Skip to main content
Springer Nature Link
Log in

Decision-Making Support Using Nonmonotonic Probabilistic Reasoning

  • Conference paper
  • First Online:
Intelligent Decision Technologies 2019

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 142))

  • 767 Accesses

Abstract

The goal of this paper is to introduce a decision-making support by rule-based nonmonotonic reasoning enhanced with probabilities. As a suitable rule-based tool, we analyze answer set programming (Asp) and explore its probabilistic extension that permits the use of probabilistic expressions of two types. The first type represents an externally given prior probability distribution on literals in an answer set program \(\varPi \). The second type represents a posterior distribution conditioned on individual decisions and choices made, together with their consequences represented by answer sets of \(\varPi \). The ability to compare aspects of both the prior and posterior probabilities in the language of the program \(\varPi \) has interesting uses in filtering solutions/decisions one is interested in. A formal characterization of this probabilistic extension to Asp is provided in addition to examples demonstrating its potential use. It is also shown that the proposed techniques do not increase the complexity of standard Asp-based reasoning.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    If \(B=\{\}\) then \(\ell \,|\,B\) is abbreviated to B.

  2. 2.

    Note that default negation is not allowed here, too.

  3. 3.

    Here the component \(\pi '\) of \(\varPi /A\) contains only rules for which Definition 4.4 is applicable.

  4. 4.

    This is, of course, a well-known complexity theoretical technique.

  5. 5.

    Of course, neither Bayesian networks nor Problog are parts of Pasp. They are used here to illustrate possible external sources, representing \(P()\). We only need to query them no matter how they are implemented.

References

  1. Adrian, W., Alviano, M., Calimeri, F., Cuteri, B., Dodaro, C., Faber, W., Fuscà, D., Leone, N., Manna, M., Perri, S., Ricca, F., Veltri, P., Zangari, J.: The ASP system DLV: advancements and applications. KI 32(2–3), 177–179 (2018)

    Google Scholar 

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

    Book  Google Scholar 

  3. Boland, L.: Scientific thinking without scientific method: two views of Popper. In: Backhouse, R. (ed.) New Directions in Economic Methodology, pp. 157–174. Routledge, New York (1994)

    Google Scholar 

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

    Article  Google Scholar 

  5. De Raedt, L., Kimmig, A.: Probabilistic (logic) programming concepts. Mach. Learn. 100(1), 5–47 (2015)

    Article  MathSciNet  Google Scholar 

  6. De Raedt, L., Kimmig, A., Toivonen, H.: ProbLog: a probabilistic prolog and its application in link discovery. In: Veloso, M. (ed.) Proceedings of the 20th IJCAI, pp. 2462–2467 (2007)

    Google Scholar 

  7. Doherty, P., Szałas, A.: Stability, supportedness, minimality and Kleene Answer Set Programs. In: Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds.) Advances in KR, Logic Programming, and Abstract Argumentation—Essays Dedicated to G. Brewka on the Occasion of His 60th Birthday. LNCS, vol. 9060, pp. 125–140. Springer (2015)

    Google Scholar 

  8. Gebser, M., Janhunen, T., Kaminski, R., Schaub, T., Tasharrofi, S.: Writing declarative specifications for clauses. In: Loizos, M., Kakas, A. (eds.) Proceedings of the 15th European Conference on Logics in Artificial Intelligence, JELIA. LNCS, vol. 10021, pp. 256–271 (2016)

    Chapter  Google Scholar 

  9. Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T.: Answer set solving in practice. In: Synthesis Lectures on AI and Machine Learning. Morgan and Claypool Publishers (2012)

    Google Scholar 

  10. Gelfond, M., Kahl, Y.: Knowledge Representation, Reasoning, and the Design of Intelligent Agents—The Answer-Set Programming Approach. Cambridge University Press (2014)

    Google Scholar 

  11. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, K. (eds.) Proceedings of International Logic Programming, pp. 1070–1080. MIT Press (1988)

    Google Scholar 

  12. Gordon, A., Henzinger, T., Nori, A., Rajamani, S.: Probabilistic programming. In: Proceedings of the on Future of Software Engineering. FOSE 2014, pp. 167–181. ACM (2014)

    Google Scholar 

  13. Janhunen, T.: Cross-translating answer set programs using the ASPTOOLS collection. KI 32(2–3), 183–184 (2018)

    Google Scholar 

  14. Lauritzen, S., Spiegelhalter, D.: Local computations with probabilities on graphical structures and their application to expert systems. J. R. Stat. Soc. Ser. B (Methodol.) 50(2), 157–224 (1988)

    MathSciNet  MATH  Google Scholar 

  15. Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV system for knowledge representation and reasoning. ACM Trans. Comput. Logic 7(3), 499–562 (2006)

    Article  MathSciNet  Google Scholar 

  16. Lierler, Y.: cmodels—SAT-based disjunctive answer set solver. In: Logic Programming and Nonmonotonic Reasoning, 8th International Conference, LPNMR 2005, pp. 447–451 (2005)

    Chapter  Google Scholar 

  17. Lifschitz, V.: Thirteen definitions of a stable model. In: Blass, A., Dershowitz, N., Reisig, W. (eds.) Fields of Logic and Computation. LNCS, vol. 6300, pp. 488–503. Springer (2010)

    Google Scholar 

  18. Lin, F., Zhao, Y.: ASSAT: computing answer sets of a logic program by SAT solvers. Artif. Intell. 157(1–2), 115–137 (2004)

    Article  MathSciNet  Google Scholar 

  19. Liu, G., Janhunen, T., Niemelä, I.: Answer set programming via mixed integer programming. In: Brewka, G., Eiter, T., McIlraith, S. (eds.) Proceedings of the 13th International Conference, KR Principles of Knowledge Representation and Reasoning. AAAI Press (2012)

    Google Scholar 

  20. Milch, B., Marthi, B., Russell, S., Sontag, D., Ong, D., Kolobov, A.: BLOG: probabilistic models with unknown objects. In: Kaelbling, L., Saffiotti, A. (eds.) Proceedings of the 19th IJCAI, pp. 1352–1359 (2005)

    Google Scholar 

  21. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc. (1988)

    Google Scholar 

  22. Pfeffer, A.: Practical Probabilistic Programming. Manning Publications Co. (2016)

    Google Scholar 

  23. Poole, D.: Logic programming, abduction and probability. In: Proceedings of the International Conference on 5th Generation Computing Systems FGCS, pp. 530–538 (1992)

    Google Scholar 

  24. Przymusinski, T.C.: The well-founded semantics coincides with the three-valued stable semantics. Fundam. Inform. 13(4), 445–463 (1990)

    MathSciNet  MATH  Google Scholar 

  25. Sato, T.: A statistical learning method for logic programs with distribution semantics. In: Proceedings of the 12th International Conference on Logic Programming ICLP, pp. 715–729. MIT Press (1995)

    Google Scholar 

  26. Shepherdson, J.: A sound and complete semantics for a version of negation as failure. Theor. Comput. Sci. 65(3), 343–371 (1989)

    Article  MathSciNet  Google Scholar 

  27. Suciu, D., Olteanu, D., Ré, C., Koch, C.: Probabilistic Databases, Synthesis Lectures on Data Management, vol. 3. Morgan & Claypool Publishers (2011)

    Google Scholar 

Download references

Acknowledgements

I would like to thank Patrick Doherty for discussions and cooperation related to this paper. My thanks are also due to Barbara Dunin-Kȩplicz for helpful comments and suggestions. This work is supported by the grant 2017/27/B/ST6/02018 of the National Science Centre Poland, the ELLIIT Network Organization for Information and Communication Technology, and the Swedish FSR (SymbiKBot Project).

Author information

Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Szałas

  2. Department of Computer and Information Science, Linköping University, 581 83, Linköping, Sweden

    Andrzej Szałas

Authors
  1. Andrzej Szałas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrzej Szałas .

Editor information

Editors and Affiliations

  1. Department of Information Systems, Gdynia Maritime University, Gdynia, Poland

    Ireneusz Czarnowski

  2. Bournemouth University and KES International, Poole, Dorset, UK

    Robert J. Howlett

  3. University of Canberra, Canberra, ACT, Australia

    Lakhmi C. Jain

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Szałas, A. (2020). Decision-Making Support Using Nonmonotonic Probabilistic Reasoning. In: Czarnowski, I., Howlett, R., Jain, L. (eds) Intelligent Decision Technologies 2019. Smart Innovation, Systems and Technologies, vol 142. Springer, Singapore. https://doi.org/10.1007/978-981-13-8311-3_4

Download citation

Publish with us

Policies and ethics