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Linking Game-Theoretical Approaches with Constructive Type Theory - Dialogical Strategies, CTT demonstrations and the Axiom of Choice (Paperback, 1st ed. 2015)
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Linking Game-Theoretical Approaches with Constructive Type Theory - Dialogical Strategies, CTT demonstrations and the Axiom of Choice (Paperback, 1st ed. 2015)
Series: SpringerBriefs in Philosophy
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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.
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