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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: sn.pub/extras
Part of the book series: Trends in Logic (TREN, volume 43)
Table of contents (16 chapters)
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
- 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.
Book Title: Advances in Proof-Theoretic Semantics
Editors: Thomas Piecha, Peter Schroeder-Heister
Series Title: Trends in Logic
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and the Author(s) 2016
License: CC BY-NC
Hardcover ISBN: 978-3-319-22685-9Published: 04 November 2015
Softcover ISBN: 978-3-319-36781-1Published: 23 August 2016
eBook ISBN: 978-3-319-22686-6Published: 24 October 2015
Series ISSN: 1572-6126
Series E-ISSN: 2212-7313
Edition Number: 1
Number of Pages: VI, 283
Topics: Logic, Mathematical Logic and Foundations, Formal Languages and Automata Theory