Breaking Paths in Atomic Flows for Classical Logic

Alessio Guglielmi (1) , Tom Gundersen (2) , Lutz Strassburger (2)

1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

This work belongs to a wider effort aimed at eliminating syntactic bureaucracy from proof systems. In this paper, we present a novel cut elimination procedure for classical propositional logic. It is based on the recently introduced atomic flows: they are purely graphical devices that abstract away from much of the typical bureaucracy of proofs. We make crucial use of the path breaker, an atomic-flow construction that avoids some nasty termination problems, and that can be used in any proof system with sufficient symmetry. This paper contains an original 2-dimensional-diagram exposition of atomic flows, which helps us to connect atomic flows with other known formalisms.

Domaines: Logique en informatique [cs.LO]

Alessio Guglielmi, Tom Gundersen, Lutz Strassburger. Breaking Paths in Atomic Flows for Classical Logic. Proceedings of the 25th Annual IEEE Symposium on Logic in Computer Science, LICS 2010, Jul 2010, Edinburgh, United Kingdom. pp.284-293, ⟨10.1109/LICS.2010.12⟩. ⟨hal-00541076⟩