Proof-Net as Graph, Taylor Expansion as Pullback

Giulio Guerrieri (1) , Luc Pellissier (2) , Lorenzo Tortora de Falco (3)

1 Department of Computer Science [Bath]
2 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
3 Dipartimento di Matematica [Roma TRE]

We introduce a new graphical representation for multiplica-tive and exponential linear logic proof-structures, based only on standard labelled oriented graphs and standard notions of graph theory. The inductive structure of boxes is handled by means of a box-tree. Our proof-structures are canonical and allows for an elegant definition of their Taylor expansion by means of pullbacks.

Domaines: Logique en informatique [cs.LO]

Giulio Guerrieri, Luc Pellissier, Lorenzo Tortora de Falco. Proof-Net as Graph, Taylor Expansion as Pullback. Logic, Language, Information, and Computation - 26th Workshop, WoLLIC 2019, Utrecht, The Netherlands, July 2-5, 2019, Proceedings, pp.282-300, 2019, ⟨10.1007/978-3-662-59533-6_18⟩. ⟨hal-02313538⟩