Interaction Graphs: Exponentials

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 th...

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Vydáno v:	Logical methods in computer science Ročník 15, Issue 3
Hlavní autor:	Seiller, Thomas
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Logical Methods in Computer Science e.V 01.01.2019
Témata:	03b70, 03f52, 28e15 computer science - logic in computer science f.3.2 f.4.1 mathematics - logic
ISSN:	1860-5974, 1860-5974
On-line přístup:	Získat plný text
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Shrnutí:	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.
ISSN:	1860-5974 1860-5974
DOI:	10.23638/LMCS-15(3:25)2019