Partial Orders, Event Structures and Linear Strategies

We introduce a Game Semantics where strategies are partial orders, and composition is a generalization of the merging of orders. Building on this, to bridge between Game Semantics and Concurrency, we explore the relation between Event Structures and Linear Strategies. The former are a true concurrency model introduced by Nielsen, Plotkin, Winskel, the latter a family of linear innocent strategies developed starting from Girard’s work in the setting of Ludics. We extend our construction on partial orders to classes of event structures, showing how to reduce composition of event structures to the simple definition of merging of orders. Finally, we introduce a compact closed category of event structures which embeds Linear Strategies.