de Morgan bisemilattices

Abstract

We study de Morgan bisemilattices, which are algebras of the form (S, /spl cup/, /spl and/, /sup -/, 1, 0), where (S, /spl cup/, /spl and/) is a bisemilattice, 1 and 0 are the unit and zero elements of S, and /sup -/ is a unary operation, called quasi-complementation, that satisfies the involution law and de Morgan's laws. de Morgan bisemilattices are generalizations of de Morgan algebras, and have applications in multi-valued simulations of digital circuits. We present some basic observations about bisemilattices, and provide a set-theoretic characterization for a subfamily of de Morgan bisemilattices, which we call locally distributive de Morgan bilattices.