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On Measuring Inconsistency Using Maximal Consistent Sets

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Book cover Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9161))

Abstract

An important problem in knowledge-based systems is inconsistency handling. This problem has recently been attracting a lot of attention in AI community. In this paper, we tackle the problem of evaluating the amount of conflicts in knowledge bases, and provide a new fine grained inconsistency measure, denoted MCSC, based on maximal consistent sets. In particular, it is suitable in systems where inconsistency results from multiple consistent sources. We show that our measure satisfies several rational postulates proposed in the literature. Moreover, we provide an encoding in integer linear programming for computing MCSC.

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Notes

  1. 1.

    In the original paper, this property is called enhanced additivity.

References

  1. Hunter, A., Konieczny, S.: On the measure of conflicts: Shapley inconsistency values. Artif. Intell. 174(14), 1007–1026 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Grant, J.: Classifications for inconsistent theories. Notre Dame J. Formal Logic 19(3), 435–444 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  3. Knight, K.: Measuring inconsistency. J. Philos. Logic 31(1), 77–98 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Konieczny, S., Lang, J., Marquis, P.: Quantifying information and contradiction in propositional logic through test actions. In: IJCAI, pp. 106–111 (2003)

    Google Scholar 

  5. Qi, G., Liu, W., Bell, D.A.: Measuring conflict and agreement between two prioritized belief bases. In: IJCAI, pp. 552–557 (2005)

    Google Scholar 

  6. Mu, K., Liu, W., Jin, Z.: A general framework for measuring inconsistency through minimal inconsistent sets. Knowl. Inf. Syst. 27(1), 85–114 (2011)

    Article  Google Scholar 

  7. Grant, J., Hunter, A.: Distance-based measures of inconsistency. In: van der Gaag, L.C. (ed.) ECSQARU 2013. LNCS, vol. 7958, pp. 230–241. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  8. Hunter, A., Parsons, S., Wooldridge, M.: Measuring inconsistency in multi-agent systems. Kunstliche Intelligenz 28, 169–178 (2014)

    Article  Google Scholar 

  9. 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)

    Chapter  Google Scholar 

  10. Martinez, A.B.B., Arias, J.J.P., Vilas, A.F.: On measuring levels of inconsistency in multi-perspective requirements specifications. In: PRISE 2004, pp. 21–30 (2004)

    Google Scholar 

  11. Hunter, A.: How to act on inconsistent news: ignore, resolve, or reject. Data Knowl. Eng. 57(3), 221–239 (2006)

    Article  Google Scholar 

  12. Grant, J., Hunter, A.: Measuring inconsistency in knowledgebases. J. Intell. Inf. Syst. 27(2), 159–184 (2006)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  14. Zhou, L., Huang, H., Qi, G., Ma, Y., Huang, Z., Qu, Y.: Measuring inconsistency in dl-lite ontologies. In: Web Intelligence, pp. 349–356 (2009)

    Google Scholar 

  15. McAreavey, K., Liu, W., Miller, P., Mu, K.: Measuring inconsistency in a network intrusion detection rule set based on snort. Int. J. Semant. Comput. 5(3), 281–322 (2011)

    Article  MATH  Google Scholar 

  16. Besnard, P.: Revisiting postulates for inconsistency measures. In: Fermé, E., Leite, J. (eds.) JELIA 2014. LNCS, vol. 8761, pp. 383–396. Springer, Heidelberg (2014)

    Google Scholar 

  17. Priest, G.: Minimally inconsistent LP. Stud. Logica. 50, 321–331 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  18. Jabbour, S., Ma, Y., Raddaoui, B.: Inconsistency measurement thanks to mus decomposition. In: AAMAS, pp. 877–884 (2014)

    Google Scholar 

  19. Thimm, M.: Inconsistency measures for probabilistic logics. Artif. Intell. 197, 1–24 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. CRIL - CNRS UMR 8188, University Artois, 62307, Lens Cedex, France

    Meriem Ammoura, Badran Raddaoui & Yakoub Salhi

  2. LAROMAD - University Mouloud Mammeri, Tizi Ouzou, Algeria

    Meriem Ammoura & Brahim Oukacha

Authors
  1. Meriem Ammoura
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  2. Badran Raddaoui
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  3. Yakoub Salhi
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  4. Brahim Oukacha
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Corresponding author

Correspondence to Yakoub Salhi .

Editor information

Editors and Affiliations

  1. Université de Technologie de Compiègne, Compiègne, France

    Sébastien Destercke

  2. Centre de Recherches de Royallieu, Université de Technologie de Compiègne, Compiègne, France

    Thierry Denoeux

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Ammoura, M., Raddaoui, B., Salhi, Y., Oukacha, B. (2015). On Measuring Inconsistency Using Maximal Consistent Sets. In: Destercke, S., Denoeux, T. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2015. Lecture Notes in Computer Science(), vol 9161. Springer, Cham. https://doi.org/10.1007/978-3-319-20807-7_24

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  • DOI: https://doi.org/10.1007/978-3-319-20807-7_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20806-0

  • Online ISBN: 978-3-319-20807-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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