Studia Logica 49 (2):215 - 239 (1990)

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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DOI 10.1007/BF00935600
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References found in this work BETA

An Essay in Classical Modal Logic.Krister Segerberg - 1971 - Uppsala, Sweden: Uppsala, Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
One Hundred and Two Problems in Mathematical Logic.Harvey Friedman - 1975 - Journal of Symbolic Logic 40 (2):113-129.

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What is an Inference Rule?Ronald Fagin, Joseph Y. Halpern & Moshe Y. Vardi - 1992 - Journal of Symbolic Logic 57 (3):1018-1045.
Rules with Parameters in Modal Logic I.Emil Jeřábek - 2015 - Annals of Pure and Applied Logic 166 (9):881-933.
Best Unifiers in Transitive Modal Logics.Vladimir V. Rybakov - 2011 - Studia Logica 99 (1-3):321-336.

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