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arXiv · 0807.2636

Topological Observations on Multiplicative Additive Linear Logic

André Hirschowitz·Michel Hirschowitz·Tom Hirschowitz
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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.

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André Hirschowitz, Michel Hirschowitz, Tom Hirschowitz. 2008-07-14. Topological Observations on Multiplicative Additive Linear Logic. https://arxiv.org/abs/0807.2636

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