Skip to main content
SpringerLink
Log in

The Possibilistic Handling of Irrelevance in Exception-Tolerant Reasoning

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

In nonmonotonic reasoning, the preferential system P is known to provide reasonable but very cautious conclusions, and in particular, preferential inference is blocked by the presence of “irrelevant” properties. When using Lehmann's rational closure, the inference machinery, which is then more productive, may still remain too cautious. These two types of inference can be represented using a possibility theory-based semantics. To overcome the cautiousness of system P, we first progressively augment preferential inference with two extensions which are in between system P and rational closure. Then, in order to overcome some remaining limitations of rational closure the second half of this paper focuses more particularly on the use of (contextual) independence assumptions of the form: the fact that δ is true (or is false) does not affect the validity of the rule “normally if α then β”. The modelling of such independence assumptions is discussed in the possibilistic framework. Algorithms are provided to jointly handle default rules and independence relations, and to check their multual consistency.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E.W. Adams, The Logic of Conditionals (Reidel, Dordrecht, 1975).

    Google Scholar 

  2. N. Ben Amor, S. Benferhat, D. Dubois, H. Geffner and H. Prade, Independence in qualitative uncertainty frameworks, in: Proc. of the 7th Internat. Conf. on Principles of Knowledge Representation and Reasoning (KR 2000), Breckenbridge, 12-14 April 2000.

  3. S. Benferhat, Handling hard rules and default rules in possibilistic logic, in: Advances in Intelligent Computing-IPMU'94, Selected Papers of the Internat. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Paris, France, July 1994, eds. B. Bouchon-Meunier, R.R. Yager and L.A. Zadeh, Lecture Notes in Computer Science, Vol. 945 (Springer, New York, 1995) pp. 302-310.

    Google Scholar 

  4. S. Benferhat, D. Dubois, L. Garcia and H. Prade, Possibilistic logic bases and possibilistic graphs, in: Proc. of the 15th Conf. on Uncertainty in Artificial Intelligence (UAI-99), 30 July-1 August 1999, Stockholm, Sweden, pp. 57-64. Extended version will appear in Internat. J. Aprox. Reason.

  5. S. Benferhat, D. Dubois, L. Garcia and H. Prade, Directed possibilistic graphs and possibilistic logic, in: Information, Uncertainty and Fusion, eds. B. Bouchon-Meunier, R.R. Yager and L.A. Zadeh (Kluwer Academic, Dordrecht, 2000) pp. 365-379.

    Google Scholar 

  6. S. Benferhat, D. Dubois and H. Prade, Representing default rules in possibilistic logic, in: Proc. of the 3rd Internat. Conf. on Principles of Knowledge Representation and Reasoning (KR'92), Cambridge, MA, 25-29 October 1992, pp. 673-684.

  7. S. Benferhat, D. Dubois and H. Prade, Expressing independence in a possibilistic framework and its application to default reasoning, in: Proc. of the 11th European Conf. on Artificial Intelligence (ECAI'94), Amsterdam, 8-12 August 1994, pp. 150-154.

  8. S. Benferhat, D. Dubois and H. Prade, Coping with the limitations of rational inference in the framework of possibility theory, in: Proc. of the 12th Conf. on Uncertainty in Artificial Intelligence, eds. E. Horvitz and F. Jensen, Portland, OR, 1-4 August 1996 (Morgan & Kaufmann, San Mateo, CA, 1996) pp. 90-97.

    Google Scholar 

  9. S. Benferhat, D. Dubois and H. Prade, Practical handling of exception-tainted rules and independence information in possibilistic logic, Appl. Intelligence 9 (1998) 101-127.

    Google Scholar 

  10. S. Benferhat and F. Dupin de Saint Cyr, Contextual handling of conditional knowledge, in: Proc. of the 6th Internat. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU'96), Granada, Spain, 1-5 July 1996, pp. 1369-1374.

  11. L.J. Cohen, The Probable and the Provable (Clarendon Press, Oxford, UK, 1977).

    Google Scholar 

  12. A. Darwiche, A logical notion of conditional independence: Properties and applications, Artificial Intelligence (1997) 45-82.

  13. J. Delgrande and F.J. Pelletier, Formal senses of relevance in default reasoning, Erkenntnis 49 (1998) 137-173.

    Google Scholar 

  14. D. Dubois, Belief structures, possibility theory, decomposable confidence measures on finite sets, Comput. Artificial Intelligence 5(5) (1986) 403-417.

    Google Scholar 

  15. D. Dubois, L. Fariñas del Cerro, A. Herzig and H. Prade, Qualitative relevance and independence: A roadmap, in: Proc. of Internat. Joint Conf. on Artificial Intelligence (IJCAI'97), Nagoya, 1997, pp. 62-67. Extended version in Fuzzy Sets, Logics and Reasoning about Knowledge (Kluwer Academic, Dordrecht, 1999) pp. 325-350.

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

    Google Scholar 

  17. D. Dubois and H. Prade (with the collaboration of H. Farreny, R. Martin-Clouaire and C. Testemale), Possibility Theory-An Approach to Computerized Processing of Uncertainty (Plenum Press, New York, 1988).

    Google Scholar 

  18. D. Dubois and H. Prade, The logical view of conditioning and its application to possibility and evidence theories, Internat. J. Approx. Reasoning 4 (1990) 23-46.

    Google Scholar 

  19. D. Dubois and H. Prade, Epistemic entrenchment and possibilistic logic, Artificial Intelligence 50 (1991) 223-239.

    Google Scholar 

  20. D. Dubois and H. Prade, Possibilistic logic, preferential models, non-monotonicity and related issues, in: Proc. of the Internat. Joint Conf. on Artificial Intelligence (IJCAI'91), Sydney, 24-30 August 1991, pp. 419-424.

  21. D. Dubois and H. Prade, Conditional objects, possibility theory and default rules, in: Conditionals: From Philosophy to Computer Sciences, eds. G. Crocco, L. Fariñas del Cerro and A. Herzig (Oxford Univ. Press, Oxford, 1995) pp. 301-336.

  22. D.M. Gabbay, Theoretical foundations for non-monotonic reasoning in expert systems, in: Logics and Models of Concurrent Systems, ed. K.R. Apt (Springer, Berlin, 1985) pp. 439-457.

    Google Scholar 

  23. P. Gärdenfors, On the logic of relevance, Synthese 37 (1978) 351-367.

    Google Scholar 

  24. P. Gärdenfors, Knowledge in Flux-Modeling the Dynamic of Epistemic States (MIT Press, Cambridge, MA, 1988).

    Google Scholar 

  25. P. Gärdenfors and D. Makinson, Non-monotonic inference based on expectations, Artificial Intelligence 65 (1994) 197-245.

    Google Scholar 

  26. M. Goldszmidt and J. Pearl, On the relation between rational closure and system Z, in: Proc. of the 3rd Internat. Workshop on Non-monotonic Reasoning, South Lake Tahoe, 1990, pp. 130-140.

  27. M. Goldszmidt and J. Pearl, On the consistency of defeasible databases, Artificial Intelligence 52 (1991) 121-149.

    Google Scholar 

  28. R. Greiner and D. Subramanian, Introduction, in: Proc. of the AAAI Fall Symp. on "Relevance", New Orleans, LO (AAAI Press, 1994) pp. 1-4.

  29. E. Hisdal, Conditional possibilities independence and non-interaction, Fuzzy Sets Systems 1 (1978) 283-297.

    Google Scholar 

  30. S. Kraus, D. Lehmann and M. Magidor, Non-monotonic reasoning, preferential models and cumulative logics, Artificial Intelligence 44 (1990) 167-207.

    Google Scholar 

  31. D. Lehmann, What does a conditional knowledge base entail? in: Proc. of the 1st Internat. Conf. on Principles of Knowledge Representation and Reasoning (KR'89), Toronto, 1989, pp. 357-367.

  32. D. Lehmann and M. Magidor, What does a conditional knowledge base entail? Artificial Intelligence 55 (1992) 1-60.

    Google Scholar 

  33. D.L. Lewis, Counterfactuals (Basil Blackwell, Oxford, 1973).

    Google Scholar 

  34. D. Makinson, General theory of cumulative inference, in: Non-Monotonic Reasoning, eds. M. Reinfrank, J. De Kleer, M.L. Ginsberg and E. Sandewall, Lecture Notes in Artificial Intelligence, Vol. 346 (Springer, Berlin, 1989) pp. 1-18.

    Google Scholar 

  35. S. Nahmias, Fuzzy variables, Fuzzy Sets Systems (1978) 97-110.

  36. J. Pearl, System Z: A natural ordering of defaults with tractable applications to default reasoning, in: Proc. of the 3rd Conf. on Theoretical Aspects of Reasoning about Knowledge (TARK'90), San Mateo, CA, 1990, pp. 121-135.

  37. N. Rescher, Plausible Reasoning: An Introduction to the Theory and Practice of Plausibilistic Inference (Van Gorcum, Amsterdam, 1976).

    Google Scholar 

  38. Y. Shoham, Reasoning About Change-Time and Causation from the Standpoint of Artificial Intelligence (MIT Press, Cambridge, MA, 1988).

    Google Scholar 

  39. G.L.S. Shackle, Decision, Order and Time in Human Affairs (Cambridge Univ. Press, Cambridge, 1961).

    Google Scholar 

  40. W. Spohn, Ordinal conditional functions: A dynamic theory of epistemic states, in: Causation in Decision, Belief Change, and Statistics, eds. W.L. Harper and B. Skyrms (Kluwer Academic, Dordrecht, 1988) pp. 105-134.

    Google Scholar 

  41. D. Subrahmanian and M.R. Genesereth, The relevance of irrelevance, in: Proc. of the Internat. Joint Conf. on Artificial Intelligence (IJCAI'87), Milan, Italy, 1987, pp. 416-422.

  42. R.R. Yager, On the specificity of a possibility distribution, Fuzzy Sets Systems 50 (1992) 279-292.

    Google Scholar 

  43. L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Systems 1 (1978) 3-28.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Recherche en Informatique de Toulouse (I.R.I.T.), Université Paul Sabatier, C.N.R.S., 118 route de Narbonne, 31062, Toulouse Cedex 4, France

    Salem Benferhat, Didier Dubois & Henri Prade

Authors
  1. Salem Benferhat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Didier Dubois
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Henri Prade
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Benferhat, S., Dubois, D. & Prade, H. The Possibilistic Handling of Irrelevance in Exception-Tolerant Reasoning. Annals of Mathematics and Artificial Intelligence 35, 29–61 (2002). https://doi.org/10.1023/A:1014537925523

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014537925523

Search

Navigation