The Decidability of Dependency in Intuitionistic Propositional Logi

Journal of Symbolic Logic 60 (2):498 - 504 (1995)
Dick De De Jongh
University of Amsterdam
A definition is given for formulae A 1 ,...,A n in some theory T which is formalized in a propositional calculus S to be (in)dependent with respect to S. It is shown that, for intuitionistic propositional logic IPC, dependency (with respect to IPC itself) is decidable. This is an almost immediate consequence of Pitts' uniform interpolation theorem for IPC. A reasonably simple infinite sequence of IPC-formulae F n (p, q) is given such that IPC-formulae A and B are dependent if and only if at least on the F n (A, B) is provable.
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DOI 10.2307/2275844
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