Topological Observations on Multiplicative Additive Linear Logic
Logic in Computer Science
2009-09-29 v1
Abstract
As an attempt to uncover the topological nature of composition of strategies in game semantics, we present a ``topological'' game for Multiplicative Additive Linear Logic without propositional variables, including cut moves. We recast the notion of (winning) strategy and the question of cut elimination in this context, and prove a cut elimination theorem. Finally, we prove soundness and completeness. The topology plays a crucial role, in particular through the fact that strategies form a sheaf.
Cite
@article{arxiv.0807.2636,
title = {Topological Observations on Multiplicative Additive Linear Logic},
author = {André Hirschowitz and Michel Hirschowitz and Tom Hirschowitz},
journal= {arXiv preprint arXiv:0807.2636},
year = {2009}
}
Comments
12 pages in two columns, submitted to POPL '09. Uses Paul Taylor's diagrams