Measuring Inconsistency Through Subformula Forgetting

  • Yakoub SalhiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11940)


In this paper, we introduce a new approach for defining inconsistency measures. The key idea consists in forgetting subformula occurrences in order to restore consistency. Thus, our approach can be seen as a generalization of the approach based on forgetting only propositional variables. We here introduce rationality postulates of inconsistency measuring that take into account in a syntactic way the internal structure of the formulas. We also describe different inconsistency measures that are based on forgetting subformula occurrences.


  1. 1.
    Besnard, P.: Revisiting postulates for inconsistency measures. In: Fermé, E., Leite, J. (eds.) JELIA 2014. LNCS (LNAI), vol. 8761, pp. 383–396. Springer, Cham (2014). Scholar
  2. 2.
    Besnard, P.: Forgetting-based inconsistency measure. In: Schockaert, S., Senellart, P. (eds.) SUM 2016. LNCS (LNAI), vol. 9858, pp. 331–337. Springer, Cham (2016). Scholar
  3. 3.
    Bona, G.D., Grant, J., Hunter, A., Konieczny, S.: Towards a unified framework for syntactic inconsistency measures. In: Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, New Orleans, Louisiana, USA (2018)Google Scholar
  4. 4.
    Chen, Q., Zhang, C., Zhang, S.: A verification model for electronic transaction protocols. In: Yu, J.X., Lin, X., Lu, H., Zhang, Y. (eds.) APWeb 2004. LNCS, vol. 3007, pp. 824–833. Springer, Heidelberg (2004). Scholar
  5. 5.
    Condotta, J., Raddaoui, B., Salhi, Y.: Quantifying conflicts for spatial and temporal information. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Fifteenth International Conference, KR 2016, Cape Town, South Africa, 25–29 April 2016, pp. 443–452 (2016)Google Scholar
  6. 6.
    Grant, J., Hunter, A.: Measuring inconsistency in knowledgebases. J. Intell. Inf. Syst. 27(2), 159–184 (2006)CrossRefGoogle Scholar
  7. 7.
    Grant, J., Hunter, A.: Distance-based measures of inconsistency. In: van der Gaag, L.C. (ed.) ECSQARU 2013. LNCS (LNAI), vol. 7958, pp. 230–241. Springer, Heidelberg (2013). Scholar
  8. 8.
    Hunter, A., Konieczny, S.: Measuring inconsistency through minimal inconsistent sets. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Eleventh International Conference, KR 2008, Sydney, Australia, 16–19 September 2008, pp. 358–366. AAAI Press (2008)Google Scholar
  9. 9.
    Hunter, A., Konieczny, S.: On the measure of conflicts: shapley inconsistency values. Artif. Intell. 174(14), 1007–1026 (2010)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hunter, A., Parsons, S., Wooldridge, M.: Measuring inconsistency in multi-agent systems. Kunstliche Intelligenz 28, 169–178 (2014)CrossRefGoogle Scholar
  11. 11.
    Lang, J., Marquis, P.: Resolving inconsistencies by variable forgetting. In: Proceedings of the Eights International Conference on Principles and Knowledge Representation and Reasoning (KR-02), Toulouse, France, 22–25 April 2002, pp. 239–250 (2002)Google Scholar
  12. 12.
    Lang, J., Marquis, P.: Reasoning under inconsistency: a forgetting-based approach. Artif. Intell. 174(12–13), 799–823 (2010)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Martinez, M.V., Pugliese, A., Simari, G.I., Subrahmanian, V.S., Prade, H.: How dirty is your relational database? An axiomatic approach. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS (LNAI), vol. 4724, pp. 103–114. Springer, Heidelberg (2007). Scholar
  14. 14.
    Thimm, M.: On the expressivity of inconsistency measures. Artif. Intell. 234, 120–151 (2016)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Thimm, M.: On the evaluation of inconsistency measures. In: Grant, J., Martinez, M.V. (eds.) Measuring Inconsistency in Information, Volume 73 of Studies in Logic. College Publications, February 2018Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.CRIL - CNRS & Université d’ArtoisLensFrance

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