Classical linear logic of implications

Authors:
Masahito Hasegawa
Affiliations:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502 Japan and PRESTO, Japan Science and Technology Agency Email: hassei@kurims.kyoto-u.ac.jp
Venue:
Mathematical Structures in Computer Science
Year:
2005

Citing 16
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Abstract

We give a simple term calculus for the multiplicative exponential fragment of Classical Linear Logic, by extending Barber and Plotkin's dual-context system for the intuitionistic case. The calculus has the non-linear and linear implications as the basic constructs, and this design choice allows a technically manageable axiomatisation without commuting conversions. Despite this simplicity, the calculus is shown to be sound and complete for category-theoretic models given by *-autonomous categories with linear exponential comonads.