Lattice induced threshold functions and Boolean functions
Rings and Algebras
2013-07-05 v1
Abstract
Lattice induced threshold function is a Boolean function determined by a particular linear combination of lattice elements. We prove that every isotone Boolean function is a lattice induced threshold function and vice versa. We also represent lattice valued up-sets on a finite Boolean lattice in the framework of cuts and lattice induced threshold functions. In terms of closure systems we present necessary and sufficient conditions for a representation of lattice valued up-sets on a finite Boolean lattice by linear combinations of elements of the co-domain lattice.
Keywords
Cite
@article{arxiv.1307.1318,
title = {Lattice induced threshold functions and Boolean functions},
author = {Eszter K. Horváth and Branimir Seselja and Andreja Tepavcevic},
journal= {arXiv preprint arXiv:1307.1318},
year = {2013}
}
Comments
14 pages, 2 small figures