Possibilistic logic: from certainty-qualified statements to two-tiered logics -- a prospective survey (Q2296691)

This paper reviews the main features, developements and applications of possibility logic (PL), a counterpart of possibility theory. Basic possibility logic extends classical logic by associating to each elementary formula a certainty level belonging to a bounded scale. Semantics are represented by epistemic states and corresponding fuzzy sets. First, the basic concepts of PL are introduced and then the focus is on numerous applications of PL, including possibilistic networks, default reasoning, belief revision, information fusion, decision under uncertainty and others. Extensions of basic PL are obtained by considering vectors of certainty levels and more abstract pure symbolic levels of certainty, paraconsistent valuations, subsets of agents, and an even more general extension to generalized possibility logic (GPL). Applications of GPL are in the realms of nonmonotonic logic programming and multiple agent reasoning. For the entire collection see [Zbl 1412.68007].