The Class of N4┴-Extensions

In this chapter, we study the structure of the lattice εN4┴ and discover a definite similarity to the structure of the lattice Jhn+ studied in the first part of the book. It should be noted that differences in the structure of these two classes of logics are also essential. Moreover, we give first applications of the developed theory: the class of extensions of the logic N4┴C obtained by adding Dummett’s linearity axiom (p → q) ∨ (q → p) to N4┴is completely described; two classical results by L.L. Maksimova, namely, the description of pretabular logics and the description of logics with Craig interpolation property, are transferred from the class of superintuitionistic logics to the class of N4┴-extensions.