Abstract

This paper studies independence of bases for admissible rules. We consider inference rules of pretabular modal logics over S4 and pretabular superintuitionistic logics. Since Maksimova-Meskhi-Esakia theorem we know there are exactly five pretabular S4-logics and exactly three pretabular superintuitionistic logics . Even tabular modal logics sometimes do not have independent bases for admissible rules . But here we show that all pretabular modal logics and all pretabular superintuitionistic logics have independent bases for admissible inference rules