Rivieccio, UmbertoLima Neto, Clodomir Silva2024-02-022024-02-022023-10-31LIMA NETO, Clodomir Silva. Algebraization in quasi-Nelson logics. Orientador: Dr. Umberto Rivieccio. 2023. 79f. Dissertação (Mestrado em Sistemas e Computação) - Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Natal, 2023.https://repositorio.ufrn.br/handle/123456789/57493Quasi-Nelson logic is a recently introduced generalization of Nelson’s constructive logic with strong negation to a non-involutive setting. The present work proposes to study the logic of some fragments of quasi-Nelson logic, namely: pocrims (ℒQNP) and semihoops (ℒQNS); in addition to the logic of quasi-N4-lattices (ℒQN4). 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 semantics of a given fragment of quasi-Nelson logic (or class of quasi-N4-lattices) can be axiomatized by means of equations or quasi-equations. The mathematical tool used in this investigation will be the twist-algebra representation. Coming to the question of algebraizability, we recall that quasi-Nelson logic (as extensions of ℱℒew) is algebraizable in the sense of Blok and Pigozzi. Furthermore, we showed the algebraizability of ℒQNP, ℒQNS and ℒQN4, which is BP-algebraizable with the set of defining equations E(x) := {x = x → x} and the set of equivalence formulas ∆(x, y) := {x → y, y → x, ∼ x → ∼ y, ∼ y → ∼ x}.Acesso AbertoComputaçãoQuasi-Nelson logicQuasi-N4-latticesAlgebraizable logicTwist-structuresmasterThesisCNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO