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Finite Models and Full Completeness

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Book cover Computer Science Logic (CSL 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1862))

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Abstract

A finite model property for fully complete denotational models of propositional logics is investigated using fully complete translations to compare programming languages and logics. The main result is that there can be no finite and fully complete models of linear or affine propositional logics. This is shown to be a consequence of Loader’s result that contextual equivalence for finitary PCF is not decidable by giving a fully complete translation from finitary PCF into a Λ(Ω)ω bda-calculus for a dual affine/non-linear logic. It is shown that the non-linear part of this logic does have a finite and fully complete model, and a conservative extension of the above translation is given from finitary PCF with control (µPCF) into the non-linear fragment which shows that the fully abstract model of µPCF is effectively presentable.

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Author information

Authors and Affiliations

  1. COGS, University of Sussex, Brighton, BN1 9QH, UK

    J. Laird

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  1. J. Laird
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Department of Biology, Boston College, Fulton Hall 410B, Chestnut Hill, MA, 02467, USA

    Peter G. Clote

  2. Mathematisches Institut, Ludwig-Maximilian-Universität München, Theresienstr. 39, 80333, München, Germany

    Helmut Schwichtenberg

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© 2000 Springer-Verlag Berlin Heidelberg

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Laird, J. (2000). Finite Models and Full Completeness. In: Clote, P.G., Schwichtenberg, H. (eds) Computer Science Logic. CSL 2000. Lecture Notes in Computer Science, vol 1862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44622-2_26

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  • DOI: https://doi.org/10.1007/3-540-44622-2_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67895-3

  • Online ISBN: 978-3-540-44622-4

  • eBook Packages: Springer Book Archive

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