Revista de la
Unión Matemática Argentina
Quasi-modal operators on distributive nearlattices
Ismael Calomino, Sergio A. Celani, and Luciano J. González
Volume 61, no. 2 (2020), pp. 339–352    

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

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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.