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Pontrjagin duality and full completeness for multiplicative linear logic (without Mix)

Published online by Cambridge University Press:  01 April 2000

MASAHIRO HAMANO
MASAHIRO HAMANO
Affiliation:
School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Tatsunokuchi, Ishikawa, 923-1292, JAPAN. Email: hamano@jaist.ac.jp
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Abstract

We prove a full completeness theorem for MLL without the Mix rule. This is done by interpreting a proof as a dinatural transformation in a *-autonomous category of reflexive topological abelian groups first studied by Barr, denoted [Rscr][Tscr][Ascr]. In Section 2, we prove the unique interpretation theorem for a binary provable MLL-sequent. In Section 3, we prove a completeness theorem for binary sequents in MLL without the Mix rule, where we interpret formulas in the category [Rscr][Tscr][Ascr]. The theorem is proved by investigating the concrete structure of [Rscr][Tscr][Ascr], especially that arising from Pontrjagin's work on duality.

Information

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 10 , Issue 2 , April 2000 , pp. 231 - 259
Copyright
© 2000 Cambridge University Press

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