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Subnets of proof-nets in multiplicative linear logic with MIX

Published online by Cambridge University Press:  01 December 1997

GIANLUIGI BELLIN
GIANLUIGI BELLIN
Affiliation:
Equipe de Logique Mathématique, Université de Paris 7 Denis Diderot, CNRS (URA 753) - UFR de Mathématiques, 2 Place Jussieu - Case 7012, 75251 Paris Cedex 05 (France)
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Abstract

This paper studies the properties of the subnets of a proof-net for first-order Multiplicative Linear Logic without propositional constants (MLL−), extended with the rule of Mix: from [vdash ]Γ and [vdash ]Δ infer [vdash ]Γ, Δ. Asperti's correctness criterion and its interpretation in terms of concurrent processes are extended to the first-order case. The notions of kingdom and empire of a formula are extended from MLL− to MLL−+MIX. A new proof of the sequentialization theorem is given. As a corollary, a system of proof-nets is given for De Paiva and Hyland's Full Intuitionistic Linear Logic with Mix; this result gives a general method for translating Abramsky-style term assignments into proof-nets, and vice versa.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 7 , Issue 6 , December 1997 , pp. 663 - 669
Copyright
1997 Cambridge University Press

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