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Advances in proof-theoretic semantics [electronic resource] / edited by Thomas Piecha, Peter Schroeder-Heister.

Piecha, Thomas. editor.; Schroeder-Heister, Peter. editor.
2016
BC135
Available Online
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Title
Advances in proof-theoretic semantics [electronic resource] / edited by Thomas Piecha, Peter Schroeder-Heister.
ISBN
9783319226866 (electronic book)
331922686X (electronic book)
9783319226859
3319226851
DOI
https://doi.org/10.1007/978-3-319-22686-6
Published
Cham : Springer, 2016.
Language
English
Description
1 online resource (vi, 283 p.)
Item Number
10.1007/978-3-319-22686-6 doi
Call Number
BC135
Dewey Decimal Classification
160
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.
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Open access.
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text file PDF
Added Author
Piecha, Thomas. editor.
Schroeder-Heister, Peter. editor.
Series
Trends in logic ; v. 43.
Available in Other Form
Print version: 9783319226859
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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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