zbMATH — the first resource for mathematics

Bases of admissible rules of the modal system Grz and of intuitionistic logic. (English. Russian original) Zbl 0617.03007
Math. USSR, Sb. 56, 311-331 (1987); translation from Mat. Sb., Nov. Ser. 128(170), No. 3, 321-338 (1985).
The paper gives an affirmative solution to problem 40 of the well-known H. Friedman’s list. Recursive bases of admissible rules for propositional intuitionistic logic Int and Grzegorczyk modal logic Grz are constructed that give algorithms recognizing admissibility of rules in Int and Grz. The paper also proves that Int and Grz have no finite bases of admissible rules, thus answering negatively a corresponding Kuznetsov’s question.
Reviewer: S.Artemov

03B45 Modal logic (including the logic of norms)
03B55 Intermediate logics
03F55 Intuitionistic mathematics
03B20 Subsystems of classical logic (including intuitionistic logic)
Full Text: DOI