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An Anytime Algorithm for Computing Inconsistency Measurement

  • Yue Ma
  • Guilin Qi
  • Guohui Xiao
  • Pascal Hitzler
  • Zuoquan Lin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5914)

Abstract

Measuring inconsistency degrees of inconsistent knowledge bases is an important problem as it provides context information for facilitating inconsistency handling. Many methods have been proposed to solve this problem and a main class of them is based on some kind of paraconsistent semantics. In this paper, we consider the computational aspects of inconsistency degrees of propositional knowledge bases under 4-valued semantics. We first analyze its computational complexity. As it turns out that computing the exact inconsistency degree is intractable, we then propose an anytime algorithm that provides tractable approximation of the inconsistency degree from above and below. We show that our algorithm satisfies some desirable properties and give experimental results of our implementation of the algorithm.

Keywords

Knowledge Base Truncation Strategy Propositional Letter Tractable Approximation Precision Threshold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Hunter, A.: How to act on inconsistent news: Ignore, resolve, or reject. Data Knowl. Eng. 57, 221–239 (2006)CrossRefGoogle Scholar
  2. 2.
    Hunter, A.: Measuring inconsistency in knowledge via quasi-classical models. In: Proc. of AAAI 2002, pp. 68–73. AAAI Press, Menlo Park (2002)Google Scholar
  3. 3.
    Hunter, A., Konieczny, S.: Approaches to measuring inconsistent information. In: Bertossi, L., Hunter, A., Schaub, T. (eds.) Inconsistency Tolerance. LNCS, vol. 3300, pp. 191–236. Springer, Heidelberg (2005)Google Scholar
  4. 4.
    Hunter, A., Konieczny, S.: Shapley inconsistency values. In: Proc. of KR 2006, pp. 249–259. AAAI Press, Menlo Park (2006)Google Scholar
  5. 5.
    Mu, K., Jin, Z., Lu, R., Liu, W.: Measuring inconsistency in requirements specifications. In: Godo, L. (ed.) ECSQARU 2005. LNCS (LNAI), vol. 3571, pp. 440–451. Springer, Heidelberg (2005)Google Scholar
  6. 6.
    Knight, K.: Measuring inconsistency. Journal of Philosophical Logic 31(1), 77–98 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hunter, A., Konieczny, S.: Measuring inconsistency through minimal inconsistent sets. In: Proc. of KR 2008, pp. 358–366 (2008)Google Scholar
  8. 8.
    Grant, J.: Classifications for inconsistent theories. Notre Dame J. of Formal Logic 19, 435–444 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Grant, J., Hunter, A.: Measuring inconsistency in knowledgebases. Journal of Intelligent Information Systems 27, 159–184 (2006)CrossRefGoogle Scholar
  10. 10.
    Grant, J., Hunter, A.: Analysing inconsistent first-order knowledge bases. Artif. Intell. 172, 1064–1093 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Coste-Marquis, S., Marquis, P.: A unit resolution-based approach to tractable and paraconsistent reasoning. In: Proc. of ECAI, pp. 803–807 (2004)Google Scholar
  12. 12.
    Ma, Y., Qi, G., Hitzler, P., Lin, Z.: An algorithm for computing inconsistency measurement by paraconsistent semantics. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS (LNAI), vol. 4724, pp. 91–102. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Belnap, N.D.: A useful four-valued logic. In: Modern uses of multiple-valued logics, pp. 7–73. Reidel Publishing Company, Boston (1977)Google Scholar
  14. 14.
    Arieli, O., Avron, A.: The value of the four values. Artif. Intell. 102, 97–141 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Papadimitriou, C.H. (ed.): Computational Complexity. Addison Wesley, Reading (1994)zbMATHGoogle Scholar
  16. 16.
    Schaerf, M., Cadoli, M.: Tractable reasoning via approximation. Artificial Intelligence 74, 249–310 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Cadoli, M., Schaerf, M.: On the complexity of entailment in propositional multivalued logics. Ann. Math. Artif. Intell. 18, 29–50 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Malouf, R.: Maximal consistent subsets. Computational Linguistics 33, 153–160 (2007)CrossRefGoogle Scholar
  19. 19.
    Mu, K., Jin, Z., Liu, W., Zowghi, D.: An approach to measuring the significance of inconsistency in viewpoints framework. Technical report, Peking University (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yue Ma
    • 1
  • Guilin Qi
    • 2
  • Guohui Xiao
    • 3
  • Pascal Hitzler
    • 4
  • Zuoquan Lin
    • 3
  1. 1.Institute LIPNUniversité Paris-Nord (LIPN - UMR 7030)France
  2. 2.School of Computer Science and EngineeringSoutheast UniversityNanjingChina
  3. 3.Department of Information SciencePeking UniversityChina
  4. 4.Kno.e.sis CenterWright State UniversityDaytonUSA

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