Variable Sharing in Connexive Logic

Abstract

However broad or vague the notion of connexivity may be, it seems to be similar to the notion of relevance even when relevance and connexive logics have been shown to be incompatible to one another. Relevance logics can be examined by suggesting syntactic relevance principles and inspecting if the theorems of a logic abide to them. In this paper we want to suggest that a similar strategy can be employed with connexive logics. To do so, we will suggest some properties that seem to be hinted at in Nelson’s work. Following this strategy will ideally shed some light over the notion of content and will also help make a clear comparison between relevance and connexive logics.