Banca de QUALIFICAÇÃO: THIAGO NASCIMENTO DA SILVA

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : THIAGO NASCIMENTO DA SILVA
DATE: 26/01/2021
TIME: 11:00
LOCAL: https://meet.google.com/xhv-nhwz-qek
TITLE:

Algebraic Semantics and Calculi for some Nelson's logics

KEY WORDS:

Algebraisable logics, Substructural logics, Residuated lattices, Nelson’s logics, Algebraic logic.

PAGES: 66
BIG AREA: Ciências Exatas e da Terra
AREA: Ciência da Computação
SUMMARY:

The aim of this Thesis is to study in two different ways a family of Nelson’s logics, namely: Nelson’s logic S, quasi-Nelson logic QN and quasi-Nelson implicative logic QNI. The first one is by means of an axiomatisation of a logic via a Hilbert Calculus and the second one is via studying some properties of a quasi-variety of algebras, although the approach taken can be different, they are in a certain sense equivalent, given that all logics studied in this present work are algebraisable. The leading contribution of this work is to fit the above-mentioned logics in the theory of algebraisable logics. Making use of this theory, we were able to prove the following results. Regarding S, we introduced the first semantics for it, axiomatised it by means of a finite Hilbert-style calculus, and we have as well established a version of the deduction-detachment theorem (DDT) for it. Regarding QN and QNI, we showed that both are algebraisable and non-self-extensional, we showed how to obtain some other well-known logics from them by axiomatic extensions and we made explicit the quaternary term that guarantees that the latter logics (QN and QNI) satisfy DDT. It is worth mentioning that QNI is the {->, ~}-fragment of QN, so some results concerning QNI may be easily extended to QN.

BANKING MEMBERS:
Interno - 1517271 - JOAO MARCOS DE ALMEIDA
Interno - 2251108 - UMBERTO RIVIECCIO
Externo à Instituição - ALDO FIGALLO-ORELLANO - UNS
Externo à Instituição - MATTHEW SPINKS