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 MaksimovaEsakia-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 superintuitionistic logics have independent bases for admissible inference rules.