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Rules of inference with parameters for intuitionistic logic

Published online by Cambridge University Press:  12 March 2014

Vladimir V. Rybakov
Vladimir V. Rybakov*
Affiliation:
Department of Mathematics, Krasnoyarsk State University, 660062 Krasnoyarsk, USSR
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Abstract

An algorithm recognizing admissibility of inference rules in generalized form (rules of inference with parameters or metavariables) in the intuitionistic calculus H and, in particular, also in the usual form without parameters, is presented. This algorithm is obtained by means of special intuitionistic Kripke models, which are constructed for a given inference rule. Thus, in particular, the direct solution by intuitionistic techniques of Friedman's problem is found. As a corollary an algorithm for the recognition of the solvability of logical equations in H and for constructing some solutions for solvable equations is obtained. A semantic criterion for admissibility in H is constructed.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 3 , September 1992 , pp. 912 - 923
Copyright
Copyright © Association for Symbolic Logic 1992

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References

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