de Mathématiques de Luminy
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.