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The decidability of dependency in intuitionistic propositional logic

Published online by Cambridge University Press:  12 March 2014

Dick de Jongh  and
L. A. Chagrova
Dick de Jongh
Affiliation:
Department of Mathematics and Computer Science, University of Amsterdam, 1018 TV Amsterdam, The Netherlands, E-mail: dickdj@fwi.uva.nl
L. A. Chagrova
Affiliation:
Tver State University, 170013 Tver, Russia
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 2 , June 1995 , pp. 498 - 504
Copyright
Copyright © Association for Symbolic Logic 1995

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References

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