Raisonnements Plausibles, Décision, Méthodes de Preuves

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      Handling rules having potential exceptions in presence of incomplete information requires a distinction to be made between the base of rules encoding default knowledge of the type "if a is true, generally b is true", and factual information describing an incompletely-informed situation.

      Our contributions to this problem includes several semantical counterparts to the preference entailment and to the rational closure entailment proposed by Kraus, Lehmann and Magidor on an axiomatic basis. These semantics for nonmonotonic reasoning are expressed in terms of
- possibility theory-based conditionals: the rule "if a is true, generally b is true" translates into "a and b" is strictly more possible than "a and not b";
- conditional objects of the form "b given a", which are compatible with the notion of conditioning in uncertainty calculi, and which provide a ternary logic-based approach to preference entailment ;
- big-stepped probabilities, a special type of probabilies such that p_i > Σ_j=i+1,n p_j for p₁ > ... > ... > p_n.

      A possibilistic logic encoding of the rational closure entailment for default knowledge has been developed, which is rather simple, since possibilistic logic is basically classical logic augmented with certainty/priority levels (understood as lower bounds of necessity measures, the dual of possibility measures)
      Methods for repairing a default knowledge, from which the rational closure entailment (but not the preference entailment) yields undesirable result, have been proposed. It amounts to adding more default rules.
      Graphical counterparts for the possibilistic logic representation framework have been also developed; see "Graphical representations. Independence".

contacts: S. Benferhat, D. Dubois, H. Prade.

some recent publications

• S. Benferhat, D. Dubois, H. Prade. Possibilistic and standard probabilistic semantics of conditional knowledge bases. Journal of Logic and Computation, 9, 873-895, 1999.
• S. Benferhat, A. Saffiotti, Ph. Smets. Belief functions and default reasoning. Artificial Intelligence J., 122/1-2, 2000, 1-69.

January 2003