We present an overview on how to perform non-monotonic reasoning based on paraconsistent logics. In particular, we show that one can define a logic programming semantics based on the paraconsistent logic G’3 which is called G’3-stable semantics. This semantics defines a frame for performing non-monotonic reasoning in domains which are pervaded with vagueness and inconsistencies. In fact, we show that, by considering also a possibilistic logic point of view, one can use this extended framework for defining a possibilistic logic programming approach able to deal with reasoning, which is at the same time non-monotonic and uncertain.

Peer Reviewed