Boolean algebra of C-algebras

Abstract

A C- algebra is the algebraic form of the 3-valued conditional logic,which was introduced by F. Guzman and C.C. Squier in 1990. In this paper, some equivalent conditions for a C- algebra to become a boolean algebra interms of congruences are given. It is proved that the set of all central elements B(A) is isomorphic to the Boolean algebra BS(A)of all C-algebras Sa, where a ∈ B(A). It is also proved that B(A) is isomorphic to the Boolean algebra BR(A) of all C-algebras Aa, where a ∈ B(A). © 2012 Published by LPPM ITB.