Sound Probabilistic Reasoning under Contradiction, Inconsistency and Incompleteness

Аннотация

I intend to show how probability theory can be regarded as logic-dependent, viewing probability as a branch of logic in a generalized way. A kind of meta-axiomatics permits us to define probability measures that are either classical, paraconsistent, intuitionistic, or simultaneously intuitionistic and paraconsistent, just by parameterizing on consequence relations. In particular, I intend to discuss theories of probability built upon the paraconsistent Logic of Formal Inconsistency Ci, and upon the paraconsistent and paracomplete Logic of Evidence and Truth LETj. I argue that Ci very naturally encodes an extension of the notion of probability able to express probabilistic reasoning under an excess of information (contradictions), while LETj encodes an extension of the notion of probability able to express probabilistic reasoning under lack of information (incompleteness), and is thus naturally connected to the notion of probability of evidence. I also discuss how interesting non-standard Bayesian updating can be defined in both cases. This is a joint project with J. Bueno-Soler and A. Rodrigues. and most results already appear in [1] and in [5].