Possibilistic logic as a logical framework for min-max discrete optimisation problems and prioritized constraints

  • Jérôome Lang
Part II Selected Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 535)


Possibilistic logic is basically a logic of uncertainty, but a significant fragment of it can also be seen as a logic for the representation of constraints with priorities. The gradation of inconsistency enables the definition of the "best" model(s) of a "partially inconsistent" set of possibilistic formulas. Many formal results have been proved for this fragment of possibilistic logic, including its axiomatisation. Besides, there are some well-adapted automated deduction procedures. Min-max discrete optimisation problems, and more generally problems with prioritized constraints, can be translated in this logical framework, and then solved by its automated deduction procedures.


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  1. [1]
    Borning A., Maher M., Martindale A., Wilson M. (1989) "Constraint hierarchies in logic programming", Proc. ICLP'89, 149–164.Google Scholar
  2. [2]
    Descotte Y., Latombe J.C. (1985), "Making compromises among antagonistic constraints in a planner", Artificial Intelligence, 27, 183–217.Google Scholar
  3. [3]
    Dubois D., Lang J., Prade H. (1987) "Theorem proving under uncertainty — A possibility theory-based approach". Proc. of the 10th Inter. Joint Conf. on Artificial Intelligence (IJCAI 87), Milano, Italy, 984–986.Google Scholar
  4. [4]
    Dubois D., Lang J., Prade H. (1989) "Automated reasoning using possibilistic logic: semantics, belief revision and variable certainty weights". Proc. of the 5th Workshop on Uncertainty in Artificial Intelligence, Windsor, Ontario, 81–87.Google Scholar
  5. [5]
    Dubois D., Lang J., Prade H. (1991) "Fuzzy Sets in Approximate Reasoning. Part 2: Logical approaches", Fuzzy Sets and Systems 40 (1), 203–244.Google Scholar
  6. [6]
    Dubois D., Prade H. (1982) "A class of fuzzy measures based on triangular norms. A general framework for the combination of uncertain information", Int. J of Intelligent Systems, 8(1), 43–61.Google Scholar
  7. [7]
    Dubois D., Prade H. (1988) (with the collaboration de Farreny H., Martin-Clouaire R., Testemale C.) "Possibility Theory: an Approach to Computerized Processing of Uncertainty". Plenum Press, New York.Google Scholar
  8. [8]
    Dubois D., Prade H. (1987) "Necessity measures and the resolution principle". IEEE Trans. on Systems, Man and Cybernetics, 17, 474–478.Google Scholar
  9. [9]
    Dubois D., Prade H. (1991) "Epistemic entrenchment and possibilistic logic", à paraître dans Artificial Intelligence.Google Scholar
  10. [10]
    Dubois D., Prade H., Testemale C. (1988) "In search of a modal system for possibility theory". Proc. of the Conf. on Artificial Intelligence (ECAI), Munich, Germany, 501–506.Google Scholar
  11. [11]
    Froidevaux C., Grossetête C. (1990) "Graded default theories for uncertainty", ECAI 90, Stockholm, 283–288.Google Scholar
  12. [12]
    Gärdenfors P., Makinson D. (1988) "Revision of knowledge systems using epistemic entrenchment", in M. Vardi ed., Proc. Second Conference on Theoretical Aspects of Reasoning about Knowledge (Morgan Kaufmann).Google Scholar
  13. [13]
    Ginsberg M.L. (1988) "Multi-valued logics: a uniform approach to reasoning in artificial intelligence". Computational Intelligence, 4, 265–316.Google Scholar
  14. [14]
    Hooker J.N. (1986) "A quantitative approach to logical inference", Decision Support Systems 4, 45–69.Google Scholar
  15. [15]
    Jeannicot S., Oxusoff L., Rauzy A. (1988) "Evaluation sémantique: une propriété de coupure pour rendre efficace la procédure de Davis et Putman". Revue d'Intelligence Artificielle, 2(1), 41–60.Google Scholar
  16. [16]
    Lang J. (1990) "Semantic evaluation in possibilistic logic", Proc. of the 3rd Inter. Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Paris, 51–55.Google Scholar
  17. [17]
    Lang J. (1991) "Logique possibiliste: aspects formels, déduction automatique, et applications", PhD thesis, University of Toulouse (France), January 1991Google Scholar
  18. [18]
    Nilsson N. "Probabilistic logic". Artificial Intelligence, 28, 71–87.Google Scholar
  19. [19]
    Purdom P.W., "Search rearrangement backtracking and polynomial average time", Artificial Intelligence 21, 117–133.Google Scholar
  20. [20]
    Satoh K. (1990), "Formalizing soft constraints by interpretation ordering", Proc. ECAI 90, Stockholm, 585–590.Google Scholar
  21. [21]
    Wrzos-Kaminski J., Wrzos-Kaminska A., "Explicit ordering of defaults in ATMS", Proc. ECAI 90, Stockholm, 714–719.Google Scholar
  22. [22]
    Zadeh L.A. "Fuzzy sets as a basis for a theory of possibility". Fuzzy Sets and Systems, 1, 3–28.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Jérôome Lang
    • 1
  1. 1.Institut de Recherche en Informatique de ToulouseUniversité Paul SabatierToulouse CedexFrance

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