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Admissible and derivable rules in intuitionistic logic

Published online by Cambridge University Press:  04 March 2009

Paul Rozière
Paul Rozière
Affiliation:
Equipe de Logique, CNRS UA 753, Universitè Paris 7, 2 place Jussieu, 75230 PARIS cedex 05, France. [email protected]
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Abstract

This paper gives some sufficient conditions for admissible rules to be derivable in intuitionistic propositional calculus. For example, if the premises are Harrop formulas, the rule is admissible only if it is derivable.

In deriving the results, a particular class of substitutes is introduced, which are also useful when dealing with other questions of admissibility.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 3 , Issue 2 , June 1993 , pp. 129 - 136
Copyright
Copyright © Cambridge University Press 1993

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References

Friedman, H. (1975) 102 problems in mathematical logic. J. Symb. Logic 40 2113–130.CrossRefGoogle Scholar
Mints, G. E. (1972) Derivability of admissible rules. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 32 85–89; English transl. in J. Soviet Math. 6 (1976).Google Scholar
Rozière, P. (1991) Règies admissibles en calcul propositionnel intuitionniste. Preprint de l'equipe de Logique no. 25, Universitè Paris VII.Google Scholar
Rybakov, V. V. (1984) A criterion for admissibility of rules in the modal system S4 and the intuitionistic logic. Algebra i Logika 23; English transl. in Algebra and logic 23 5369–384 (1984).CrossRefGoogle Scholar
Rybakov, V. V. (1985) Bases of admissible rules of the logics S4 and Int. Algebra i Logika 24; English transl. in Algebra and logic 24 155–68 (1985).CrossRefGoogle Scholar
Rybakov, V. V. (1986) Decidability of admissibility in the modal system Grz and in intuitionistic logic. Izv. Akad. Nauf. SSSR, ser. Mat. 50; English transl. in Math. USSR Izvestia 28 3 (1987).Google Scholar
Troelsta, A. S. and Van-Dalen, D. (1988) Constructivism in Mathematics, an introduction. Studies in Logic and the Foundations of Mathematics 121, North-Holland.Google Scholar