Skip to main content

Reasoning with Multiple-Agent Possibilistic Logic

  • Conference paper
  • First Online:
Scalable Uncertainty Management (SUM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9858))

Included in the following conference series:

  • 808 Accesses

Abstract

In multiple-agent logic, a formula is in the form of (aA) where a is a propositional formula and A is a subset of agents. It states that at least all agents in A believe that a is true. This paper presents a method of refutation for this logic, based on a general resolution principle and using a linear strategy, which is sound and complete. This strategy is then extended so as to deal with certainty levels. It manipulates formulas in the form \((a,\alpha /A)\) expressing that all agents in set A believe at least at some level \(\alpha \) that a is true. Finally, an experimental study is provided with the aim to estimate the performance of the proposed algorithms.

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

Access this chapter

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.

    It should be noticed that a base \(\varSigma =\{(a_1, \alpha _1/A_1), ..., (a_n, \alpha _n/ A_n)\}\) can be equivalently rewritten as a collection of at most \(2^n\) possibilistic logic bases, each of them associated with an element of the partition of All induced by the \(A_i\)’s. However, it is in generally computationally better to handle the initial base in a global way using the procedure described in this paper.

References

  1. Belhadi, A., Dubois, D., Khellaf-Haned, F., Prade, H.: Multiple agent possibilistic logic. J. Appl. Non-Class. Logics 23(4), 299–320 (2013)

    Article  MathSciNet  Google Scholar 

  2. Belhadi, A., Dubois, D., Khellaf-Haned, F., Prade, H.: Reasoning about the opinions of groups of agents. In: 11th Europe Workshop on Multi-Agent Systems (EUMAS 2013), Toulouse, France, 12–13 December (2013). https://www.irit.fr/EUMAS2013/Papers/eumas2013_submission_68.pdf

  3. Belhadi, A., Dubois, D., Khellaf-Haned, F., Prade, H.: Algorithme d’infrence pour la logique possibiliste multi-agents. In: Actes Rencontres francophones sur la logique floue et ses applications (LFA 2014), Cargese, France, 22–24 October, pp. 259–266. Cépaduès (2014)

    Google Scholar 

  4. Belhadi, A., Dubois, D., Khellaf-Haned, F., Prade, H.: Lalogique possibiliste multi-agents: Une introduction. In: Actes Rencontres francophones sur la logique floue et ses applications (LFA 2015), Poitiers, France, 5-6 November, pp. 271–278. Cépaduès (2015)

    Google Scholar 

  5. Dubois, D., Prade, H., Schockaert, S.: Stable models in generalized possibilistic logic. In: Brewka, G., Eiter, Th., McIlraith, S.A. (eds.) Proceedings of the 13th International Conference on Principles of Knowledge Representation and Reasoning (KR 2012), Roma, June 10–14, pp. 519–529. AAAI Press (2012)

    Google Scholar 

  6. Cholvy, L.: How strong can an agent believe reported information? In: Liu, W. (ed.) ECSQARU 2011. LNCS, vol. 6717, pp. 386–397. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  7. Dubois, D., Lang, J., Prade, H.: Theorem proving under uncertainty - a possibility theory-based approach. In: McDermott, J.P. (ed.) Proceedings of the 10th International Joint Conference on Artificial Intelligence (IJCAI 1987), Milan, August, pp. 984–986. Morgan Kaufmann (1987)

    Google Scholar 

  8. Dubois D., Lang J., Prade H.: Possibilistic logic. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A., Nute, D. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press (1994)

    Google Scholar 

  9. Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets Syst. 144, 3–23 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dubois D., Prade H.: Extensions multi-agents de la logique possibiliste. In: Proceedings of the Rencontres Francophones sur la Logique Floue et ses Applications (LFA 2006), Toulouse, 19–20 October, pp. 137–144. Cépaduès (2006)

    Google Scholar 

  11. Dubois, D., Prade, H.: Toward multiple-agent extensions of possibilistic logic. In: Proceedings of the IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2007), London, 23–26 July, pp. 187–192 (2007)

    Google Scholar 

  12. Gutscher, A.: Reasoning with uncertain and conflicting opinions in open reputation systems. Electron. Notes Theor. Comput. Sci. 244, 67–79 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Henri Prade .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Belhadi, A., Dubois, D., Khellaf-Haned, F., Prade, H. (2016). Reasoning with Multiple-Agent Possibilistic Logic. In: Schockaert, S., Senellart, P. (eds) Scalable Uncertainty Management. SUM 2016. Lecture Notes in Computer Science(), vol 9858. Springer, Cham. https://doi.org/10.1007/978-3-319-45856-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45856-4_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45855-7

  • Online ISBN: 978-3-319-45856-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics