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Geometry of interaction. V: Logic in the hyperfinite factor. (English) Zbl 1230.03093
Summary: Geometry of Interaction is a transcendental syntax developed in the framework of operator algebras. This fifth installment of the program takes place inside a von Neumann algebra, the hyperfinite factor. It provides a built-in interpretation of cut elimination as well as an explanation for light, i.e., complexity-sensitive, logics.
For Part IV of this series of papers see [Lect. Notes Log. 24, 76–117 (2006; Zbl 1105.03064)].

03F52 Proof-theoretic aspects of linear logic and other substructural logics
03F05 Cut-elimination and normal-form theorems
Full Text: DOI
[1] Connes, A., Non-commutative geometry, (1994), Academic Press San Diego, CA · Zbl 0933.46069
[2] Fuglede, B.; Kadison, R.V., Determinant theory in finite factors, Annals of mathematics, 2, 55, 520-530, (1952) · Zbl 0046.33604
[3] Girard, J.-Y., Towards a geometry of interaction, (), 69-108
[4] Girard, J.-Y., Geometry of interaction I: interpretation of system \(F\), (), 221-260
[5] Girard, J.-Y., Geometry of interaction II: deadlock-free algorithms, (), 76-93
[6] Girard, J.-Y., Geometry of interaction III: accommodating the additives, (), 329-389 · Zbl 0828.03027
[7] Girard, J.-Y., Geometry of interaction IV: the feedback equation, (), 76-117 · Zbl 1105.03064
[8] Girard, J.-Y., Locus solum, Mathematical structures in computer science, 11, 301-506, (2001) · Zbl 1051.03045
[9] Girard, J.-Y., Le point aveugle, tome 1: vers la perfection, tome 2: vers !’imperfection, (), 296 pp; 2007, 299 pp
[10] Kadison, R. V.; Ringrose, J. R., Fundamentals of the theory of operator algebras, vol. I & II, () · Zbl 0888.46039
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