Séminaire de Logiques Non Classiques : Walter Carnielli
Centre for Logic,Epistemology and the History of Science and Department of Philosophy State University of Campinas, Brazil
On rational belief under contradiction: foundations of paraconsistent probability
Understanding paraconsistent probability measures as "degrees of rational belief under contradiction", I intend to show that the distribution of degrees of belief under the pressure of contradictions by an ideally rational agent can be combined with logic by satisfying certain paraconsistent probability axioms. I also intend to discuss how this philosophical stance leads to a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs). It will be shown that LFIs very naturally encode an extension of the notion of probability able to express sophisticate probabilistic reasoning under contradictions by means of appropriate notions of conditional probability and updating, via a version of Bayes' Theorem for conditionalization. It will be also shown that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in this proposed extension of the notion of probability. Joint work with J. Bueno-Soler.