A note on globally admissible inference rules for modal and superintuitionistic logics

Rimatski, V. V. and Rybakov, Vladimir V. (2005) A note on globally admissible inference rules for modal and superintuitionistic logics. Bulletin of the section of logic, 34 (2). pp. 93-100. ISSN 0138-0680

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Abstract

In this short note we consider globally admissible inference rules. A rule r is globally admissible in a logic L if r is admissible in all logics with the finite model property which extend L. Here we prove a reduction theorem: we show that, for any modal logic L extending K4, a rule r is globally admissible in L iff r is admissible in all tabular logics extending L. The similar result holds for superintuitionistic logics.