Visible acyclic differential nets, Part I: Semantics

Michele Pagani (1, 2)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 PPS - Preuves, Programmes et Systèmes

We give a geometric condition that characterizes the differential nets having a finitary interpretation in finiteness spaces: visible acyclicity. This is based on visible paths, an extension to differential nets of a class of paths we introduced in the framework of linear logic nets. The characterization is then carried out as follows: the differential nets having no visible cycles are exactly those whose interpretation is a finitary relation. Visible acyclicity discloses a new kind of correctness for the promotion rule of linear logic, which goes beyond sequent calculus correctness.

Domaines: Logique en informatique [cs.LO]

Michele Pagani. Visible acyclic differential nets, Part I: Semantics. Annals of Pure and Applied Logic, 2011, 163 (3), pp.238-265. ⟨10.1016/j.apal.2011.09.001⟩. ⟨hal-00698973⟩