![]() ĭesigns and behaviours 13.1 Designs-dessins. 175Ī hypothesis: polarisation 12.1 Faithfulness of coherent spaces 12.2 A prototype. ![]() 11.3 The correctness criterion 11.A More on multiplicatives. 10.3 The world is imperfect 10.A Focalisation. ![]() Linear logic 9.1 Linearity in coherent spaces 9.2 Perfect linear connectives. 6.F Essence, existence and typingĬoherent spaces 163 8.1 Grandeur and misery of Scott domains. 5.A Kreisel and functional interpretation 5.B Combinatory logic. įunctional interpretations 5.1 Proofs as functions. The category-theoretic interpretation 7.1 The three layers. Intuitionistic logic: LJ, NJ 4.1 The intuitionistic sequent calculus LJ 4.2 The Hauptsatz in LJ. 3.A Around sequent calculus 3.B Semantic aspects. 2.A More on the classification of predicates 2.B Formal arithmetic. 2.2 Hilbert in the face of incompleteness. 1.2 Essentialist and existentialist projects 1.3 Gödel and after. essence 1.1 The opposition existence/essence. Zimmermann, Freiburg Printing and binding: Beltz Bad Langensalza GmbH, Bad Langensalza, Germany The cover picture shows the syllogism Barbara as a proof-net, see p. Phone: +41 (0)44 632 34 36 Email: Homepage: Typeset using the author’s T E X files: I. © 2011 European Mathematical SocietyĮuropean Mathematical Society Publishing House Seminar for Applied Mathematics ETH-Zentrum FLI C4 CH-8092 Zürich Switzerland For any kind of use permission of the copyright owner must be obtained. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. ![]() ISBN 978-3-03719-088-3 The Swiss National Library lists this publication in The Swiss Book, the Swiss national bibliography, and the detailed bibliographic data are available on the Internet at. ![]() Author: Jean-Yves Girard CNRS, Institut de Mathématiques de Luminy UMR 6206 163 Avenue de Luminy, Case 907 13288 Marseille cedex 9 France E-mail: Ģ010 Mathematics Subject Classification: 03-01, 03A05, 03B40, 03F(03-05-07-10-20-40-52-99), 18A15, 68Q(05-10-12-15-55) Key words: Logic, proof-theory, incompleteness, sequent calculus, natural deduction, lambda-calculus, Curry–Howard isomorphism, system F, coherent spaces, linear logic, proof-nets, ludics, implicit complexity, geometry of interaction ![]()
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