This article is cited in 1 paper

Criteria for admissibility of rules of inference with parameters in the intuituonistc propositional calculus

V. V. Rybakov

Krasnoyarsk State University

Abstract: The author studies the problem of recognizing admissibility of rules of inference of a general form – rules of inference with parameters – in the intuitionistic propositional calculus. Algorithmic and semantic criteria are found for recognizing admissibility of such rules, based on special intuitionistic Kripke models. In particular, Friedman's problem generalized to rules of inference with parameters is solved. These results are applied to recognizing the solvability of logical equations and constructing their solutions.

UDC: 517.11+519.48

MSC: Primary 03B45; Secondary 03B20, 03B25

Received: 06.02.1989

 English version: Mathematics of the USSR-Izvestiya, 1991, 37:3, 693–703

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