The decidability of dependency in intuitionistic propositional Logi

Journal of Symbolic Logic 60 (2):498-504 (1995)
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Abstract

A definition is given for formulae $A_1,\ldots,A_n$ 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 $\mathbf{IPC}$, dependency (with respect to $\mathbf{IPC}$ itself) is decidable. This is an almost immediate consequence of Pitts' uniform interpolation theorem for $\mathbf{IPC}$. A reasonably simple infinite sequence of $\mathbf{IPC}$-formulae $F_n(p, q)$ is given such that $\mathbf{IPC}$-formulae $A$ and $B$ are dependent if and only if at least on the $F_n(A, B)$ is provable

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original Jongh, Dick De; Chagrova, L. A. (1995) "The Decidability of Dependency in Intuitionistic Propositional Logi". Journal of Symbolic Logic 60(2):498 - 504

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Dick De De Jongh
University of Amsterdam

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