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Gentzen's Logical Calculi

(the theory pamphlet)

  • Book
  • Jul 2025

Overview

Authors:
  1. Curtis Franks

    1. Department of Philosophy, University of Notre Dame, Notre Dame, USA

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  • Provides the first-ever comprehensive presentation of the relational definition scheme
  • Gives a comprehensive presentation of Gentzen's internal completeness paradigm
  • Includes dozens of exercises directing students to the theory behind the logical systems they are learning

Part of the book series: SpringerBriefs in Philosophy (BRIEFSPHILOSOPH)

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About this book

The Theory Pamphlet presents Gerhard Gentzen's natural deduction and sequent calculi with emphasis on the theory behind the formalism. Its five chapters serve as an advanced logic textbook, introducing universal properties, proof normalization techniques, and decision procedures for classical, intuitionistic, and linear logics. The same material serves also as a philosophical treatise, describing the meaning of, significance of, and relationships among three different ways to conceptualize the idea of logical completeness. Most of the material featured has never before been presented in a systematic and accessible manner.

Keywords

  • Gerhard Gentzen
  • Universal Property
  • Natural Deduction
  • Sequent Calculus
  • Completeness
  • philosophical logic
  • Gentzen's Logical Calculi

Authors and Affiliations

  • Department of Philosophy, University of Notre Dame, Notre Dame, USA

    Curtis Franks

About the author

Curtis Franks is an associate professor of Philosophy at the University of Notre Dame. He has been on the Philosophy faculty at Notre Dame since 2006. He earned B.A. degrees in Mathematics and Philosophy from Rice University in 2000 and a Ph.D. from the University of California in Irvine's Department of Logic and Philosophy of Science in 2006. Since 2019, he has been, with Anand Pillay, co-editor in chief of the Notre Dame Journal of Formal Logic. He is currently the director of Notre Dame's Joint Program in Logic and Foundations of Mathematics.  

Bibliographic Information

  • Book Title: Gentzen's Logical Calculi

  • Book Subtitle: (the theory pamphlet)

  • Authors: Curtis Franks

  • Series Title: SpringerBriefs in Philosophy

  • Publisher: Springer Cham

  • eBook Packages: Religion and Philosophy, Philosophy and Religion (R0)

  • Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2025

  • Softcover ISBN: 978-3-031-91998-5Due: 06 August 2025

  • eBook ISBN: 978-3-031-91999-2Due: 06 August 2025

  • Series ISSN: 2211-4548

  • Series E-ISSN: 2211-4556

  • Edition Number: 1

  • Number of Pages: XVIII, 102

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