May be and may be not: paraconsistent probabilities from the LFI
This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs). We show that LFIs encode very naturally na extension of the notion of probability able to express sophisticate probabilistic reasoning under contradictions by means of appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes' Theorem for conditionalization. Several examples of application are discussed, and some philosophical and conceptual aspects on probability and its relation to logic are addressed. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability.