Abstract
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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© 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. https://doi.org/10.1007/BFb0022564
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DOI: https://doi.org/10.1007/BFb0022564
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