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Dualization of a monotone Boolean function on a finite lattice can berepresented by transforming the set of its minimal 1 to the set of its maximal0 values. In this paper we consider finite lattices given by ordered sets oftheir meet and join irreducibles (i.e., as a concept lattice of a formalcontext). We show that in this case dualization is equivalent to theenumeration of so-called minimal hypotheses. In contrast to usual dualizationsetting, where a lattice is given by the ordered set of its elements,dualization in this case is shown to be impossible in output polynomial timeunless P = NP. However, if the lattice is distributive, dualization is shown tobe possible in subexponential time.

Dualization in Lattices Given by Ordered Sets of Irreducibles