Journal of Symbolic Logic

Interpolation in Fragments of Classical Linear Logic

Dirk Roorda

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 $(\rightarrow, +)$, 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.

Article information

Source
J. Symbolic Logic, Volume 59, Issue 2 (1994), 419-444.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744488

Mathematical Reviews number (MathSciNet)
MR1276623

Zentralblatt MATH identifier
0804.03005

JSTOR