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The structure of exponentials: Uncovering the dynamics of linear logic proofs

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Computational Logic and Proof Theory (KGC 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 713))

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We construct the exponential graph of a proof π in (second order) linear logic, an artefact displaying the interdependencies of exponentials in π. Within this graph superfluous exponentials are defined, the removal of which is shown to yield a correct proof π with essentially the same set of reductions.

Applications to intuitionistic and classical proofs are given by means of reduction-preserving embeddings into linear logic.

The last part of the paper puts things the other way round, and defines families of linear logics in which exponential dependencies are ruled by a given graph. We sketch some work in progress and possible applications.

supported by an HCM Research Training Fellowship of the European Economic Community

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Georg Gottlob Alexander Leitsch Daniele Mundici

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© 1993 Springer-Verlag Berlin Heidelberg

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Danos, V., Joinet, J.B., Schellinx, H. (1993). The structure of exponentials: Uncovering the dynamics of linear logic proofs. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1993. Lecture Notes in Computer Science, vol 713. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57184-1

  • Online ISBN: 978-3-540-47943-7

  • eBook Packages: Springer Book Archive

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