Thomas Seiller - Interaction Graphs: Exponentials

lmcs:5712 - Logical Methods in Computer Science, August 30, 2019, Volume 15, Issue 3 -
Interaction Graphs: Exponentials

Authors: Thomas Seiller

This paper is the fourth of a series exposing a systematic combinatorial approach to Girard's Geometry of Interaction (GoI) program. The GoI program aims at obtaining particular realisability models for linear logic that accounts for the dynamics of cut-elimination. This fourth paper tackles the complex issue of defining exponential connectives in this framework. For that purpose, we use the notion of \emph{graphings}, a generalisation of graphs which was defined in earlier work. We explain how to define a GoI for Elementary Linear Logic (ELL) with second-order quantification, a sub-system of linear logic that captures the class of elementary time computable functions.

Volume: Volume 15, Issue 3
Published on: August 30, 2019
Accepted on: August 30, 2019
Submitted on: August 26, 2019
Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic,03B70, 03F52, 28E15,F.3.2,F.4.1


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