Quasi-modal operators on distributive nearlattices

Ismael Calomino ^[1] ; Sergio A. Celani ^[1] ; Luciano J. González ^[2]
1. [1] Universidad Nacional del Centro de la Provincia de Buenos Aires
  
  Universidad Nacional del Centro de la Provincia de Buenos Aires
  
  Argentina
2. [2] Universidad Nacional de La Pampa
  
  Universidad Nacional de La Pampa
  
  Argentina
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 61, Nº. 2, 2020, págs. 339-352
Idioma: inglés
DOI: 10.33044/revuma.v61n2a10
Enlaces
- Texto completo
Resumen
- 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.