Handling Uncertainty, Context, Vague Predicates, and Partial Inconsistency in Possibilistic Logic

This short paper intends to provide an introduction to possibilistic logic, a logic with weighted formulas, to its various capabilities and to its potential applications. Possibilistic logic, initially proposed in [11], see also Lea Sombe [26] for an introduction, can be viewed as an important fragment of Zadeh[32]’ s possibility distribution-based theory of approximate reasoning, put in a logical form. Possibilistic logic also relies on an ordering relation reflecting the relative certainty of the formulas in the knowledge base. As it will be seen, its semantics is based on a possibility distribution which is nothing but a convenient encoding of a preference relation a la Shoham[29], between interpretations. This kind of semantics should not be confused with the similarity relation-based semantics recently proposed by Ruspini[28] for fuzzy logics which rather extends the idea of interchangeable interpretations in a coarsened universe, e.g. Farinas del Cerro and Orlowska[17], and which corresponds to another issue.