On the relation of negations in Nelson algebras

Conrado  Gomez; Miguel Andres  Marcos; Hernan Javier San Martin

On the relation of negations in Nelson algebras

Publication date: 10.11.2021

Reports on Mathematical Logic, 2021, Number 56, pp. 15 - 56

https://doi.org/10.4467/20842589RM.21.002.14374

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Titles

On the relation of negations in Nelson algebras

Abstract

The aim of this paper is to investigate the relation between the strong and the "weak" or intuitionistic negation in Nelson algebras. To do this, we define the variety of Kleene algebras with intuitionistic negation and explore the Kalman's construction for pseudocomplemented distributive lattices. We also study the centered algebras of this variety.

AMS subject classification: 06D16, 03G25.

Keywords

negations, A Nelson algebras, pseudocomplemented distributive lattices, Kleene algebras.

References

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Information

Information: Reports on Mathematical Logic, 2021, Number 56, pp. 15 - 56

DOI: https://doi.org/10.4467/20842589RM.21.002.14374

Article type: Original article

Titles:

Polish:

On the relation of negations in Nelson algebras

English:

On the relation of negations in Nelson algebras

Authors

Conrado Gomez

Instituto de Matematica Aplicada del Litoral, UNL, CONICET, FIQ. Predio Dr. Alberto Cassano del CCT-CONICET-Santa Fe, Colectora de la Ruta Nacional no. 168, Santa Fe (3000), Argentina

Miguel Andres Marcos

Facultad de Ingenieria Quimica, CONICET-Universidad Nacional del Litoral. Santiago del Estero 2829, Santa Fe (3000), Argentina

Hernan Javier San Martin

Departamento de Matematica, Facultad de Ciencias Exactas (UNLP), and CONICET. Casilla de correos 172, La Plata (1900), Argentina.

Published at: 10.11.2021

Received at: 21.10.2020

Article status: Open

Licence: CC BY-NC-ND

Percentage share of authors:

Conrado Gomez (Author) - 33%

Miguel Andres Marcos (Author) - 33%

Hernan Javier San Martin (Author) - 34%

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English

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