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Duploid situations in concurrent games

Abstract : Polarisation describes in logic the presence of an evaluation order by distinguishing positive connectives and negative connectives at a formal level. This approach has recently been characterised with duploids [1], a generalisation of categories where the associativity of composition is relaxed. Following Melliès [2], we understand the Blass problem of game semantics (lack of associativity) as a polarisation of games. In this talk we exhibit duploid structures at work in Rideau and Winskel's concurrent games [3]. To this end we introduce “duploid situations”, an equivalent but more verbose characterisation of duploids, and exhibit such structures in concurrent games. Previous notions of polarised games force the evaluation order indirectly by restricting to a call-by-push-value format, and then exhibit the Blass phenomenon via some form of CPS translation. This amounts to constructing a duploid but the construction is a completion. In contrast, the new duploids are a conservative extension of structures found in concurrent games. In other words, we describe the polarisation of games directly without forcing sequentiality artificially, and the new notion is a convenient description to help recognise duploids as they occur in practice. [1] G. Munch-Maccagnoni, “Models of a Non-Associative Composition,” in Proc. FoSSaCS, 2014, vol. 8412, pp. 397–412. [2] P.-A. Melliès, “Asynchronous Games 3 An Innocent Model of Linear Logic,” Electr. Notes Theor. Comput. Sci., vol. 122, pp. 171–192, 2005. [3] S. Rideau and G. Winskel, “Concurrent Strategies,” in LICS, 2011, pp. 409–418.
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https://hal.inria.fr/hal-01991555
Contributor : Guillaume Munch-Maccagnoni Connect in order to contact the contributor
Submitted on : Wednesday, January 23, 2019 - 10:17:23 PM
Last modification on : Tuesday, November 22, 2022 - 12:08:14 AM

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  • HAL Id : hal-01991555, version 1

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Pierre Clairambault, Guillaume Munch-Maccagnoni. Duploid situations in concurrent games. Games for Logic and Programming Languages XII (GaLoP), Apr 2017, Uppsala, Sweden. pp.1. ⟨hal-01991555⟩

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