Skip to main content
SpringerLink
Log in
Book cover

Linking Game-Theoretical Approaches with Constructive Type Theory

Dialogical Strategies, CTT demonstrations and the Axiom of Choice

  • Book
  • © 2015

Overview

Authors:
  1. Nicolas Clerbout

    1. Instituto de Filosofía, CDHACS, Universidad de Valparaíso, Vina del Mar, Chile

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Shahid Rahman

    1. UMR-CNRS 8163: STL, University of Lille III, Villeneuve d'Ascq, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Philosophy (BRIEFSPHILOSOPH)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (7 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Brief Reminder of Constructive Type Theory

    • Nicolas Clerbout, Shahid Rahman
    Pages 1-8

  3. Dialogues with Play-Objects

    • Nicolas Clerbout, Shahid Rahman
    Pages 9-38

  4. From Dialogical Strategies to CTT Demonstrations

    • Nicolas Clerbout, Shahid Rahman
    Pages 39-52

  5. The Dialogical Take on the Axiom of Choice, and Its Translation into CTT

    • Nicolas Clerbout, Shahid Rahman
    Pages 53-85

  6. Building a Winning \(\mathbf {P}\)-strategy Out of a CTT Demonstration

    • Nicolas Clerbout, Shahid Rahman
    Pages 87-96

  7. Conclusions and Work in Progress

    • Nicolas Clerbout, Shahid Rahman
    Pages 97-99

  8. Errata to: Linking Game-Theoretical Approaches with Constructive Type Theory

    • Nicolas Clerbout, Shahid Rahman
    Pages E1-E2
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Instituto de Filosofía, CDHACS, Universidad de Valparaíso, Vina del Mar, Chile

    Nicolas Clerbout

  • UMR-CNRS 8163: STL, University of Lille III, Villeneuve d'Ascq, France

    Shahid Rahman

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation