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Section: New Results

Geometry of Interaction

Participant : Jean Goubault-Larrecq.

We have developed a categorical model of Girard's geometry of interaction that generalizes the Girard-Danos-Regnier algebra of weights [18] , in the guise of the so-called Danos-Regnier category Im2 ${{\#119967 R}(M)}$ of a linear inverse monoid M . The aim is to turn this into a categorical model of linear logic.

It was known that this could not be done by adding any equation to the usual presentations of the geometry of interaction. We have proved that this could not be achieved even by changing the underlying linear inverse monoid M altogether, e.g., by changing the existing generators and relations.

However, we have shown that Im2 ${{\#119967 R}(M)}$ was a categorical model of classical multiplicative linear logic, under mild conditions on M , and that coherence completions à la Hu-Joyal could be used to build categorical models of full (classical) linear logic from just models of (classical) multiplicative linear logic.

Thus we obtained the first categorical models of full classical linear logic based on the geometry of interaction.


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