From Thin Concurrent Games to Relational Models

Pierre Clairambault
LIS, Aix-Marseille

Date(s) : 12/10/2023   iCal
11 h 00 min - 12 h 30 min

Denotational models can roughly be classified in two kinds: static models (domains, relations, coherence spaces, etc), which record atemporal final « states » of completed executions; and dynamic models (game semantics, GoI, etc), which additionally describe how such final states are reached with temporal or causal information. The link between the two seems intuitively simple as it suffices to « forget time ». But the question hides surprising conceptual depth and led to an active line of research in the 2000s, with landmark results by Melliès and Boudes among others.

Recently, there has been renewed interest in various extensions of relational models; either quantitative (e.g. the weighted relational model), or proof-relevant (e.g. distributors / generalized species of structure). In this talk, I will present recent results examining this dynamic-to-static question for such generalized relational models; in particular I will aim to arrive at a recent result obtained together with Olimpieri and Paquet: a cartesian closed pseudofunctor from the cartesian closed bicategory of thin concurrent games, to that of Fiore, Gambino, Hyland and Winskel’s generalized species of structure.

Site Sud, Luminy, Ancienne BU


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