Book/Printed Material Advances in Proof-Theoretic Semantics

Title

• Advances in Proof-Theoretic Semantics

Summary

• 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.

Names

• Piecha, Thomas. editor
• Schroeder-Heister, Peter. editor

Created / Published

• Cham : Springer International Publishing : Imprint: Springer, 2016.

Contents

• Chapter 1. Introduction; Thomas Piecha and Peter-Schroeder-Heister -- Chapter 2. On Brouwer-Heyting-Kolmogorov provability semantics; Sergei N. Artëmov -- Chapter 3. Two Ways of General Proof Theory; Kosta Došen -- Chapter 4. Generalised elimination rules; Roy Dyckhoff -- Chapter 5. On the proof theoretic foundations of set theory; Lars Hallnäs -- Chapter 6. The choice of semantics as a methodological question; Wilfrid Hodges -- Chapter 7. The mode of presentation; Reinhard Kahle -- Chapter 8. Remarks on relations between Gentzen and Heyting inspired PTS; Dag Prawitz -- Chapter 9. Unification of logics by reflection; Giovanni Sambin -- Chapter 10. BHK and Brouwer's Theory of the Creative Subject; Göran Sundholm -- Chapter 11. Compositional semantics for predicate logic: Eliminating bound variables from formulas and deductions; William W. Tait -- Chapter 12. Intuitionism, the Paradox of Knowability and Empirical Negation; Gabriele Usberti -- Chapter 13. Explicit composition and its application in normalization proofs; Jan von Plato -- Chapter 14. A two-sorted typed lambda-calculus; Heinrich Wansing -- Chapter 15. Kreisel's second clause and the Theory of Constructions; Walter Dean and Hidenori Kurokawa -- Chapter 16. On Paradoxes in Proof-Theoretic Semantics; Yoshihiro Maruyama.

Headings

• -  Logic
• -  Mathematical logic
• -  Mathematical Logic and Formal Languages
• -  Mathematical Logic and Foundations

Notes

• -  Description based on publisher-supplied MARC data.
• -  Mathematics and Statistics (R0) (SpringerNature-43713)
• -  Mathematics and Statistics (SpringerNature-11649)

Medium

• 1 online resource (VI, 283 pages)

Digital Id

• https://hdl.loc.gov/loc.gdc/gdcebookspublic.2019761224

Library of Congress Control Number

• 2019761224

Rights Advisory

• Creative Commons Attribution-NonCommercial 4.0 International CC-BY-NC 4.0 https://creativecommons.org/licenses/by-nc/4.0/legalcode External

Access Advisory

• Unrestricted online access

Online Format

• image
• epub

LCCN Permalink

• https://lccn.loc.gov/2019761224

Additional Metadata Formats

• MARCXML Record
• MODS Record
• Dublin Core Record