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Elsevier Masson, Annals of Pure and Applied Logic, 2(168), p. 278-320

DOI: 10.1016/j.apal.2016.10.007



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Interaction Graphs: Graphings

Journal article published in 2014 by Thomas Seiller ORCID
This paper is available in a repository.
This paper is available in a repository.

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In two previous papers, we exposed a combinatorial approach to the program of Geometry of Interaction, a program initiated by Jean-Yves Girard. The strength of our approach lies in the fact that we interpret proofs by simpler structures - graphs - than Girard's constructions, while generalizing the latter since they can be recovered as special cases of our setting. This third paper extends this approach by considering a generalization of graphs named graphings, which is in some way a geometric realization of a graph. This very general framework leads to a number of new models of multiplicative-additive linear logic which generalize Girard's geometry of interaction models and opens several new lines of research. As an example, we exhibit a family of such models which account for second-order quantification without suffering the same limitations as Girard's models.