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Interpolation in fragments of classical linear logic

Published online by Cambridge University Press:  12 March 2014

Dirk Roorda
Dirk Roorda*
Affiliation:
Department of Computer Science, Rijksuniversiteit Groningen, 9747 AC Groningen, The Netherlands
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Abstract

We study interpolation for elementary fragments of classical linear logic. Unlike in intuitionistic logic (see [Renardel de Lavalette, 1989]) there are fragments in linear logic for which interpolation does not hold. We prove interpolation for a lot of fragments and refute it for the multiplicative fragment (→, +), using proof nets and quantum graphs. We give a separate proof for the fragment with implication and product, but without the structural rule of permutation. This is nearly the Lambek calculus. There is an appendix explaining what quantum graphs are and how they relate to proof nets.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 2 , June 1994 , pp. 419 - 444
Copyright
Copyright © Association for Symbolic Logic 1994

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References

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