09/02/2015, 11:00— Room P3.10, Mathematics Building
Walter Carnielli, CLE / UNICAMP - Brazil
TITLE: Towards a new way to algebraize FOL (and several others).
ABSTRACT: The algebraic method for theorem proving based on the reduction of first-order formulas within certain rings (commutative rings with unity) equipped with infinitary operations is shown to indicate a possible didate for a new version of algebrization of FOL, at the same time where the notion of logical derivability is characterized by the notion of algebraic solubility. The topics I intend to discuss are the following: i) the polynomial ring method as an alternative to algebraizing logic; ii) the notion of M-ring, that allows us to operate with some kind of infinitary version of Boolean sums and products; iii) FOL in polynomial version; iv) soundness and completeness of the polynomial ring method for FOL.
Work in progress, joint with M. Matulovic and H. L. Mariano. More Information..
09/02/2015, 15:00 — Room P3.10, Mathematics Building
Juliana Bueno-Soler, UNICAMP
TITLE: Amending probability with consistency.
ABSTRACT: I will discuss the first step towards constructing 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. This is achieved by means of appropriate notions of conditional probability and paraconsistent 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.
Work in progress. Joint work with W. A. Carnielli. More Information..