Algebraization in quasi-Nelson logics
Quasi-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 q...
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| Formato: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | Brasil |
| Recursos: | Universidade Federal do Rio Grande do Norte (UFRN) |
| Repositorio: | Repositório Institucional da UFRN |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufrn.br:123456789/57493 |
| Acesso em linha: | https://repositorio.ufrn.br/handle/123456789/57493 |
| Access Level: | acceso abierto |
| Palavra-chave: | Computação Quasi-Nelson logic Quasi-N4-lattices Algebraizable logic Twist-structures CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO |
| Resumo: | Quasi-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}. |
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