Sound Probabilistic Reasoning under Contradiction, Inconsistency and Incompleteness

Walter Carnielli


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].

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J. Bueno-Soler andW. Carnielli. May be and may be not: paraconsistent probability from the lfi viewpoint. CLE e-prints, 15(2), 2015.

J. Bueno-Soler and W. A. Carnielli. Experimenting with consistency. Experimenting with consistency. In V. Markin and D. Zaitsev, editors, The Logical Legacy of Nikolai Vasiliev and Modern Logic. Synthese Library — Studies in Epistemology, Logic, Methodology, and Philosophy of Science-Springer, 2015.

W. A. Carnielli, M. E. Coniglio, and J. Marcos. Logics of formal inconsistency. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume 14, pages 1–93, Amsterdam, 2007. Springer-Verlag

W. Carnielli, M.E. Coniglio, R. Podiacki, and T. Rodrgues. On the way to a wider model theory: Completeness theorems for first-order logics of formal inconsistency. Review of Symbolic Logic, 3:548–578, 2015

W. Carnielli and A. Rodrigues. A logic for evidence and truth. CLE e-prints, 15(5), 2015.

E. Mares. Paraconsistent probability theory and paraconsistent Bayesianism. Logique et Analyse, 160:375–384, 1997

G. Priest. In Contradiction: A Study of the Transconsistent. Martinus Nijhoff, Amsterdam, 1987

L. Roberts. Maybe, maybe not: Probabilistic semantics for two paraconsistent logics. In D. Batens, C. Mortensen, G. Priest, and J. P van Bendegem, editors, Frontiers of Paraconsistent Logic: Proceedings of the I World Congress on Paraconsistency, Logic and Computation Series, pages 233–254. Baldock: Research Studies Press, King’s College Publications, 2000

J. N. Williams. Inconsistency and contradiction. Mind, 90:600-602, 1981


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(c) 2016 Walter Carnielli

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