Abramsky's game semantic and dialogic
My first presentation in this GdT, "Vers une définition de stratégie sans hypothèse métalogique", began by questioning a metaphoric sentence from Girard: "Game semantics is a fighting sport; but a polite and civilised one: there is an arbiter who prevents nasty moves and bad behaviours. Ludics is more like wrestling: we knocked down the arbiter." I tried to interpret this "arbiter" as "metalogical hypotheses", I exposed some ideas about what should be a strategical behaviour in this context, inspired by different analyses of the Nim games (classic MeX-calculus, categorical analysis, question of the meaning of the cheat.
In my second intervention, "Formalism towards strategical behaviours", I showed the formal problems underlying the precedent talk: materialized players, variable number of players, both legal and illegal moves are possible... It gives us a "research plan". Then I finished by suggesting a "convergence" between the representation of dialogues and the representation of the trace in Abramsky's game semantics (with arenas etc).
For this session, "Abramsky's game semantics and dialogic", I will do more than suggesting, I will construct algorithms of translation between them, thanks to one little but new theorem of "arena-making dialogue":
For each set of particle rules , for each game, there exists a concrete justification [legitimation] such that this game forms a justified sequence of moves in an arena
It shall allow us to implement new results in dialogic (from categorial GS: Abramsky, Hyland, Ong ...) and fulfill the desiderata of the precedent talk. But we won't go too fast: to prove this theorem, I shall present and discuss the concepts of Abramsky's GS.