Proof Theoretic Semantics

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Advances In Proof Theoretic Semantics

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Author : Thomas Piecha
language : en
Publisher: Springer
Release Date : 2015-10-24

Advances In Proof Theoretic Semantics written by Thomas Piecha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-24 with Philosophy categories.

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.

Proof Theoretic Semantics

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Author : Reinhard Kahle
language : en
Publisher:
Release Date : 2006

Proof Theoretic Semantics written by Reinhard Kahle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.

Harmony And Paradox

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Author : Luca Tranchini
language : en
Publisher: Springer Nature
Release Date :

Harmony And Paradox written by Luca Tranchini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

What Logics Mean

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Author : James W. Garson
language : en
Publisher: Cambridge University Press
Release Date : 2013-11-14

What Logics Mean written by James W. Garson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-14 with Language Arts & Disciplines categories.

This book explains how the meanings of the symbols of logic are determined by the rules that govern them.

Proof Theoretic Semantics

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Author : Nissim Francez
language : en
Publisher:
Release Date : 2015-10-29

Proof Theoretic Semantics written by Nissim Francez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-29 with Computers categories.

This book is a monograph on the topic of Proof-Theoretic Semantics, a theory of meaning constituting an alternative to the more traditional Model-Theoretic Semantics. The latter regards meaning as truth-conditions (in arbitrary models), the former regards meaning as canonical derivability conditions in a meaning-conferring natural-deduction proof-system. In the first part of the book, the Proof-Theoretic Semantics for logic is presented. It surveys the way a natural-deduction system can serve as meaning-conferring, and in particular analyses various criteria such a system has to meet in order to qualify as meaning-conferring. A central criterion is harmony, a balance between introduction-rules and elimination-rules. The theory is applied to various logics, e.g., relevance logic, and various proof systems such as multi-conclusion natural-deduction and bilateralism. The presentation is inspired by recent work by the author, and also surveys recent developments. In part two, the theory is applied to fragments of natural language, both extensional and intensional, a development based on the author's recent work. For example, conservativity of determiners, once set up in a proof-theoretic framework, becomes a provable property of all (regular) determiners. It is shown that meaning need not carry the heavy ontological load characteristic of Model-Theoretic Semantics of complex natural language constructs. Nissim Francez is an emeritus professor of computer science at the Technion, Israel Institute of Technology. At a certain point in his career he moved from research related to concurrent and distributed programming and program verification to research in computational linguistics, mainly formal semantics of natural language. In recent years, he has worked on Proof-Theoretic Semantics, in particular for natural language.

Proof Theoretic Semantics Sep Entry

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Author : Peter Schroeder-Heister
language : en
Publisher:
Release Date : 2022

Proof Theoretic Semantics Sep Entry written by Peter Schroeder-Heister and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.

This manuscript is the first version of the entry "Proof-Theoretic Semantics" in the Stanford Encyclopedia of Philosophy, which was submitted in 2011. For the version which finally appeared in 2012 it was reduced to one third of its length, which means that there is significant unpublished content in this original version.

Proof Theoretic Semantics

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Author : Patrizio Contu
language : en
Publisher:
Release Date : 2006

Proof Theoretic Semantics written by Patrizio Contu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.

Peter Schroeder Heister On Proof Theoretic Semantics

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Author : Thomas Piecha
language : en
Publisher: Springer
Release Date : 2024-02-13

Peter Schroeder Heister On Proof Theoretic Semantics written by Thomas Piecha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-13 with Philosophy categories.

This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. The chapters of which this book is composed discuss the subject from a rich variety of angles, including the history of logic, the proper interpretation of logical validity, natural deduction rules, the notions of harmony and of synonymy, the structure of proofs, the logical status of equality, intentional phenomena, and the proof theory of second-order arithmetic. All chapters relate directly to questions that have driven Schroeder-Heister's own research agenda and to which he has made seminal contributions. The extensive autobiographical chapter not only provides a fascinating overview of Schroeder-Heister's career and the evolution of his academic interests but also constitutes a contribution to the recent history of logic in its own right, painting an intriguing picture of the philosophical, logical, and mathematical institutional landscape in Germany and elsewhere since the early 1970s. The papers collected in this book are illuminatingly put into a unified perspective by Schroeder-Heister's comments at the end of the book. Both graduate students and established researchers in the field will find this book an excellent resource for future work in proof-theoretic semantics and related areas.

Dag Prawitz On Proofs And Meaning

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Author : Heinrich Wansing
language : en
Publisher: Springer
Release Date : 2014-11-27

Dag Prawitz On Proofs And Meaning written by Heinrich Wansing and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Philosophy categories.

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.

Proof Theoretic Semantics Some Basic Ideas

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Author : Peter Schroeder-Heister
language : en
Publisher:
Release Date : 2022

Proof Theoretic Semantics Some Basic Ideas written by Peter Schroeder-Heister and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.

This manuscript of 2003 describes and compares two basic approaches to what the author has called “proof-theoretic semantics”. The “standard” approach, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. The second one, which is based on ideas by Hallnäs and the author, understands proofs semantically by reading the application of certain proof rules directly as semantical steps. Whereas the first one is a global approach, dealing with proofs as a whole and imposing requirements on them, the second one is local as is interprets individual proof steps without demanding from the very beginning that a proof composed of such single steps has special features. -- The attached manuscript on proof-theoretic vs. constructive consequence argues that the proof-theoretic notion fully specifies reduction procedures and is nearer to term rewriting than the more general constructive notion.