Relating Semantics as Compatibility Semantics

Abstract

The question I address here is whether the relating semantics currently available for connexive logics provide a good account of what connexivity is, or at least as good as some of the proposals already in circulation. I will argue that relating semantics for Boolean connexive logics, in its current state, does not give a satisfactory account of connexivity, as it is merely designed to validate the connexive schemas. Nonetheless, following the initial ideas of Jarmużek and Malinowski, I will suggest that the relation in such a semantics can be understood as a sort of compatibility, and that the relating semantics can be naturally enriched so as to make it virtually indistinguishable from the incompatibility approach. To put it boldly, my claim is that, if relating semantics for Boolean connexive logics is going to be more than a means to validate the connexive schemas, and if the relating relation to model connexive logics is to be understood as connectedness, as Jarmużek and Malinowski want, the relating relation must have more properties than those currently allowed. Further arguments for those additional properties come from considering highly desirable properties of an implication.