Liberating classical negation from falsity conditions
Damián Szmuc, Hitoshi Omori · 2022
In one of their papers, Michael De and Hitoshi Omori observed that the notion of classical negation is not uniquely determined in the context of so-called Belnap-Dunn logic, and in fact there are 16 unary operations that qualify to be called classical negation. These varieties are due to different falsity conditions one may assume for classical negation. The aim of this paper is to observe that there is an interesting way to make sense of classical negation independent of falsity conditions. We discuss two equivalent semantics, and offer a Hilbert-style system that is sound and complete with respect to the semantics.