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  • Open Access
  • © 2016

Advances in Proof-Theoretic Semantics

  • Open Access: this content is freely downloadable as an eBook!

  • Demonstrates the state of the art in proof-theoretic semantics

  • Discusses topics including semantics as a methodological question and general proof theory

  • Includes supplementary material:

Part of the book series: Trends in Logic (TREN, volume 43)

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Softcover Book USD 69.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)

Table of contents (16 chapters)

  1. Front Matter

    Pages i-vi
  2. Advances in Proof-Theoretic Semantics: Introduction

    • Thomas Piecha, Peter Schroeder-Heister
    Pages 1-4Open Access
  3. On the Paths of Categories

    • Kosta Došen
    Pages 65-77Open Access
  4. Some Remarks on Proof-Theoretic Semantics

    • Roy Dyckhoff
    Pages 79-93Open Access
  5. Categorical Harmony and Paradoxes in Proof-Theoretic Semantics

    • Yoshihiro Maruyama
    Pages 95-114Open Access
  6. The Paradox of Knowability from an Intuitionistic Standpoint

    • Gabriele Usberti
    Pages 115-137Open Access
  7. Towards a Proof-Theoretic Semantics of Equalities

    • Reinhard Kahle
    Pages 153-160Open Access
  8. On the Proof-Theoretic Foundations of Set Theory

    • Lars Hallnäs
    Pages 161-171Open Access
  9. A Strongly Differing Opinion on Proof-Theoretic Semantics?

    • Wilfrid Hodges
    Pages 173-188Open Access
  10. Comments on an Opinion

    • Kosta Došen
    Pages 189-193Open Access
  11. Self-contradictory Reasoning

    • Jan Ekman
    Pages 211-229Open Access
  12. Completeness in Proof-Theoretic Semantics

    • Thomas Piecha
    Pages 231-251Open Access
  13. Open Problems in Proof-Theoretic Semantics

    • Peter Schroeder-Heister
    Pages 253-283Open Access

About this book

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.


  • 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

  • Department of Computer Science, University of Tübingen, Tübingen, Germany

    Thomas Piecha, Peter Schroeder-Heister

About the editors

Thomas Piecha graduated both in Philosophy and in Physics,and holds a Ph.D. in Computer Science. He has published on proof-theoretic and dialogical approaches in logic, and currently works on the proof-theoretic analysis of hypothetical reasoning.

Peter Schroeder-Heister is professor of logic and philosophy of language at the University of Tübingen, holding a joint appointment in the Departments of Philosophy and of Computer Science. He works in particular on philosophical aspects of proof theory and is a leading expert in the area of proof-theoretic semantics.

Bibliographic Information

Buying options

Softcover Book USD 69.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)