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Paraconsistent Probability and Uncertainty: How a Computer should Reason about Evidence (Master Class 8)

Walter Carnielli (University of Campinas – Unicamp, Brazil)

Abstract: 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 of 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 interpreted by Kripke-style models and quantified by giving probabilistic and possibilistic semantics for LETF in terms of measures of evidence. This exposition is a preview of a chapter of a forthcoming book by Carnielli, Coniglio and Rodrigues to appear. in the Synthese Library – Studies in Epistemology, Logic, Methodology, and Philosophy of Science.

References:
N. Belnap, How a computer should think. In G. Ryle (Editor), Contemporary Aspects of Philosophy, Oriel Press, Stocksfield, pages 30-56, 1977

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

W. A. Carnielli and A. Rodrigues. An epistemic approach to paraconsistency: a logic of evidence and truth. Synthese 196, 3789-3813 (2019). https://doi.org/10.1007/s11229-017-16...

A. Rodrigues, J. Bueno-Soler and W. A Carnielli. Measuring evidence: a probabilistic approach to an extension of Belnap–Dunn logic. Synthese 198, 5451-5480 (2021). https://doi.org/10.1007/s11229-020-02...

H. Antunes, W. A. Carnielli, A. Kapsner and A. Rodrigues. Kripke-style models for Logics of Evidence and Truth Axioms 2020, 9(3), 100; Online at https://doi.org/10.3390/axioms9030100

W. A. Carnielli, M. E. Coniglio and A. Rodrigues. Contradictions, Evidence, and Truth -An Epistemic Account of Paraconsistency Synthese Library – Studies in Epistemology, Logic, Methodology, and Philosophy of Science. Springer, to appear.