170–1177.Google Scholar
Nickles, M. 2016. A tool for probabilistic reasoning based on logic programming and first-order theories under stable model semantics. In Proc. of European Conference on Logics in Artificial Intelligence (JELIA), 369–384.Google Scholar
Pearl, J. 2000. Causality: Models, Reasoning and Inference. Vol. 29. Cambridge University Press.Google Scholar
Richardson, M. and Domingos, P. 2006. Markov logic networks. Machine Learning 62, 1–2, 107–136.CrossRefGoogle Scholar
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