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...
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Universidade Federal do Rio Grande do Norte
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ri-123456789-574932024-02-02T20:13:37Z Algebraization in quasi-Nelson logics Lima Neto, Clodomir Silva Rivieccio, Umberto https://orcid.org/0000-0001-9835-9481 http://lattes.cnpq.br/6847191906266562 http://lattes.cnpq.br/0597230560325577 Almeida, João Marcos de https://orcid.org/0000-0003-2601-8164 http://lattes.cnpq.br/3059324458238110 Santiago, Regivan Hugo Nunes Biraben, Rodolfo Ertola Computação Quasi-Nelson logic Quasi-N4-lattices Algebraizable logic Twist-structures CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO 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}. A lógica quase-Nelson é uma generalização recentemente introduzida da lógica construtiva com negação forte de Nelson para um cenário não involutivo. O presente trabalho se propõe a estudar a lógica de alguns fragmentos da lógica de quase-Nelson, a saber: pocrims (ℒQNP) e semihoops (ℒQNS); além da lógica de quase-N4-reticulados (ℒQN4). Isso é feito por meio de uma axiomatização através de um cálculo finito no estilo Hilbert. A principal questão que abordaremos é se a semântica algébrica de um determinado fragmento da lógica quase-Nelson (ou classe quase-N4-reticulados) pode ser axiomatizada por meio de equações ou quase-equações. A ferramenta matemática utilizada nesta investigação será a representação twist-álgebra. Chegando à questão da algebrização, lembramos que a lógica quase-Nelson (como extensão de ℱℒew) é algebrizável no sentido de Blok e Pigozzi. Além disso, mostramos a algebrizabilidade de ℒQNP, ℒQNS e LQN4, que é BPalgebrizável com o conjunto de equações definidoras E(x) := {x = x → x} e o conjunto de fórmulas de equivalência ∆(x, y) := {x → y, y → x, ∼ x →∼ y, ∼ y → ∼ x}. 2024-02-02T20:13:03Z 2024-02-02T20:13:03Z 2023-10-31 masterThesis LIMA 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/123456789/57493 pt_BR Acesso Aberto application/pdf Universidade Federal do Rio Grande do Norte Brasil UFRN PROGRAMA DE PÓS-GRADUAÇÃO EM SISTEMAS E COMPUTAÇÃO |
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RI - UFRN |
| language |
pt_BR |
| topic |
Computação Quasi-Nelson logic Quasi-N4-lattices Algebraizable logic Twist-structures CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO |
| spellingShingle |
Computação Quasi-Nelson logic Quasi-N4-lattices Algebraizable logic Twist-structures CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO Lima Neto, Clodomir Silva Algebraization in quasi-Nelson logics |
| description |
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}. |
| author2 |
Rivieccio, Umberto |
| author_facet |
Rivieccio, Umberto Lima Neto, Clodomir Silva |
| format |
masterThesis |
| author |
Lima Neto, Clodomir Silva |
| author_sort |
Lima Neto, Clodomir Silva |
| title |
Algebraization in quasi-Nelson logics |
| title_short |
Algebraization in quasi-Nelson logics |
| title_full |
Algebraization in quasi-Nelson logics |
| title_fullStr |
Algebraization in quasi-Nelson logics |
| title_full_unstemmed |
Algebraization in quasi-Nelson logics |
| title_sort |
algebraization in quasi-nelson logics |
| publisher |
Universidade Federal do Rio Grande do Norte |
| publishDate |
2024 |
| url |
https://repositorio.ufrn.br/handle/123456789/57493 |
| work_keys_str_mv |
AT limanetoclodomirsilva algebraizationinquasinelsonlogics |
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1790055918902181888 |