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This monograph proposes a new way of implementing interaction in
logic. It also provides an elementary introduction to Constructive
Type Theory (CTT). The authors equally emphasize basic ideas and
finer technical details. In addition, many worked out exercises and
examples will help readers to better understand the concepts under
discussion. One of the chief ideas animating this study is that the
dialogical understanding of definitional equality and its execution
provide both a simple and a direct way of implementing the CTT
approach within a game-theoretical conception of meaning. In
addition, the importance of the play level over the strategy level
is stressed, binding together the matter of execution with that of
equality and the finitary perspective on games constituting
meaning. According to this perspective the emergence of concepts
are not only games of giving and asking for reasons (games
involving Why-questions), they are also games that include moves
establishing how it is that the reasons brought forward accomplish
their explicative task. Thus, immanent reasoning games are
dialogical games of Why and How.
This monograph proposes a new way of implementing interaction in
logic. It also provides an elementary introduction to Constructive
Type Theory (CTT). The authors equally emphasize basic ideas and
finer technical details. In addition, many worked out exercises and
examples will help readers to better understand the concepts under
discussion. One of the chief ideas animating this study is that the
dialogical understanding of definitional equality and its execution
provide both a simple and a direct way of implementing the CTT
approach within a game-theoretical conception of meaning. In
addition, the importance of the play level over the strategy level
is stressed, binding together the matter of execution with that of
equality and the finitary perspective on games constituting
meaning. According to this perspective the emergence of concepts
are not only games of giving and asking for reasons (games
involving Why-questions), they are also games that include moves
establishing how it is that the reasons brought forward accomplish
their explicative task. Thus, immanent reasoning games are
dialogical games of Why and How.
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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