Interaction graphs: Graphings

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• 作者：Thomas Seiller^a ; ^b ; ¹ ; ^{seiller@ihes.fr} ; ^{seiller@di.ku.dk}
• 关键词：03B70 ; 03F52 ; 68Q55 ; 37A40
• 刊名：Annals of Pure and Applied Logic
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：168
• 期：2
• 页码：278-320
• 全文大小：953 K
• 卷排序：168

文摘

In two previous papers  and , we exposed a combinatorial approach to the program of Geometry of Interaction, a program initiated by Jean-Yves Girard [16]. The strength of our approach lies in the fact that we interpret proofs by simpler structures – graphs – than Girard's constructions, while generalising the latter since they can be recovered as special cases of our setting. This third paper extends this approach by considering a generalisation of graphs named graphings, which is in some way a geometric realisation of a graph on a measured space. This very general framework leads to a number of new models of multiplicative-additive linear logic which generalise 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.