Quasi-modal operators on distributive nearlattices

Authors

  • Ismael Calomino CIC and Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto 399, 7000 Tandil, Argentina
  • Sergio A. Celani CONICET and Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto 399, 7000 Tandil, Argentina
  • Luciano J. González Universidad Nacional de La Pampa. Facultad de Ciencias Exactas y Naturales. Santa Rosa, Argentina

DOI:

https://doi.org/10.33044/revuma.v61n2a10

Abstract

 We introduce the notion of quasi-modal operator in the variety of distributive nearlattices, which turns out to be a generalization of the necessity modal operator studied in [S. Celani and I. Calomino, Math. Slovaca 69 (2019), no. 1, 35-52]. We show that there is a one to one correspondence between a particular class of quasi-modal operators on a distributive nearlattice and the class of possibility modal operators on the distributive lattice of its finitely generated filters. Finally, we consider the concept of quasi-modal congruence, and we show that the lattice of quasi-modal congruences of a quasi-modal distributive nearlattice is isomorphic to the lattice of congruences of the lattice of finitely generated filters with a possibility modal operator.

Downloads

Download data is not yet available.

Downloads

Published

2020-12-05

Issue

Vol. 61 No. 2 (2020)

Section

Article

License

Copyright (c) 2023 Ismael María Calomino, Sergio Celani

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following terms:

Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal. The Journal may retract the paper after publication if clear evidence is found that the findings are unreliable as a result of misconduct or honest error.