Skip to main content
SpringerLink
Log in

o-LPMLN: A Combination of LPMLN and LPOD

  • Chapter
  • First Online:
Advances in Integrations of Intelligent Methods

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 170))

  • 239 Accesses

Abstract

Nowadays, our lives are surrounded by various information, where large pieces of information are uncertain even inconsistent. And in user-oriented applications, users’ preferences should also be taken into account. Therefore, for knowledge-based systems, it is significant to find a knowledge representation and reasoning tool that is able to handle uncertainty, inconsistencies, and preferences. In this paper, we present a logic formalism o-LPMLN that is created by introducing ordered disjunctions in LPMLN. LPMLN provides a powerful framework to handle uncertainty and inconsistencies by combining the ideas of Answer Set Programming (ASP) and Markov Logic Networks (MLN); and logic programming with ordered disjunctions (LPOD) is a simple yet effective way to handle preferences in ASP. By combining LPMLN and LPOD, o-LPMLN is able to handle uncertainty, inconsistencies, and preferences in a unified framework. After defining the language o-LPMLN, we present two modular translations from o-LPMLN to LPMLN and LPOD respectively, which leads to some solving algorithms of the language. Due to the close relationship between o-LPMLN and LPOD, the translations also present an approach to implementing LPOD via using LPMLN solvers. Throughout the paper, we use a prototype application to show the knowledge representation and reasoning with o-LPMLN, which can be regarded as a start point of further work.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Rule (8.2) does not have a positive body.

  2. 2.

    https://www.kaggle.com/msainani/gsmarena-mobile-devices.

References

  1. Balai, E., Gelfond, M.: On the relationship between P-log and LP\({{}^{{\rm MLN}}}\). In: Kambhampati, S. (ed.) Proceedings of the 25th International Joint Conference on Artificial Intelligence, pp. 915–921 (2016)

    Google Scholar 

  2. Balai, E., Gelfond, M., Zhang, Y.: Towards answer set programming with sorts. In: Proceedings of the 12th International conference on Logic Programming and Nonmonotonic Reasoning, pp. 135–147 (2013)

    Chapter  Google Scholar 

  3. Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge, MA (2003)

    Book  Google Scholar 

  4. Baral, C., Gelfond, M., Rushton, N.: Probabilistic reasoning with answer sets. Theory Pract. Logic Program. 9(1), 57–144 (2009)

    Article  MathSciNet  Google Scholar 

  5. Becerra-Fernandez, I., Sabherwal, R.: Knowledge Management Systems and Processes. M.E. Sharpe, London (2010)

    Google Scholar 

  6. Brewka, G.: Logic programming with ordered disjunction. In: Proceedings of the 9th International Workshop on Non-Monotonic Reasoning, pp. 100–105 (2002)

    Google Scholar 

  7. Brewka, G.: Answer sets: from constraint programming towards qualitative optimization. In: Proceedings of the 7th Logic Programming and Nonmonotonic Reasoning, vol. 2923, pp. 34–46. Fort Lauderdale, USA (2004)

    Chapter  Google Scholar 

  8. Brewka, G.: Preferences in answer set programming. In: Proceedings of the 11th Conference of the Spanish Association for Artificial Intelligence on Current Topics in Artificial Intelligence, pp. 1–10 (2005)

    Google Scholar 

  9. Brewka, G., Delgrande, J.P., Romero, J.: asprin: Customizing Answer Set Preferences without a Headache. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence, pp. 1467–1474 (2015)

    Google Scholar 

  10. Brewka, G., Eiter, T., Truszczyński, M.: Answer set programming at a glance. Commun. ACM 54(12), 92–103 (2011)

    Article  Google Scholar 

  11. Brewka, G., Niemelä, I., Syrjänen, T.: Implementing ordered disjunction using answer set solvers for normal programs. In: Proceedings of the 8th European Conference On Logics In Artificial Intelligence, pp. 444–456. Cosenza, Italy (2002)

    Chapter  Google Scholar 

  12. Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Ricca, F., Schaub, T.: ASP-Core-2 Input language format. ASP Standardization Working Group (2012)

    Google Scholar 

  13. Confalonieri, R., Nieves, J.C., Osorio, M., Vázquez-Salceda, J.: Dealing with explicit preferences and uncertainty in answer set programming. Ann. Math. Artif. Intell. 65(2–3), 159–198 (2012)

    Article  MathSciNet  Google Scholar 

  14. Confalonieri, R., Prade, H.: Using possibilistic logic for modeling qualitative decision: answer set programming algorithms. Int. J. Approximate Reasoning 55(2), 711–738 (2014)

    Article  MathSciNet  Google Scholar 

  15. De Raedt, L., Kimmig, A., Toivonen, H.: ProbLog: A probabilistic prolog and its application in link discovery. In: Veloso, M.M. (ed.) Proceedings of the 20th International Joint Conference on Artificial Intelligence, pp. 2468–2473 (2007)

    Google Scholar 

  16. Gebser, M., Kaminski, R., Schaub, T.: Complex optimization in answer set programming. Theory Pract. Logic Program. 11(4–5), 821–839 (2011)

    Article  MathSciNet  Google Scholar 

  17. Gelfond, M., Kahl, Y.: Knowledge Representation, Reasoning, and the Design of Intelligent Agents. Cambridge University Press, Cambridge, MA (2014)

    Book  Google Scholar 

  18. Gelfond, M., Lifschitz, V.: The Stable Model Semantics for Logic Programming. In: Kowalski, R.A., Bowen, K.A. (eds.) Proceedings of the Fifth International Conference and Symposium on Logic Programming, pp. 1070–1080. MIT Press, Cambridge, MA (1988)

    Google Scholar 

  19. Lee, J., Talsania, S., Wang, Y.: Computing LP\({^{{\rm MLN}}}\) using ASP and MLN solvers. Theory Pract. Logic Program. 17(5–6), 942–960 (2017)

    Article  MathSciNet  Google Scholar 

  20. Lee, J., Wang, Y.: Weighted rules under the stable model semantics. In: Baral, C., Delgrande, J.P., Wolter, F. (eds.) Proceedings of the Fifteenth International Conference on Principles of Knowledge Representation and Reasoning, pp. 145–154. AAAI Press (2016)

    Google Scholar 

  21. Lee, J., Wang, Y.: Weight learning in a probabilistic extension of answer set programs. In: Proceedings of the 16th International Conference on the Principles of Knowledge Representation and Reasoning, pp. 22–31 (2018)

    Google Scholar 

  22. Lee, J., Yang, Z.: LP\(^{{\rm MLN}}\) , Weak Constraints, and P-log. In: Singh, S.P., Markovitch, S. (eds.) Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, pp. 1170–1177. AAAI Press (2017)

    Google Scholar 

  23. Lee, J., Yang, Z.: Translating LPOD and CR-Prolog2 into standard answer set programs. Theory Pract. Logic Program. 18(3–4), 589–606 (2018)

    Article  MathSciNet  Google Scholar 

  24. Nicolas, P., Garcia, L., Stéphan, I., Lefèvre, C.: Possibilistic uncertainty handling for answer set programming. Ann. Math. Artif. Intell. 47(1–2), 139–181 (2006)

    Article  MathSciNet  Google Scholar 

  25. Richardson, M., Domingos, P.: Markov logic networks. Mach. Learn. 62(1–2), 107–136 (2006)

    Article  Google Scholar 

  26. Wang, B., Zhang, Z.: A Parallel LP\({^{{\rm MLN}}}\) solver: primary report. In: Bogaerts, B., Harrison, A. (eds.) Proceedings of the 10th Workshop on Answer Set Programming and Other Computing Paradigms, pp. 1–14. CEUR-WS, Espoo, Finland (2017)

    Google Scholar 

Download references

Acknowledgements

We are grateful to the anonymous referees for their useful comments. The work was supported by the National Key Research and Development Plan of China (Grant No. 2017YFB1002801).

Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, Southeast University, Nanjing, China

    Bin Wang, Shutao Zhang, Hongxiang Xu & Zhizheng Zhang

  2. Science and Technology on Information System Engineering Lab, The 28th Research Institute of China Electronics Technology Group Corporation, Nanjing, China

    Wei Wu, Chenglong He & Shiqiang Zong

Authors
  1. Bin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shutao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongxiang Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhizheng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wei Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Chenglong He
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Shiqiang Zong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhizheng Zhang .

Editor information

Editors and Affiliations

  1. Department of Computer Engineering and Informatics, School of Engineering, University of Patras, Patras, Greece

    Ioannis Hatzilygeroudis

  2. Department of Computer Engineering and Informatics, University of Patras, Patras, Greece

    Isidoros Perikos

  3. Department of Computer Engineering and Informatics, University of Patras, Patras, Greece

    Foteini Grivokostopoulou

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Wang, B. et al. (2020). o-LPMLN: A Combination of LPMLN and LPOD. In: Hatzilygeroudis, I., Perikos, I., Grivokostopoulou, F. (eds) Advances in Integrations of Intelligent Methods. Smart Innovation, Systems and Technologies, vol 170. Springer, Singapore. https://doi.org/10.1007/978-981-15-1918-5_8

Download citation

Publish with us

Policies and ethics

Search

Navigation