Disjoint Logics

Abstract

We will present all the mixed and impure disjoint three-valued logics based on the Strong Kleene schema. Some, but not all of them, are (inferentially) empty logics, while one of them is trivial. We will compare them regarding their relative strength. We will also provide a recipe for building philosophical interpretations for each of these logics, and show why the kind of permeability that characterises them is not such a bad feature. Finally, we will present a three-side sequent system for most of these logics.