Linking Game-Theoretical Approaches with Constructive Type Theory: Dialogical St

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This title links two of the most dominant research streams in philosophy of logic, namely game theory and proof theory. The fifth chapter develops the algorithm from CTT-demonstrations to dialogical strategies.

FORMATPaperback LANGUAGEEnglish CONDITIONBrand New Publisher Description

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.

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.  

Feature

Links two of the most dominant research streams in philosophy of logic - game theory and proof theory Builds a link between the two main theories using the dialogical approach to logic Focuses on the logically valid fragment of Constructive Type Theory

Details ISBN3319190628 Year 2015 ISBN-10 3319190628 ISBN-13 9783319190624 Format Paperback Short Title LINKING GAME-THEORETICAL APPRO Language English Media Book DEWEY 005.131 Author Shahid Rahman Pages 99 Edition 1st Imprint Springer International Publishing AG Subtitle Dialogical Strategies, CTT demonstrations and the Axiom of Choice Place of Publication Cham Country of Publication Switzerland Illustrations 26 Illustrations, black and white; XIX, 99 p. 26 illus. DOI 10.1007/978-3-319-19063-1 Publisher Springer International Publishing AG Edition Description 1st ed. 2015 Series SpringerBriefs in Philosophy Publication Date 2015-07-21 Audience Professional & Vocational We've got this

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