Isotone lattice-valued Boolean functions and cuts

Abstract

© 2015 Bolyai Institute, University of Szeged. For an integer n > 1, an n-ary lattice-valued Boolean function is a map from the n-th direct power of the 2-element Boolean lattice to a bounded lattice. In terms of closure systems and cuts, we characterize lattice-valued Boolean functions that can be given by linear combinations of elements of the co-domain lattice.