Interpolation in fragments of classical linear logic

Journal of Symbolic Logic 59 (2):419-444 (1994)
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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

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Citations of this work

Interpolation Via Translations.João Rasga, Walter Carnielli & Cristina Sernadas - 2009 - Mathematical Logic Quarterly 55 (5):515-534.

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References found in this work

The Structure of Multiplicatives.Vincent Danos & Laurent Regnier - 1989 - Archive for Mathematical Logic 28 (3):181-203.

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