Logical equations and admissible rules of inference with parameters in modal provability logics

Studia Logica 49 (2):215 - 239 (1990)
Abstract
This paper concerns modal logics of provability — Gödel-Löb systemGL and Solovay logicS — the smallest and the greatest representation of arithmetical theories in propositional logic respectively. We prove that the decision problem for admissibility of rules (with or without parameters) inGL andS is decidable. Then we get a positive solution to Friedman''s problem forGL andS. We also show that A. V. Kuznetsov''s problem of the existence of finite basis for admissible rules forGL andS has a negative solution. Afterwards we give an algorithm deciding the solvability of logical equations inGL andS and constructing some solutions.
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    References found in this work BETA
    Krister Segerberg (1971). An Essay in Classical Modal Logic. Uppsala,Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
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