Independent bases for admissible rules in pretable logics

Independent bases of admissible inference rules are studied; namely, we treat inference rules in pretable modal logics over S4, and in pretable superintuitionistic logics. The Maksimova-Esakia-Meskhi theorem holds that there exist exactly five pretable S4-logics and precisely three pretable superintuitionistic ones. We argue that all pretable modal logics and all pretable super-intuitionistic logics have independent bases for admissible inference rules. Supported by RFFR, and Rybakov’s part, by the Turkish Scientific Technical Research Council (TUBITAK, Ankara). Translated fromAlgebra i Logika, Vol. 39, No. 2, pp. 206–226, March–April, 2000.