Skip to Main content Skip to Navigation
New interface
Journal articles

A System of Interaction and Structure V: The Exponentials and Splitting

Alessio Guglielmi 1 Lutz Strassburger 2 
1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : System NEL is the mixed commutative/non-commutative linear logic BV augmented with linear logic's exponentials, or, equivalently, it is MELL augmented with the non-commutative self-dual connective seq. System NEL is Turing-complete, it is able to directly express process algebra sequential composition and it faithfully models causal quantum evolution. In this paper, we show cut elimination for NEL, based on a property that we call splitting. NEL is presented in the calculus of structures, which is a deep-inference formalism, because no Gentzen formalism can express it analytically. The splitting theorem shows how and to what extent we can recover a sequent-like structure in NEL proofs. Together with the decomposition theorem, proved in the previous paper of the series, this immediately leads to a cut-elimination theorem for NEL.
Document type :
Journal articles
Complete list of metadata

Cited literature [30 references]  Display  Hide  Download
Contributor : Lutz Straßburger Connect in order to contact the contributor
Submitted on : Wednesday, January 28, 2015 - 7:29:06 PM
Last modification on : Saturday, June 25, 2022 - 7:47:15 PM
Long-term archiving on: : Wednesday, April 29, 2015 - 11:36:08 AM


Files produced by the author(s)




Alessio Guglielmi, Lutz Strassburger. A System of Interaction and Structure V: The Exponentials and Splitting. Mathematical Structures in Computer Science, 2011, pp.1-22. ⟨10.1017/S096012951100003X⟩. ⟨inria-00441254v2⟩



Record views


Files downloads