EAN: 9783319190624

SPRINGERBRIEFS IN PHILOSOPHY LINKING GAME-THE...

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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