Interpolation in Linear Logic and Related Systems
Logic
2023-08-04 v2 Logic in Computer Science
Abstract
We prove that there are continuum-many axiomatic extensions of the full Lambek calculus with exchange that have the deductive interpolation property. Further, we extend this result to both classical and intuitionistic linear logic as well as their multiplicative-additive fragments. None of the logics we exhibit have the Craig interpolation property, but we show that they all enjoy a guarded form of Craig interpolation. We also exhibit continuum-many axiomatic extensions of each of these logics without the deductive interpolation property.
Cite
@article{arxiv.2305.05051,
title = {Interpolation in Linear Logic and Related Systems},
author = {Wesley Fussner and Simon Santschi},
journal= {arXiv preprint arXiv:2305.05051},
year = {2023}
}