On the dependencies of logical rules

Marc Bagnol 1 Amina Doumane 2, 3 Alexis Saurin 2, 3
3 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, Inria Paris-Rocquencourt, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique : UMR7126
Abstract : Many correctness criteria have been proposed since linear logic was introduced and it is not clear how they relate to each other. In this paper, we study proof-nets and their correctness criteria from the perspective of dependency, as introduced by Mogbil and Jacobé de Naurois. We introduce a new correctness criterion, called DepGraph, and show that together with Danos' contractibility criterion and Mogbil and Naurois criterion, they form the three faces of a notion of dependency which is crucial for correctness of proof-structures. Finally, we study the logical meaning of the dependency relation and show that it allows to recover and characterize some constraints on the ordering of inferences which are implicit in the proof-net.
Document type :
Conference papers
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01110340
Contributor : Alexis Saurin <>
Submitted on : Tuesday, January 27, 2015 - 10:45:33 PM
Last modification on : Sunday, March 31, 2019 - 1:24:46 AM

Identifiers

  • HAL Id : hal-01110340, version 1

Citation

Marc Bagnol, Amina Doumane, Alexis Saurin. On the dependencies of logical rules. FOSSACS, 18th International Conference on Foundations of Software Science and Computation Structures, Apr 2015, London, United Kingdom. ⟨hal-01110340⟩

Share

Metrics

Record views

269