ACTA issues

Isotone lattice-valued Boolean functions and cuts

Eszter K. Horváth, Branimir Šešelja, Andreja Tepavčevič

Acta Sci. Math. (Szeged) 81:3-4(2015), 375-380

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.)