On Geometry of Interaction

  • Jean-Yves Girard
Conference paper
Part of the NATO ASI Series book series (volume 139)


The paper expounds geometry of interaction, for the first time in the full case, i.e. for all connectives of linear logic, including additives and constants. The interpretation is done within a C*-algebra which is induced by the rule of resolution of logic programming, and therefore the execution formula can be presented as a simple logic programming loop. Part of the data is public (shared channels) but part of it can be viewed as private dialect (defined up to isomorphism) that cannot be shared during interaction, thus illustrating the theme of communication without understanding. One can prove a nilpotency (i.e. termination) theorem for this semantics, and also its soundness w.r.t. a slight modification of familiar sequent calculus in the case of exponential-free conclusions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Jean-Yves Girard
    • 1
  1. 1.Laboratoire de Mathématiques DiscrètesUPR 9016 — CNRSMarseille Cedex 09France

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