A system of interaction and structure V: the exponentials and splitting

Alessio Guglielmi, L Straburger

Research output: Contribution to journalArticle

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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. NEL is presented in deep inference, because no Gentzen formalism can express it in such a way that the cut rule is admissible. Other recent work shows that system NEL is Turing-complete, and is able to express process algebra sequential composition directly and model causal quantum evolution faithfully. In this paper, we show cut elimination for NEL, based on a technique that we call splitting. The splitting theorem shows how and to what extent we can recover a sequent-like structure in NEL proofs. When combined with a 'decomposition' theorem, proved in the previous paper of this series, splitting yields a cut-elimination procedure for NEL.
LanguageEnglish
Pages563-584
Number of pages22
JournalMathematical Structures in Computer Science
Volume21
Issue number3
DOIs
StatusPublished - Jun 2011

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Algebra
Cut-elimination
Linear Logic
Decomposition
Express
Chemical analysis
Interaction
Causal Model
Process Algebra
Decomposition Theorem
Turing
Series
Theorem

Cite this

A system of interaction and structure V: the exponentials and splitting. / Guglielmi, Alessio; Straburger, L.

In: Mathematical Structures in Computer Science, Vol. 21, No. 3, 06.2011, p. 563-584.

Research output: Contribution to journalArticle

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