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Abstract. For an integer $n\geq1$, 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.
DOI: 10.14232/actasm-014-331-1
AMS Subject Classification
(1991): 06E30, 06B23, 06B99, 06D99, 06A15
Keyword(s):
isotone,
Boolean function,
lattice operations,
closure systems
Received December 11, 2014, and in revised form December 23, 2014. (Registered under 81/2014.)
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