Cut-Down Operations on Bilattices

Abstract

In this paper, Melvin Fitting's notion of a "cut-down" operation on a bilattice is considered. It is shown that the logic of cut-down operations on bilattices is equivalent to Harry Deutsch's four-valued Sfde, demonstrating that Sfde is as intimately connected to the theory of bilattices as is the Dunn-Belnap logic Efde. The paper concludes by observing that the "not ¬" operation of Carlos Damásio and Luís Pereira serves as a cut-down in Fitting's sense and that the logic of Damásio-Pereira cut-down operations on the bilattice NINE is equivalent to Richard Angell's AC.