Independent bases for rules admissible in pretabular logics
Vladimir Vladimirovich Rybakov · Logic Journal of IGPL · 1999
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 (Maksimova). Even tabular modal logics sometimes do not have independent bases for admissible rules (Theorem 4.5.5). But here we show that all pretabular modal logics and all pretabular superintuitionistic logics have independent bases for admissible inference rules. Key words: Modal logic, Superintuitionistic Logic, Kripke Model, Infernece Rule, Admissible Rule, Independent Rules