Paraconsistent Probability and Uncertainty: How a Computer should Reason about Evidence
Evidence, probability, and logic are intrinsically related, and reasoning with evidence is a topic with higher interest not only for philosophy, but also for machine learning and AI. Evidence may be contradictory as well as incomplete, thus demanding a paracomplete and paraconsistent logic. This talk discusses an intuitively appealing probabilistic semantics for LETF, a paracomplete and paraconsistent extension of the logic of First-Degree Entailment (FDE, cf. Belnap, 1977) expanded with operators for consistency and inconsistency, typical in the Logics of Formal Inconsistency. It is shown that LETF is suitable for an interpretation in terms of preservation of non-conclusive and conclusive evidence, the later being understood as truth. Extending work done in Carnielli & Rodrigues, 2019 and Rodrigues, Bueno-Soler & Carnielli 2019, evidence can be quantified by giving a probabilistic semantics for LETF in terms of measures of evidence.
N. Belnap, How a computer should think. In G. Ryle (Editor), Contemporary Aspects of Philosophy, Oriel Press, Stocksfield, pages 30-56, 1977.
W. A. Carnielli and A. Rodrigues. An epistemic approach to paraconsistency: a logic of evidence and truth. Synthese. On line at https://link.springer.com/article.
J. Bueno-Soler and W. A. Carnielli. Paraconsistent probabilities: consistency, contradictions and Bayes’ theorem. Entropy 18(9) 2016. Open acess at http://www.mdpi.com/ 1099-4300/18/9/325/htm.
A. Rodrigues, J. Bueno-Soler and W. A. Carnielli. Measuring evidence: a probabilistic approach to an extension of Belnap-Dunn logic. Submitted for publication.