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Advances in proof-theoretic semantics

Author: Thomas Piecha; Peter Joseph Schroeder-Heister
Publisher: Cham : Springer, [2016] ©2016
Series: Trends in logic, v. 43.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
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Genre/Form: Conference papers and proceedings
Congresses
Additional Physical Format: Print version:
Advances in proof-theoretic semantics.
Cham [Switzerland] ; New York : Springer, ©2016
(DLC) 2015949264
(OCoLC)932396126
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Thomas Piecha; Peter Joseph Schroeder-Heister
ISBN: 9783319226866 331922686X
OCLC Number: 932168519
Notes: "This volume collects the contributions of many of the participants, not necessarily in the form presented, and also some additional papers by authorswho did not speak at the conference [i.e. the second conference on proof-theoretic semantics in Tübingen in 2013]".--page 2.
Description: 1 online resource (vi, 283 pages).
Contents: Advances in Proof-Theoretic Semantics: Introduction/ Thomas Piecha and Peter Schroeder-Heister --
On the Relation Between Heyting's and Gentzen's Approaches to Meaning/ Dag Prawitz --
Kreisel's Theory of Constructions, the Kreisel-Goodman Paradox, and the Second Clause/ Walter Dean and Hidenori Kurokawa --
On the Paths of Categories/ Kosta Došen --
Some Remarks on Proof-Theoretic Semantics/ Roy Dyckhoff --
Categorical Harmony and Paradoxes in Proof-Theoretic Semantics/ Yoshihiro Maruyama --
The Paradox of Knowability from an Intuitionistic Standpoint/ Gabriele Usberti --
Explicit Composition and Its Application in Proofs of Normalization/ Jan von Plato --
Towards a Proof-Theoretic Semantics of Equalities/ Reinhard Kahle --
On the Proof-Theoretic Foundations of Set Theory/ Lars Hallnäs --
A Strongly Differing Opinion on Proof-Theoretic Semantics? / Wilfrid Hodges --
Comments on an Opinion/ Kosta Došen --
On Dummett's "Proof-Theoretic Justifications of Logical Laws"/ Warren Goldfarb --
Self-contradictory Reasoning/ Jan Ekman --
Completeness in Proof-Theoretic Semantics/ Thomas Piecha --
Open Problems in Proof-Theoretic Semantics/ Peter Schroeder-Heister.
Series Title: Trends in logic, v. 43.
Responsibility: Thomas Piecha, Peter Schroeder-Heister, editors.

Abstract:

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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