A logic of graded possibility and certainty coping with partial inconsistency

Authors:
Jérôme Lang;Didier Dubois;Henri Prade
Affiliations:
Institut de Recherche en Informatique de Toulouse, Université Paul Sabatier, Toulouse Cedex, France;Institut de Recherche en Informatique de Toulouse, Université Paul Sabatier, Toulouse Cedex, France;Institut de Recherche en Informatique de Toulouse, Université Paul Sabatier, Toulouse Cedex, France
Venue:
UAI'91 Proceedings of the Seventh conference on Uncertainty in Artificial Intelligence
Year:
1991

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Abstract

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The proposed semantics is based on fuzzy sets of interpretations. It is tolerant to partial inconsistency. Satisfiability is extended from interpretations to fuzzy sets of interpretations, each fuzzy set representing a possibility distribution describing what is known about the state of the world. A possibilistic knowledge base is then viewed as a set of possibility distributions that satisfy it. The refutation method of automated deduction in possibilistic logic, based on previously introduced generalized resolution principle is proved to be sound and complete with respect to the proposed semantics, including the case of partial inconsistency.