Games semantics for linear logic
Yves Lafont, Thomas Streicher · 2002
An attempt is made to relate various notions of duality used in mathematics with the denotational semantics of linear logic. The author proposes a naive semantics for linear logic that, in a certain sense, generalizes various notions such as finite-dimensional vector spaces, topological spaces, and J.-Y. Girard's (1987) coherence spaces. A game consists of a set of vectors (or strategies), a set of forms (or co-strategies) and an evaluation bracket. This is enough to interpret the connectives of full propositional linear logic, including exponentials.>