Computing Inconsistency Using Logical Argumentation

Badran Raddaoui


Measuring the degree of conflict of a knowledge base can help us to deal with inconsistencies. Several semantic and syntax based approaches have been proposed separately. In this paper, we use logical argumentation as a field to compute the inconsistency measure for propositional formulae. We show using the complete argumentation tree that our family of measures is able to express finely the inconsistency of a formula following their context and allows us to distinguish between formulae. We extend our measure to quantify the degree of inconsistency of set of formulae and give a general formulation of the inconsistency using some logical properties.


  1. Benferhat, S. and Garcia, L. (1998). A local handling of inconsistent knowledge and default bases. In Applications of Uncertainty Formalisms, pages 325-353.
  2. Bertossi, L. E., Hunter, A., and Schaub, T. (2005). Introduction to inconsistency tolerance. In Inconsistency Tolerance, pages 1-14.
  3. Besnard, P., Grégoire, Ó ., Piette, C., and Raddaoui, B. (2010). Mus-based generation of arguments and counter-arguments. In IRI, pages 239-244.
  4. Besnard, P., Grégoire, Ó., and Raddaoui, B. (2012). An argumentation framework for reasoning about bounded resources. In ICTAI, pages 540-547.
  5. Besnard, P., Grégoire, Ó., and Raddaoui, B. (2013). A conditional logic-based argumentation framework. In SUM, pages 44-56.
  6. Besnard, P. and Hunter, A. (2001). A logic-based theory of deductive arguments. Artif. Intell., 128(1-2):203-235.
  7. Besnard, P. and Hunter, A. (2005). Practical first-order argumentation. In AAAI, pages 590-595.
  8. Black, E., Hunter, A., and Pan, J. Z. (2009). An argumentbased approach to using multiple ontologies. In SUM, pages 68-79.
  9. Chen, Q., Zhang, C., and Zhang, S. (2004). A verification model for electronic transaction protocols. In APWeb, pages 824-833.
  10. Doder, D., Raskovic, M., Markovic, Z., and Ognjanovic, Z. (2010). Measures of inconsistency and defaults. Int. J. Approx. Reasoning, 51(7):832-845.
  11. Dung, P. M. (1995). On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell., 77(2):321-358.
  12. Grant, J. (1978). Classifications for inconsistent theories. Notre Dame Journal of Formal Logic, 19(3):435-444.
  13. Grant, J. and Hunter, A. (2006). Measuring inconsistency in knowledgebases. J. Intell. Inf. Syst., 27(2):159-184.
  14. Grant, J. and Hunter, A. (2008). Analysing inconsistent first-order knowledgebases. Artif. Intell., 172(8- 9):1064-1093.
  15. Hunter, A. (2002). Measuring inconsistency in knowledge via quasi-classical models. In AAAI/IAAI, pages 68- 73.
  16. Hunter, A. (2004). Logical comparison of inconsistent perspectives using scoring functions. Knowl. Inf. Syst., 6(5):528-543.
  17. Hunter, A. (2006). How to act on inconsistent news: Ignore, resolve, or reject. Data Knowl. Eng., 57(3):221-239.
  18. Hunter, A. and Konieczny, S. (2006). Shapley inconsistency values. In KR, pages 249-259.
  19. Hunter, A. and Konieczny, S. (2008). Measuring inconsistency through minimal inconsistent sets. In KR, pages 358-366.
  20. Hunter, A. and Konieczny, S. (2010). On the measure of conflicts: Shapley inconsistency values. Artif. Intell., 174(14):1007-1026.
  21. Hunter, A., Parsons, S., and Wooldridge, M. (2014). Measuring inconsistency in multi-agent systems. Kunstliche Intelligenz, 28:169-178.
  22. Jabbour, S., Ma, Y., and Raddaoui, B. (2014a). Inconsistency measurement thanks to mus decomposition. In AAMAS, pages 877-884.
  23. Jabbour, S., Ma, Y., Raddaoui, B., and Saïs, L. (2014b). On the characterization of inconsistency: A prime implicates based framework. In ICTAI, pages 146-153.
  24. Jabbour, S., Ma, Y., Raddaoui, B., and Saïs, L. (2014c). Prime implicates based inconsistency characterization. In ECAI, pages 1037-1038.
  25. Jabbour, S. and Raddaoui, B. (2013). Measuring inconsistency through minimal proofs. In ECSQARU, pages 290-301.
  26. Knight, K. (2002). Measuring inconsistency. J. Philosophical Logic, 31(1):77-98.
  27. Ma, Y., Qi, G., and Hitzler, P. (2011). Computing inconsistency measure based on paraconsistent semantics. J. Log. Comput., 21(6):1257-1281.
  28. Ma, Y., Qi, G., Xiao, G., Hitzler, P., and Lin, Z. (2010). Computational complexity and anytime algorithm for inconsistency measurement. Int. J. Software and Informatics, 4(1):3-21.
  29. Martinez, A. B. B., Arias, J. J. P., and and, A. F. V. (2004). On measuring levels of inconsistency in multiperspective requirements specifications. In PRISE'04, pages 21-30.
  30. Martinez, M. V., Pugliese, A., Simari, G. I., Subrahmanian, V. S., and Prade, H. (2007). How dirty is your relational database? an axiomatic approach. In ECSQARU, pages 103-114.
  31. McAreavey, K., Liu, W., Miller, P., and Mu, K. (2011). Measuring inconsistency in a network intrusion detection rule set based on snort. Int. J. Semantic Computing, 5(3).
  32. Mu, K., Liu, W., and Jin, Z. (2011a). A general framework for measuring inconsistency through minimal inconsistent sets. Knowl. Inf. Syst., 27(1):85-114.
  33. Mu, K., Liu, W., and Jin, Z. (2012). Measuring the blame of each formula for inconsistent prioritized knowledge bases. J. Log. Comput., 22(3):481-516.
  34. Mu, K., Liu, W., Jin, Z., and Bell, D. A. (2011b). A syntax-based approach to measuring the degree of inconsistency for belief bases. Int. J. Approx. Reasoning, 52(7):978-999.
  35. Oller, C. A. (2004). Measuring coherence using lp-models. J. Applied Logic, 2(4):451-455.
  36. Qi, G., Liu, W., and Bell, D. A. (2005). Measuring conflict and agreement between two prioritized belief bases. In IJCAI, pages 552-557.
  37. Raddaoui, B. (2013). Contributions aux approches logiques de l'argumentation en intelligence artificielle. PhD thesis, University of Artois.
  38. Reiter, R. (1987). A theory of diagnosis from first principles. Artif. Intell., 32(1):57-95.
  39. Xiao, G., Lin, Z., Ma, Y., and Qi, G. (2010). Computing inconsistency measurements under multi-valued semantics by partial max-sat solvers. In KR.
  40. Xiao, G. and Ma, Y. (2012). Inconsistency measurement based on variables in minimal unsatisfiable subsets. In ECAI, pages 864-869.
  41. Zhou, L., Huang, H., Qi, G., Ma, Y., Huang, Z., and Qu, Y. (2009). Measuring inconsistency in dl-lite ontologies. In Web Intelligence, pages 349-356.

Paper Citation

in Harvard Style

Raddaoui B. (2015). Computing Inconsistency Using Logical Argumentation . In Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-074-1, pages 164-172. DOI: 10.5220/0005221301640172

in Bibtex Style

author={Badran Raddaoui},
title={Computing Inconsistency Using Logical Argumentation},
booktitle={Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

in EndNote Style

JO - Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - Computing Inconsistency Using Logical Argumentation
SN - 978-989-758-074-1
AU - Raddaoui B.
PY - 2015
SP - 164
EP - 172
DO - 10.5220/0005221301640172