terça-feira, 18 de setembro de 2007

Programação: "Oficina ConsRel- CLE 30 Anos"

Programação: "Oficina ConsRel- CLE 30 Anos "

Objetivo: A Oficina pretende um intercâmbio de idéas em torno da visita do Prof. Daniele Mundici da Universidade de Florença no âmbito das atividades do "CLE 30 Anos", além da exposição crítica de projetos e resultados por parte dos participantes do Projeto Temático FAPESP ConsRel.

A iniciativa é desenvolvida dentro da programação das atividades do Projeto Temático FAPESP ConsRel e da GT Lógica da ANPOF.

Coordenação e organização:
Prof. Walter Carnieli, Coordenador do Projeto Temático FAPESP ConsRel


21/09 (Sexta-feira)

9h00- 13h00: Tutorial: Prof. Daniele Mundici (Departamento de Matemática, Universidade de Florença, Itália).

"Many-valued reasoning: from foundations to applications"

This tutorial intends to introduce the foundations of many-valued reasoning, starting from scratch and reaching the most recent applications.
14h30 - 15h10: Prof. Walter Carnielli (CLE e IFCH- UNICAMP)

"Logics in polynomial form: motivation and perspectives"

I discuss here how proof-theory and semantics for several non-classical logics, specially many-valued logics, can be approached from an elementary algebraic perspective by means of polynomial series over appropriate fields. I show how this form of representation (called "polynomizing") can lead to the recovering of some ideas with roots in G. W. Leibniz and G. Boole. The polynomial representation not only contributes as a unifying perspective to integrate logic, algebra and the differential calculus but also works as an interesting heuristic
tool for logic.
15h10 -15h50: Pietro Carolino (Mestrando DF\IFCH- UNICAMP) A ser anunciado.
15h50- 16h30: Juan Carlos Agudelo (Doutorando DF\IFCH- UNICAMP)

"Unconventional models of computation through non-standard logic circuits"

The classical (boolean) circuit model of computation is generalized via polynomial ring calculus, an algebraic proof method adequate to non-standard logics (namely, to all truth-functional propositional logics and to some non-truth-functional logics). Such generalization allows us to
define models of computation based on non-standard logics in a natural way by using "hidden variables" in the constitution of the model. Paraconsistent circuits for the paraconsistent logic
mbC (and for some extensions) are defined as an example of such models. Some potentialities are explored with respect to computability and computational complexity.
16h50- 17h30: Rodrigo de Alvarenga Freire (Doutorando DF\IFCH-UNICAMP)

"Observações sobre Teoria de Modelos e os fundamentos do pensamento matemático"

A proposta da exposição é a de tentar esclarecer o papel de alguns desenvolvimentos da Teoria de Modelos (ligados à definabilidade) nos últimos vinte anos no contexto dos fundamentos da matemática. Para isso faremos uma discussão razoavelmente ampla sobre a questão dos fundamentos do pensamento matemático contemporâneo.
17h30 -18h10: Prof. Daniel Tausk (IME- USP). A ser anunciado.
18h10 -18h50: Leandro Suguitani (Mestrando DF\IFCH- UNICAMP)

"Tarski's axiomatization of Relation Algebra"

In 1975, Alfred Tarski delivered two lectures at Unicamp (Campinas)about Relation Algebra (RA). He was quite involved with the development of that theory, which could be seen as a branch of the so called "algebraic logic". Tarski (like De Morgan, Peirce and Schröder and others, who worked with the theory of binary relations before him) was concerned about providing an apparatus for representing the first-order logic algebraically. It was shown, afterwards, that RA could not be such an apparatus. However, Tarski's axiomatization of RA was used by him and Givant to axiomatize Set Theory. Many people kept working on some open problems left by Tarski about RA. This work aims to analyze Tarski's lectures in Brazil and put it into the historical context of the development of RA. This will be done by sketching a brief history of RA before Tarski's axiomatization, presenting the open problems which Tarski was concerned at the occasion of the lectures in Brazil and studying the different approaches that other researchers have made to these problems ever since.


24/09 (Segunda-feira)

9h30- 10h10: Prof. Marcelo E. Coniglio (CLE e IFCH- UNICAMP)

"The art of combining logics"

This talk is a quick tour on the subject of combining and decomposing logic systems. Emphasis is given to fibring, in its algebraic version. Preservation of meta-properties (such as soundness and completeness) are also addressed. Additionally, some applications are outlined. The material presented in this talk is based on the forthcoming material:

W.A. Carnielli, M.E. Coniglio, D. Gabbay, P. Gouveia and C. Sernadas, "Analysis and Synthesis of Logics: How To Cut And Paste Reasoning Systems". Volume 35 in the Applied Logic Series,
Springer, 2008, in print (book).

W.A. Carnielli and M.E. Coniglio, "Combining Logics" (entry in the Stanford Encyclopedia of Philosophy) http://plato.stanford.edu/entries/logic-combining/
10h20- 11h00: Teófilo Reis (Mestrando DF\IFCH- UNICAMP)
"Possible-Translations Coverings: a formalism of decomposition of logics"

In this seminar we present a general study of a new formalism of decomposition of logics, the "Possible-Translations Coverings", in short PTCs. The PTCs constitute a formal version of Possible-Translations Semantics, introduced by W. Carnielli in 1990. We show how the adoption of a more general notion of propositional signatures morphism allows us to define a category Sig, in which the connectives, when translated from a signature to another one, enjoy of great flexibility. The situation is the following: let f be a morphism from C to C' and c a n-ary connective in C; then f(c) is a non empty finite set of C'-formulas in which occur, at most, the first n propositional variables. From Sig we construct the category Log of tarskian logics and morphisms between them (these are functions obtained from signature morphisms, that is, from a multi-function). We show how to define in Log the set of possible translations of a given formula, and we define the notion of a PTC for a logic L. We analyze the existence of countable products in Log (what opens the possibility of characterizing a PTC as a conservative translation from L in a product of logics), as well as the relation between PTCs and Avron's Non-Deterministic Semantics. We still investigate the possibility of defining a category of PTCs,
what includes, among other things, the possibility of composing them. Finally, we give concrete examples of morphisms in Sig and PTCs.
11h10- 1h50: Juliana Bueno-Soler (Doutoranda DF\IFCH-UNICAMP)

"The roots of possible-translations algebraization"

I explain here the ideas behind a new notion of algebraizability, the "possible-translations algebraic semantics", based upon the possible-translations semantics introduced by W. A. Carnielli developed by him and J. Marcos. This semantics is naturally adequate to obtain an algebraic interpretation to paraconsistent logics, and generalizes the well-known method of algebraization by W. Blok and D. Pigozzi. This generalization obtains algebraic semantics up to translations, a method applicable to some non-classical logics. Part of this work is being developed in collaboration with M. E. Coniglio and W. A. Carnielli.
12h00- 14h00: Pausa para almoço
14h00 - 14h40: Profa. Itala M. Loffredo D'Ottaviano (CLE e IFCH- UNICAMP)
(joitn work with Prof. Hércules de Araújo Feitosa (Depto. de Matemática, UNESP- Bauru)

"Is there a translation from intuitionistic logic into classical logic?"

The historial "translations" of Kolmogorov (1925), Gödel (1933) and Gentzen (1933) interpret the classical propositional calculus (CPC) into the intuitionistic propositional calculus (IPC). In
this work, based on some previous papers, we study the problem of the existence of a conservative translation from intuitionistic logic (IPC) into classical logic (CPC). By using the respective algebraic semantics associated to CPC and IPC, we prove that if the language of CPC has an infinite and denumerable set of propositional variables then, differently of what has been
supposed in the literature, there is a conservative translation from IPC into CPC – our proof is non-constructive.
14h50 -15h30: Eberth Eleutério da Silva (Doutorando DF\IFCH-UNICAMP)
15h40- 16h20: Milton Augustinis de Castro (Pos-Doutorando, CLE- UNICAMP)
16h30- 17h10: Prof. Marcelo Finger (IME- USP)

"Minimality in axiomatizations: an algebraic approach" (work in progress)

There are several one-axiom axiomatizations for classical propositional logics using only the NAND connective, all with 23 symbols. There is a one-axiom axiomatizations for classical
propositional logics over implication and falsum, with 19 symbols only.

We show a relationship between these two possibly minimal axiomatizations and Boolean Rings. This coincidence predicts that the minimal sizes for each set of connectives is exactly 23 and
19. We present some initial results in actually trying to prove that this coincidence is no coincidence at all.

This is a joint work with Walter Carnielli.
17h20 -18h00: Fábio M. Bertato (Doutorando DF\IFCH- UNICAMP)

"A perspectiva como disciplina matemática nas obras de Luca Pacioli e Leonardo da Vinci"

Considera-se, tradicionalmente, que o advento da Perspectiva Linear ocorreu em Florença, no início do Quattrocento. Para alguns autores renascentistas, os infinitos e diversos aspectos
da realidade ordenam-se em um sistema racional e universal, o espaço, que é idealmente representado pela Perspectiva. O sistema das artes liberais, considerado como parte da herança recebida da Antigüidade Clássica, estava bem estabelecido até esse período. As disciplinas matemáticas, Aritmética, Geometria, Astronomia e Música, constituíam o chamado Quadrivium. Luca Pacioli (1445 –1517?) e Leonardo Da Vinci (1452 - 1519) estavam entre aqueles autores que defendiam a elevação do status da Perspectiva, ou seja, sua inclusão no Quadrivium. Nosso objetivo é apresentar um breve panorama das classificações das matemáticas da Antigüidade
ao Renascimento e analisar alguns paralelos entre as posições de Leonardo e Luca, com base, especialmente, nos capítulos iniciais da "De Divina Proportione" e no "Paragone" do "Trattato della Pittura".

18h00 - Confraternização


Nenhum comentário: