Notes on Do\v{s}en's logic $\mathsf{N}$ and its extensions

Abstract

This paper collects some observations about Do\v{s}en's logic $\mathsf{N}$, where negation is treated as a modal operator, and its extensions. We shall see what happens when we add the~contraposition axiom to several important extensions of $\mathsf{N}$, show that certain extensions of $\mathsf{N}$ are canonical, and also revisit the method of filtration.