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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| Format: | Dissertação |
| Jezik: | pt_BR |
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Universidade Federal do Rio Grande do Norte
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| Online dostop: | https://repositorio.ufrn.br/handle/123456789/57493 |
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| Izvleček: | 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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