On the structure of paraconsistent extensions of Johansson's logic

The aim of this article is to give a compact and self-contained description of the class of paraconsistent extensions of Johansson's (or minimal) logic (denoted Lj). The class of all non-trivial Lj-extensions is divided into three classes: the class Int of intermediate logics, the class Neg of negative logics (with axiom ¬p), and the class Par of proper paraconsistent Lj-extensions. For elements of Par, we define their intuitionistic and negative counterparts from classes Int and Par, respectively, and study to which extend paraconsistent logics are determined by their counterparts. To this end we need special presentation of j-algebras, which is also given in the article. In conclusion, we study Kripke semantics for paraconsistent Lj-extensions.