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.
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Conference papers
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Contributor : Alexis Saurin <>
Submitted on : Tuesday, January 27, 2015 - 10:45:33 PM
Last modification on : Sunday, March 31, 2019 - 1:24:46 AM


  • HAL Id : hal-01110340, version 1


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⟩



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