Constructive Classifications of Modal Logics and Extensions of Minimal Logic

Classifications of logics over Johansson’s minimal logic J and modal logics are considered. The paper contains a partial review of the results obtained after 2010. It is known that there is a duality between the lattice of normal logics and the lattice of varieties of modal algebras, as well as between the lattice of varieties of J-algebras and the lattice of J-logics. For a logic L, by V (L) we denote its corresponding variety of algebras.