Linking game-theoretical approaches with constructive type theory [electronic resource] : dialogical strategies, CTT demonstrations and the axiom of choice / Nicolas Clerbout, Shahid Rahman.
2015
B809.13
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Title
Linking game-theoretical approaches with constructive type theory [electronic resource] : dialogical strategies, CTT demonstrations and the axiom of choice / Nicolas Clerbout, Shahid Rahman.
Author
Clerbout, Nicolas, author.
ISBN
9783319190631 electronic book
3319190636 electronic book
9783319190624
3319190636 electronic book
9783319190624
Published
Cham : Springer, 2015.
Language
English
Description
1 online resource (xix, 99 pages) : illustrations.
Call Number
B809.13
Dewey Decimal Classification
149
Summary
This title links two of the most dominant research streams in philosophy of logic, namely game theory and proof theory. As the work's subtitle expresses, the authors will build this link by means of the dialogical approach to logic. One important aspect of the present study is that the authors restrict themselves to the logically valid fragment of Constructive Type Theory (CTT). The reason is that, once that fragment is achieved the result can be extended to cover the whole CTT system. The first chapters in the brief offer overviews on the two frameworks discussed in the book with an emphasis on the dialogical framework. The third chapter demonstrates the left-to-right direction of the equivalence result. This is followed by a chapter that demonstrates the use of the algorithm in showing how to transform a specific winning strategy into a CCT-demonstration of the axiom of choice. The fifth chapter develops the algorithm from CTT-demonstrations to dialogical strategies. This brief concludes by introducing elements of discussion which are to be developed in subsequent work.
Bibliography, etc. Note
Includes bibliographical references.
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Source of Description
Online resource; title from PDF title page (SpringerLink, viewed July 15, 2015).
Added Author
Rahman, Shahid, 1956- author.
Series
SpringerBriefs in philosophy.
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Table of Contents
Chapter 1. Brief Reminder of Constructive Type Theory
Chapter 2. Dialogues with Play-Objects
Chapter 3. From dialogical strategies to CTT demonstrations
Chapter 4. The dialogical take on the Axiom of Choice, and its translation into CTT
Chapter 5. Building a winning P-strategy out of a CTT demonstration
Chapter 6. Conclusions and Work in Progress. .
Chapter 2. Dialogues with Play-Objects
Chapter 3. From dialogical strategies to CTT demonstrations
Chapter 4. The dialogical take on the Axiom of Choice, and its translation into CTT
Chapter 5. Building a winning P-strategy out of a CTT demonstration
Chapter 6. Conclusions and Work in Progress. .