Interpolation in Fragments of Classical Linear Logic

Dirk Roorda

doi:10.2307/2275398

Interpolation in Fragments of Classical Linear Logic

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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.

Originele taal-2	Engels
Pagina's (van-tot)	419
Aantal pagina's	25
Tijdschrift	Journal of Symbolic Logic
Volume	59
Nummer van het tijdschrift	2
DOI's	https://doi.org/10.2307/2275398
Status	Gepubliceerd - 1994

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10.2307/2275398Licentie: CC BY

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Interpolation in Fragments of Classical Linear Logic

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