A semantic analysis of stone and dual stone negations with regularity

Abstract

This article investigates whether a few well-known ‘negation’ operators may be termed as negations, using Dunn’s approach. The semantics of the Stone negation is investigated in perp frames, that of dual Stone negation in exhaustive frames, and that of Stone and dual Stone negations with the regularity property, in K_ frames. The study leads to new semantics for the logics corresponding to the classes of Stone algebras, dual Stone algebras and regular double Stone algebras.