The decidability of dependency in intuitionistic propositional logic
Dick de Jongh, L. A. Chagrova · Journal of Symbolic Logic · 1995
Abstract A definition is given for formulae A1, …, An 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 Fn (p, q) is given such that IPC-formulae A and B are dependent if and only if at least on of the Fn (A, B) is provable.