Contrariety and Subcontrariety: The Anatomy of Negation (with Special Reference to an Example of J.‐Y. Béziau)
Lloyd Humberstone · Theoria · 2005
Abstract: We discuss aspects of the logic of negation bearing on an issue raised by Jean‐Yves Béziau, recalled in §1. Contrary‐ and subcontrary‐forming operators are introduced in §2, which examines some of their logical behaviour, leading on naturally to a consideration in §3 of dual intuitionistic negation (as well as implication), and some further operators related to intuitionistic negation. In §4, a historical explanation is suggested as to why some of these negation‐related connectives have attracted more attention than others. The remaining sections (§§5, 6) briefly address a question about a certain notion of global contrariety and the provision of Kripke semantics for the various operators in play in our discussion.