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Classical Linear Logic of Implications

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Computer Science Logic (CSL 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2471))

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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 system for the intuitionistic case. The calculus has the nonlinear and linear implications as the basic constructs, and this design choice allows a technically managable axiomatization 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.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Japan

    Masahito Hasegawa

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  1. Masahito Hasegawa
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Editors and Affiliations

  1. Laboratory for Foundations of Computer Science Division of Informatics, University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK

    Julian Bradfield

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© 2002 Springer-Verlag Berlin Heidelberg

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Hasegawa, M. (2002). Classical Linear Logic of Implications. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_31

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  • DOI: https://doi.org/10.1007/3-540-45793-3_31

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44240-0

  • Online ISBN: 978-3-540-45793-0

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