# 09/ 11/2016 — Guilherme Araújo Cardoso

As tentativas de soluções propostas ao Paradoxo do Mentiroso podem ser agrupadas em famílias de abordagens. Uma classificação razoável é aquela que distingue as Abordagens Parciais, as Abordagens Inconsistentes e as Abordagens Contextuais. As Abordagens Parciais se caracterizam pela admissão de truth value gaps. Podemos citar, como exemplos desta família de abordagens, os seguintes trabalhos (dentre outros): Van Frasseen (1968), Herzberger, H. (1970), Kripke, S. (1975) e Martin, R. (1984). As Abordagens Inconsistentes se caracterizam pela admissão de truth value gluts. Podemos citar, como exemplos desta família de abordagens, os seguintes trabalhos (dentre outros): Eklund, M. (2002), Priest, G. (2006) e Patterson, D. (2007). Finalmente, as Abordagens Contextuais se caracterizam pela admissão de algum tipo de interferência do contexto na avaliação das sentenças (ou proposições), o que permite preservar interpretações clássicas e evitar os gaps e gluts. Podemos citar, como exemplos desta família de abordagens, os seguintes trabalhos (dentre outros): Parsons, C. (1974), Barwise, J. e Etchemendy, J. (1987), Glanzberg, M. (2001) e Simmons, K. (2007). A rigor, existem objeções às três famílias de abordagens. Estas objeções são disponibilizadas pelos Argumentos de Vingança que, por sua vez, permitem reconstruir versões do Mentiroso que sejam imunes ao tipo de solução proposta. Nesta apresentação, tentaremos defender as Abordagens Contextuais do Mentiroso, dando atenção especial à Teoria de Situações de Barwise, J. e Etchemendy, J. (1987) e ao modo como tal teoria permitiria desarmar o argumento da vingança.

# 05/10/2016 — Exequiel Rivas

Título: Logic, categories and programming languages.
Abstract: Categorical logic connects two separate fields in mathematics:
logic and category theory. Can we add the mathematical study of
programming
languages to this picture? In this talk we will explore how programming
languages connect to logic (via Curry-Howard isomorphisms) and categories
(via categorical semantics). In addition, the speaker will try to show how
his research fits into this setting

# 28/09/2016 — Ana Claudia Golzio

Title: Towards an hyperalgebraic theory of non-algebrizable logics

Authors:
Marcelo Esteban Coniglio (CLE-UNICAMP),
Aldo Figallo Orellano (Dep. de Mat.- Universidad Nacional del Sur and CLE-UNICAMP) and
Ana Claudia Golzio (PhD Program IFCH/CLE-UNICAMP)

Abstract:
Multialgebras (or hyperalgebras) have been very much studied in the literature. In the realm of Logic, they were considered by Avron and his collaborators under the name of non-deterministic matrices (or Nmatrices) as a useful semantics tool for characterizing some logics (in particular, several logics of formal inconsistency or LFIs) which cannot be characterized by a single finite matrix. In particular, these LFIs are not algebraizable by any method, including Blok and Pigozzi general theory. Carnielli and Coniglio introduced a semantics of swap structures for LFIs, which are Nmatrices defined over triples in a Boolean algebra, generalizing Avron’s semantics. In this paper we develop the first steps towards the possibility of defining an algebraic theory of swap structures for LFIs, by adapting concepts of universal algebra to multialgebras in a suitable way.

# 22/06/2016 – Aldo Figallo

A preliminary study of MV-algebras with two quantifiers which commute

Aldo Figallo Orellano ( Dep. de Mat.- Universidad Nacional del Sur and CLE-UNICAMP)

We investigate the class of MV-algebras equipped with two quantifiers which commute as a natural generalization of diagonal–free two–dimensional cylindric algebras (see [2]). In the 40’s, Tarski first introduced cylindric algebras in order to provide an algebraic apparatus for the study of classical predicate calculus. The diagonal–free two–dimensional cylindric algebras are special cylindric algebras. The treatment here of MV-algebras is done in terms of implication and negation. This allows us to simplify some results due to Di Nola and Grigolia in [1] related to the characterization of a quantifier in terms of some special subalgebra associated to it. On the other hand, we present a topological duality for this class of algebras and we apply it to characterize the congruences of one algebra via certain closed sets. Finally, we study the subvariety of this class generated by a chain of length $n+1$ ($n<\omega$). We prove that the subvariety is semisimple and we characterize their simple algebras. Using a special functional algebra, we determine all the simple finite algebras of this subvariety.

[1] A. Di Nola and R. Grigolia, On monadic $MV$–algebras, Ann. Pure Appl. Logic 128 (2004), no. 1-3, 125–-139.

[2] L. Henkin, D. Monk and A. Tarski, {\em Cylindric Algebras}, Parts I & II, North-Holland, 1971 & 1985

The paper of our talk can be consulted in:

http://www.cle.unicamp.br/e-prints/vol_15,n_3,2015.html

or

# 01/06/2016 — Rodolfo Ertola

On some modal connectives
José Luis Castiglioni (CONICET and UNLP – Argentina)
and
Rodolfo C. Ertola-Biraben (CLE/Unicamp – Brazil)

Abstract

We investigate some modal operators of necessity and possibility in the context of meet-complemented (not necessarily distributive) lattices. We proceed in stages, considering the distributive case and Heyting algebras. We also compare our operators with others in the literature. We pay special attention to modalities. For details, please check http://arxiv.org/abs/1603.02489

# 11/05/2016 — Bruno Ramos Mendonça

A Fraïssé-Hintikka theorem for LFIs:

In this talk we show that in QmbC it holds a result analogous to Fraïssé-Hintikka theorem for classical logic. Firstly, we define partial isomorphism between models of QmbC. Finally, we prove that there is partial isomorphism of lenght k between models of QmbC if and only if both agree in any formula A with prefix of quantifiers of lenght at most k such that every quantifier occurring in A outside the scope of that prefix of quantifiers is in the scope of a negation or a consistency operator. Our central motivation is to be able to, with this result in hand, classify inconsistent formulas in the language of QmbC, result that we still did not achieve.

Keywords: Fraïssé-Hintikka theorem; Logics of formal inconsistency; QmbC; Partial isomorphism.