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
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
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.
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Alessio Guglielmi, Lutz Straßburger. A System of Interaction and Structure V: The Exponentials and Splitting. Mathematical Structures in Computer Science, Cambridge University Press (CUP), 2011, pp.1-22. ⟨10.1017/S096012951100003X⟩. ⟨inria-00441254v2⟩

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