Overview

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 toprovide 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.

Full Product Details

Author:   Thomas Piecha ,  Peter Schroeder-Heister
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   Softcover reprint of the original 1st ed. 2016
Volume:   43
Weight:   4.453kg
ISBN:  

9783319367811

ISBN 10:   3319367811
Pages:   283
Publication Date:   23 August 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Chapter 1. Introduction; Thomas Piecha & 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 & Hidenori Kurokawa.- Chapter 16. On Paradoxes in Proof-Theoretic Semantics; Yoshihiro Maruyama.

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Author Information

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.

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