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КОНФЕРЕНЦИИ
Walter Carnielli mini course "A Glimpse of The Brazilian School of Logic: its Philosophy and Mathematics"
(13–15 августа 2024 г., МИАН, ауд. 110 + Zoom, г. Москва)

Walter Carnielli's visit and tutorial got CANCELLED for personal reasons.


Lecture #1. A Survey of the Paraconsistency Program and its Potentialities
This lecture is dedicated to offering an overview of the paraconsistency program as developed by the Brazilian group at CLE-Unicamp and discussing its potentialities and new directions, as well as the problems still to be tackled.

I intend to discuss the main lines of the philosophy of paraconsistency and paracompleteness, the Logics of Formal Inconsistency, and the Possible-Translation Semantics and Swap Structures. I will also touch on the question of algebraizability, the First-Order LFIs, new forms of set theory, and novel forms of probability.

Lecture #2. Paraconsistency, Evidence, and Probability
Evidence is vital in science, law, and medicine. It is the cornerstone of scientific inquiry, enabling researchers to validate hypotheses and build reliable knowledge. The presentation of solid evidence in the law helps to protect the rights of individuals. However, evidence can be missing (“the absence of evidence is not the evidence of absence”) or contradictory, and there is little investigation into the logics and philosophy of evidence. In this lecture, I will expound on the research program around the Logics of Evidence and Truth.

I will discuss several aspects of such logics, emphasizing three different forms of semantics (valuation, Kripke-style, and probabilistic), and pointing out some plausible applications to databases and Artificial Intelligence.

Lecture #3. Many-valued Logics of Evidence and Truth
In this lecture, I discuss the Logic of Evidence and Truth LETF+ together with a sound, complete, and decidable six-valued deterministic semantics. This logic extends the Belnap-Dunn four-valued logic with rules for propagation of classicality, which are inferences that express how the classicality operator " o " is transmitted from less complex to more complex sentences. The six-valued semantics proposed extends the four values of Belnap-Dunn with two more values that intend to represent (positive and negative) reliable information.

LETF+ is one of the few really relevant six-valued logics and has some nice properties, including the fact that its implication-free fragment coincides with the degree-preserving logic of the involutive Stone algebras. The results are being published by M. E. Coniglio and A. Rodrigues in Studia Logica (2024).


Руководитель
Carnielli Walter




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