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Rules of inference with parameters for intuitionistic logic. (English) Zbl 0788.03007
Let $$A(x_ 1,\dots,x_ n,p_ 1,\dots,p_ m)$$ and $$B(x_ 1,\dots,x_ n,p_ 1, \dots,p_ m)$$ be formulas of the intuitionistic propositional calculus in variables $$x_ i$$, $$p_ j$$. The rule $$A/B$$ with parameters $$p_ j$$ is admissible, if for all $$n$$-tuples of formulas $$B_ 1,\dots,B_ n$$ derivability of $$A(B_ 1,\dots,B_ n,p_ 1,\dots,p_ m)$$ implies derivability of $$B(B_ 1,\dots,B_ n,p_ 1,\dots,p_ m)$$. An algorithm for deciding admissibility with parameters is given here by testing the rule on certain finite sets of finite Kripke models. In particular this decides existence of formulas $$B_ 1,\dots,B_ n$$ such that $$A(B_ 1,\dots,B_ n,p_ 1,\dots,p_ n)$$ is derivable: this is equivalent to the nonadmissibility of the rule $$A/$$false.
Reviewer: G.Mints (Stanford)

##### MSC:
 03B20 Subsystems of classical logic (including intuitionistic logic)
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##### References:
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