Modal operators for meet-complemented lattices

CASTIGLIONI, JOSÉ LUIS; ERTOLA-BIRABEN, RODOLFO C.

LOGIC JOURNAL OF THE IGPL (PRINT)

OXFORD UNIV PRESS

Año: 2017

1367-0751

We investigate some modal operators of necessity and possibility that form an adjoint pair in the context of meet-complemented lattices. We prove that they form an equational class and we study the modalities, i.e. the finite sequences of unary operators. We proceed in stages, first considering the not necessarily distributive case and also considering the case with the algebraic version of the 4 axiom in modal logic. We compare our operators with other operators in the literature, to wit, the maximum Boolean below and operations defined using the dual of the meet-complement.