Banca de QUALIFICAÇÃO: CLODOMIR SILVA LIMA NETO
Uma banca de QUALIFICAÇÃO de MESTRADO foi cadastrada pelo programa.STUDENT : CLODOMIR SILVA LIMA NETO
DATE: 27/04/2023
TIME: 14:00
LOCAL: DIMAp
TITLE:
Algebraization in quasi-Nelson logics
KEY WORDS:
Quasi-Nelson logic. Quasi-N4-lattices. Algebraizable logic. Non-involutive. Twist-structures.
PAGES: 65
BIG AREA: Ciências Exatas e da Terra
AREA: Ciência da Computação
SUBÁREA: Teoria da Computação
SPECIALTY: Lógicas e Semântica de Programas
SUMMARY:
Quasi-Nelson logic is a recently introduced generalization of Nelson's cons\-tructive logic with strong negation to a non-involutive setting. The present work proposes to study the logic of quasi-Nelson pocrims ($\mathbf{L}_{\mathrm{QNP}}$) and the logic of quasi-N4-lattices ($\mathbf{L}_{\mathrm{QN4}}$). This is done by means of an axiomatization via a finite Hilbert-style calculus. The principal question which we will address is whether the algebraic counterpart of a given fragment of quasi-Nelson logic (or class of quasi-N4-lattices) can be axiomatized abstractly by means of identities or quasi-identities. Our main mathematical tool in this investigation will the twist-algebra representation. Coming to the question of algebraiza\-bility, we recall that quasi-Nelson logic (as extensions of $\mathbf{FL_{ew}}$) is obviously algebraizable in the sense of Blok and Pigozzi. Furthermore, we showed the algebraizability of $\mathbf{L}_{\mathrm{QNP}}$ and $\mathbf{L}_{\mathrm{QN4}}$, which is BP-algebraizable with the set of defining identity $E(\alpha) := \{ \alpha \approx \alpha \to \alpha \}$ and the set of equivalence formula $\Delta(\alpha, \beta) := \{ \alpha \to \beta, \beta \to \alpha, \nnot \alpha \to \nnot \beta, \nnot \beta \to \nnot \alpha \}$. In this document, we register the achieved results up to the present moment and indicate a plan for the developments to be included in the final version of this thesis.
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