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 
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 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.
