  We establish a formal connection between algorithmic correspondence theory
and certain dual characterization results for finite lattices, similar to
Nation's characterization of a hierarchy of pseudovarieties of finite lattices,
progressively generalizing finite distributive lattices. This formal connection
is mediated through monotone modal logic. Indeed, we adapt the correspondence
algorithm ALBA to the setting of monotone modal logic, and we use a certain
duality-induced encoding of finite lattices as monotone neighbourhood frames to
translate lattice terms into formulas in monotone modal logic.
