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23 April 2024 |
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Dynamic Games and Strategies | | Norihiro Yamada
; Samson Abramsky
; | | Date: |
16 Jan 2016 | | Abstract: | In the present paper, we propose a variant of game semantics to characterize
the syntactic notion of reduction syntax-independently. For this purpose, we
introduce the notion of "external" and "internal" moves and the so-called
"hiding operation" in game semantics, resulting in a "dynamic" variant of games
and strategies. Categorically, the dynamic games and strategies give rise to a
cartesian closed bicategory which is a generalization of the category of
HO-games and strategies, where all the standard entities and constructions in
game semantics are accommodated. In formulating it, we obtained a
generalization of the existing notions and established some algebraic laws
which are new to the literature. As a future work, we shall establish the exact
correspondence between the hiding operation and reduction, which is the main
aim of the dynamic variant of game semantics. Also, we are planning to develop
it as a mathematical model of computation. Moreover, we shall consider
connections with homotopy type theory. | | Source: | arXiv, 1601.4147 | | Services: | Forum | Review | PDF | Favorites | |
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