Topological Observations on Multiplicative Additive Linear Logic

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.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: André Hirschowitz, Michel Hirschowitz, Tom Hirschowitz
• Keywords: CORR 2008, Cut Elimination, Education, Multiplicative Additive Linear, Topological Nature