Skip to main content
SpringerLink
Log in

A New Default Theories Compilation for MSP-Entailment

  • Published:
Journal of Automated Reasoning Aims and scope Submit manuscript

Abstract

Handling exceptions represents one of the most important problems in Artificial Intelligence. Several approaches have been proposed for reasoning on default theories. This paper focuses on a possibilistic approach, and more precisely on the MSP-entailment (where MSP stands for Minimum Specificity Principle) from default theories which is equivalent to System P augmented by rational monotony. In order to make this entailment tractable from a computational point of view, we propose here a compilation of default theories with respect to a target compilation language. This allows us to provide polynomial algorithms to derive efficiently the MSP-conclusions of a compiled default theory. Moreover, the proposed compilation is qualified to be flexible since it efficiently takes advantage of any classical compiler and generally provides a low recompilation cost when updating a compiled default theory.

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. AbouElKalam, A., Benferhat, S., Miège, A., ElBaida, R., Cuppens, F., Saurel, C., Balbiani, P., Deswarte, Y., Trouessin, G.: Organization based access control. In: Policies for Distributed Systems and Networks (POLICY’03), pp. 120–128 (2003)

  2. Benferhat, S., Bonnefon, J.-F., Neves, R.D.S.: An experimental analysis of possibilistic default reasoning. In: 9th International Conference on the Principles of Knowledge Representation and Reasoning (KR’04), pp. 130–140 (2004)

  3. Benferhat, S., Dubois, D., Cayrol, C., Lang, J., Prade, H.: Inconsistency management and prioritized syntaxbased entailment. In: 13th International Joint Conference on Artificial Intelligence (IJCAI’93), pp. 640–645 (1993)

  4. Benferhat, S., Dubois, D., Prade, H.: Practical Handling of Exception-tainted rules and independence information in possibilistic logic. J. Appl. Intell. 9(2), 101–127 (1998)

    Article  Google Scholar 

  5. Benferhat, S., Yahi, S., Drias, H.: On the compilation of stratified belief bases under linear and possibilistic logic policies. In: 20th International Joint Conference on Artificial Intelligence (IJCAI’ 07), pp. 2428–2430 (2007)

  6. Benferhat, S., Yahi, S., Drias, H.: On the compilation of possibilistic default theories. In: 21st International Florida Artificial Intelligence Research Society Conference (Flairs’08), pp. 613–618. AAAI, Menlo Park (2008)

    Google Scholar 

  7. Boufkhad, Y., Grégoire, É., Marquis, P., Mazure, B., Sais, L.: Tractable Cover Compilations. In: IJCAI (1), pp. 122–127 (1997)

  8. Bouquet, F., Jégou, P.: Using OBDDs to handle dynamic constraints. In: Information Processing Letters, pp. 111–120 (1997)

  9. Cadoli, M., Donini, F.M.: A survey on knowledge compilation. Artif. Intell. Commun. 10, 137–150 (1997)

    Google Scholar 

  10. Darwiche, A.: Decomposable negation normal form. J. ACM 48(4), 608–647 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. Darwiche, A.: A compiler for deterministic, decomposable negation normal form. In: Proceedings of the Eighteenth National Conference on Artificial Intelligence (AAAI), pp. 627–634. AAAI, Menlo Park (2002)

    Google Scholar 

  12. Darwiche, A.: New advances in compiling CNF to decomposable negational normal form. In: Proceedings of European Conference on Artificial Intelligence (2004)

  13. Darwiche, A., Hopkins, M.: Using recursive decomposition to construct elimination orders, jointrees and dtrees. In: Trends in Artificial Intelligence. Lecture Notes in AI, 2143, pp. 180–191. Springer, New York (2001)

    Google Scholar 

  14. Darwiche, A., Marquis, P.: A knowledge compilation map. J. Artif. Intell. Res. 17, 229–264 (2002)

    MATH  MathSciNet  Google Scholar 

  15. de Kleer, J.: Problem solving with the ATMS. Artif. Intell. 28, 197–224 (1986)

    Article  Google Scholar 

  16. Dubois, D., Lang, J., Prade, H.: Possibilistic logic. Handb Log. Art. Intell. Log. Program. 3, 439–513 (1994)

    MathSciNet  Google Scholar 

  17. Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum, New York (1988)

    MATH  Google Scholar 

  18. Goldszmidt, M., Pearl, J.: System-Z+: a formalism for reasoning with variable-strength defaults. In: 9th National conference in Artificial Intelligence (AAAI’91), pp. 399–404 (1991)

  19. Kraus, S., Lehmann, D.J., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artif. Intell. 44(1–2), 167–207 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  20. Lang, J.: Possibilistic logic: complexity and algorithms. Handb. Defeasible Reason. Uncertain. Manag. Sys. 5, 179–220 (2000)

    Google Scholar 

  21. Lehmann, D.J.: Another perspective on default reasoning. Ann. Math. Artif. Intell. 15(1), 61–82 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  22. Lehmann, D.J., Magidor, M.: What does a Conditional Knowledge Base Entail?. Artif. Intell. 55(1), 1–60 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  23. Linke, T., Schaub, T.: An approach to query-answering in Reiter’s default logic and the underlying existence of extensions problem. In: 6th Logics in Artificial Intelligence (JELIA’98), pp. 233–247 (1998)

  24. Linke, T., Schaub, T.: Alternative foundations for Reiter’s default logic. Artif. Intell. 124(1), 31–86 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  25. McCarthy, J.: Circumscription—a form of non-monotonic reasoning. Artif. Intell. 13(1–2), 27–39 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  26. Mengin, J.: A theorem prover for default logic based on prioritized conflict resolution and an extended resolution principle. In: 3th Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU’95), pp. 301–310 (1995)

  27. Morgenstern, L.: Inheritance comes of age: applying nonmonotonic techniques to problems in industry. In: 15 th International Joint Conference on Artificial Intelligence (IJCAI’97), pp. 1613–1613 (1997)

  28. Nebel, B.: How hard is it to revise a belief base?. In: Handbook of Defeasible Reasoning and Uncertainty Management Systems, pp. 77–145 (1998)

  29. Papadimitriou, C.H.: Computational Complexity. Addison Wesley, Reading (1994)

    MATH  Google Scholar 

  30. Pearl, J.: System Z: a natural ordering of defaults with tractable applications to default reasoning. In: 6th Theoretical Aspects of Rationality and Knowledge (TARK’90), pp. 121–135 (1990)

  31. Reiter, R.: A logic for default reasoning. Artif. Intell. 13(1–2), 81–132 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  32. Sandhu, R.S., Coyne, E.J., Feinstein, H.L., Youman, C.E.: Role-based access control models. IEEE Comput. 29(2), 38–47 (1996)

    Google Scholar 

  33. Schrag, R., Crawford, J.M.: Implicates and prime implicates in random 3-SAT. Artif. Intell. 81(1–2), 199–222 (1996)

    Article  MathSciNet  Google Scholar 

  34. Yager, R.R.: On the specificity of a possibility distribution. Fuzzy Sets Syst. 50, 279–292 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  35. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université Lille-Nord de France, Artois, 62307, Lens, France

    Salem Benferhat & Safa Yahi

  2. CRIL, 62307, Lens, France

    Salem Benferhat & Safa Yahi

  3. CNRS UMR 8188, 62307, Lens, France

    Salem Benferhat & Safa Yahi

  4. Ecole nationale Supérieure d’Informatique, BP 68M, 16270, Oued-Smar, Algiers, Algeria

    Safa Yahi

  5. Université des Sciences et de la Technologie Houari Boumediene, BP 32 El Alia 16111 Bab Ezzouar, Algiers, Algeria

    Habiba Drias

Authors
  1. Salem Benferhat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Safa Yahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Habiba Drias
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Salem Benferhat.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Benferhat, S., Yahi, S. & Drias, H. A New Default Theories Compilation for MSP-Entailment. J Autom Reasoning 45, 39–59 (2010). https://doi.org/10.1007/s10817-009-9150-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10817-009-9150-9

Keywords

Search

Navigation