## Journal of Symbolic Logic

### The Decidability of Dependency in Intuitionistic Propositional Logi

#### 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.

#### Article information

Source
J. Symbolic Logic, Volume 60, Issue 2 (1995), 498-504.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744749

Mathematical Reviews number (MathSciNet)
MR1335130

Zentralblatt MATH identifier
0836.03010

JSTOR