Quasi-modal operators on distributive nearlattices

CALOMINO, ISMAEL; CELANI, SERGIO; GONZÁLEZ, LUCIANO J.

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

UNION MATEMATICA ARGENTINA

Lugar: Bahia Blanca; Año: 2020

0041-6932

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 [Celani, S., Calomino, I.: extit{Distributive nearlattices with a necessity modal operator}. Math. Slovaca extbf{69} (2019), 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.