Institut de Mathématiques de Luminy

Abstract 2004-4

Girard Jean-Yves.
Geometry of interaction IV: the feedback equation.

The first papers on Geometry of Interaction followed an essentialist methodology: we interpreted extant logical systems by means of operators on the Hilbert space and showed that everything works fine, i.e, by solving the feedback equation corresponding to cut-elimination. In this paper, we adopt the opposite approach, i.e., we study the general feedback equation, for an arbitary cut-system (H, h, ). The main novelty is that logic is no longer presupposed, so that we can expect surprises from that existentialist approach, e.g., connections with the quantum world.
In this paper we limit ourselves with the structural properties of the feedback equation, mainly associativity —Church-Rosser—, stability, winning and continuity, the latter not being taken in the standard topological sense, but rather in the sense of commutation to (directed) suprema and infima.


Last update : february 16, 2004, EL.