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In this paper we present a propositional logic programming language forreasoning under possibilistic uncertainty and representing vague knowledge.Formulas are represented by pairs (A, c), where A is a many-valued propositionand c is value in the unit interval [0,1] which denotes a lower bound on thebelief on A in terms of necessity measures. Belief states are modeled bypossibility distributions on the set of all many-valued interpretations. Inthis framework, (i) we define a syntax and a semantics of the generalunderlying uncertainty logic; (ii) we provide a modus ponens-style calculus fora sublanguage of Horn-rules and we prove that it is complete for determiningthe maximum degree of possibilistic belief with which a fuzzy propositionalvariable can be entailed from a set of formulas; and finally, (iii) we show howthe computation of a partial matching between fuzzy propositional variables, interms of necessity measures for fuzzy sets, can be included in our logicprogramming system.

A Complete Calculus for Possibilistic Logic Programming with Fuzzy Propositional Variables