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Table of contents

  1. Front Matter
    Pages i-vi
  2. Thomas Piecha, Peter Schroeder-Heister
    Pages 1-4 Open Access
  3. Kosta Došen
    Pages 65-77 Open Access
  4. Roy Dyckhoff
    Pages 79-93 Open Access
  5. Yoshihiro Maruyama
    Pages 95-114 Open Access
  6. Gabriele Usberti
    Pages 115-137 Open Access
  7. Reinhard Kahle
    Pages 153-160 Open Access
  8. Lars Hallnäs
    Pages 161-171 Open Access
  9. Wilfrid Hodges
    Pages 173-188 Open Access
  10. Kosta Došen
    Pages 189-193 Open Access
  11. Jan Ekman
    Pages 211-229 Open Access
  12. Thomas Piecha
    Pages 231-251 Open Access
  13. Peter Schroeder-Heister
    Pages 253-283 Open Access

About this book

Introduction

This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory.

The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.

Keywords

Gentzen’s approach to meaning Heyting’s approach to meaning foundations of logic general proof theory logical constants proof-theory theory of constructions

Editors and affiliations

  • Thomas Piecha
    • 1
  • Peter Schroeder-Heister
    • 2
  1. 1.Department of Computer ScienceUniversity of TübingenTübingenGermany
  2. 2.Department of Computer ScienceUniversity of TübingenTübingenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-22686-6
  • Copyright Information The Editor(s) (if applicable) and the Author(s) 2016
  • License CC BY-NC
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-22685-9
  • Online ISBN 978-3-319-22686-6
  • Series Print ISSN 1572-6126
  • Series Online ISSN 2212-7313
  • Buy this book on publisher's site