Banca de QUALIFICAÇÃO: THIAGO NASCIMENTO DA SILVA

Uma banca de QUALIFICAÇÃO de MESTRADO foi cadastrada pelo programa.
DISCENTE : THIAGO NASCIMENTO DA SILVA
DATA : 14/09/2017
HORA: 14:00
LOCAL: DIMAp / Auditório 1
TÍTULO:

Nelson's logic S and its algebraic semantics

PALAVRAS-CHAVES:

Logic, Algebraic Logic; Nelson's Logic; Constructive logic; Semantics

PÁGINAS: 50
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Ciência da Computação
SUBÁREA: Teoria da Computação
ESPECIALIDADE: Lógicas e Semântica de Programas
RESUMO:

Besides the better-known Nelson logic (N3) and paraconsistent Nelson logic (N4), David Nelson introduced, in the 1959 paper "Negation and separation of concepts in constructive systems”, with motivations of arithmetic and constructibility, a logic that he called “S”. In the present study, the logic is defined by means of a calculus (which crucially lacks the contraction rule) having infinitely many rule schemata, and no semantics is provided for it.

We look at the propositional fragment of S, showing that it is algebraizable (in fact, implicative) in the sense of Blok & Pigozzi with respect to a class of involutive residuated lattices. We thus provide the first known (algebraic) semantics for S as well as a Hilbert-style calculus equivalent to Nelson’s presentation. We also compare S with the other logics in the Nelson family N3 and N4.

MEMBROS DA BANCA:
Interno - 1517271 - JOAO MARCOS DE ALMEIDA
Externo à Instituição - MARCO CERAMI - UFBA
Presidente - 2251108 - UMBERTO RIVIECCIO