Lattice theory has intimate connections with modal logic via algebraic semantics and lattices of modal logics. However, one less explored direction is to view lattices as relational structures extending partial orders, and study the modal logic over them. In this paper, following the earlier steps of Burgess and van Benthem in the 1980s, we use the basic tense logic and its extension with infimum and supremum binary modalities and nominals to talk about lattices based on Kripke semantics. As the main results and also the first steps of a general research program, we obtain a series of complete finite axiomatizations of lattices and (un)bounded lattices.
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