Qi, Guilin and Perrussel, Laurent (2013) Prime Forms in Possibilistic Logic. In: 2nd workshop on Weighted Logic For Artificial Intelligence, August 2013, Beijing, China.

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Abstract

Possibilistic logic is a weighted logic used to represent uncertain and inconsistent knowledge. Its semantics is often defined by a possibility distribution, which is a function from a set of interpretations to a totally ordered scale. In this paper, we consider a new semantic characteristics of knowledge bases in possibilistic logic (or possibilistic knowledge bases) by a generalized notion of propositional prime implicant, which we call prioritized
prime implicant. We first consider several desirable
properties of a prioritized prime implicant for characterizing possibilistic knowledge bases. Some examples show that existing generalizations of prime
implicant in possibilistic logic do not satisfy all of
these properties. We then provide a novel definition of prioritized prime implicant, which is a set
of weighted literals that may be inconsistent. We
show that the prioritized prime implicants satisfy
all the desirable properties. Finally, we discuss the
problem of computing prioritized prime implicants
of a possibilistic knowledge base.