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From action calculi to linear logic

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Computer Science Logic (CSL 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1414))

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Abstract

Milner introduced action calculi as a framework for investigating models of interactive behaviour. We present a type-theoretic account of action calculi using the propositions-as-types paradigm; the type theory has a sound and complete interpretation in Power's categorical models. We go on to give a sound translation of our type theory in the (type theory of) intuitionistic linear logic, corresponding to the relation between Benton's models of linear logic and models of action calculi. The conservativity of the syntactic translation is proved by a model-embedding construction using the Yoneda lemma. Finally, we briefly discuss how these techniques can also be used to give conservative translations between various extensions of action calculi.

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Author information

Authors and Affiliations

  1. Dept. Computer Science, University of Edinburgh, EH9 3JZ, Edinburgh, Scotland

    Andrew Barber & Gordon Plotkin

  2. Computing Laboratory, University of Cambridge, CB2 3QG, Cambridge, England

    Philippa Gardner

  3. RIMS, Kyoto University, 606-8502, Kyoto, Japan

    Masahito Hasegawa

Authors
  1. Andrew Barber
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  2. Philippa Gardner
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  3. Masahito Hasegawa
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  4. Gordon Plotkin
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Editor information

Mogens Nielsen Wolfgang Thomas

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© 1998 Springer-Verlag Berlin Heidelberg

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Barber, A., Gardner, P., Hasegawa, M., Plotkin, G. (1998). From action calculi to linear logic. In: Nielsen, M., Thomas, W. (eds) Computer Science Logic. CSL 1997. Lecture Notes in Computer Science, vol 1414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028008

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  • DOI: https://doi.org/10.1007/BFb0028008

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64570-2

  • Online ISBN: 978-3-540-69353-6

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