Two families of denotational models have emerged from the semantic analysis of linear logic: dynamic models, typically presented as game semantics, and static models, typically based on a category of relations. In this paper we introduce a formal bridge between a dynamic model and a static model: the model of thin concurrent games and strategies, based on event structures, and the model of generalized species of structures, based on distributors. A special focus of this paper is the two-dimensional nature of the dynamic-static relationship, which we formalize with double categories and bicategories. In the first part of the paper, we construct a symmetric monoidal oplax functor from linear concurrent strategies to distributors. We highlight two fundamental differences between the two models: the composition mechanism, and the representation of resource symmetries. In the second part of the paper, we adapt established methods from game semantics (visible strategies, payoff structure) to enforce a tighter connection between the two models. We obtain a cartesian closed pseudofunctor, which we exploit to shed new light on recent results in the theory of the lambda-calculus.

翻译：从线性逻辑的语义分析中衍生出两类指称模型：动态模型（通常以博弈语义形式呈现）与静态模型（通常基于关系范畴构建）。本文在动态模型与静态模型之间建立形式化桥梁：基于事件结构的细并发博弈与策略模型，以及基于分布子的广义结构物种模型。本文特别关注动态-静态关系的二维本质，我们通过双范畴与双函子对其进行形式化。论文第一部分构建了从线性并发策略到分布子的对称幺半松弛函子。我们强调两模型间的两个根本差异：组合机制与资源对称性的表示方式。第二部分借鉴博弈语义的成熟方法（可见策略、收益结构），以强化两模型间的关联。我们获得一个笛卡尔闭伪函子，并借此对λ演算理论中的最新成果提供新的阐释视角。