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P2 From Thin Concurrent Games to Generalized Species of Structures

从薄并发博弈到广义结构种(generalized species of structures)
LICS 2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)2023匹配度 1/10 · 该论文属于纯形式语义与范畴论研究,聚焦薄并发博弈、分配子、双范畴和λ演算理论,与用户关注的静态分析、LLM/Agent、浮点程序分析及贝叶斯程序分析均无直接交集。引用 7 inbox
Pierre Clairambault, Federico Olimpieri, Hugo Paquet
crossref: 2026-09-12dblp: 2026-09-12

AI 速览

一句话:在基于事件结构的薄并发博弈与基于分配子的广义结构种之间建立双范畴桥接,并获得笛卡尔闭伪函子。

线性逻辑的指称语义产生了动态模型(以博弈语义为代表)与静态模型(以关系范畴/分配子为代表)两族。本文在二维层面为二者建立形式桥接:把基于事件结构的薄并发博弈与策略的双范畴,连到基于分配子的广义结构种双范畴。第一部分构造从薄并发博弈(线性双范畴)到分配子的 oplax 函子,从而将策略视为分配子,并揭示复合机制与资源对称表示两个根本差异。第二部分借用博弈语义中的可见策略与 payoff 结构等方法,收紧两模型联系,得到一个笛卡尔闭伪函子,并用它重新解释 λ-演算双范畴理论中的近期结果。

问题
如何沟通线性逻辑指称语义中动态的博弈模型与静态的关系/分配子模型,尤其是它们的二维双范畴结构。
方法
构造从薄并发博弈与策略双范畴到分配子双范畴的 oplax 函子,并引入可见策略与 payoff 结构来加强两模型之间的联系。
评估
以形式构造与证明为主:建立笛卡尔闭伪函子,并据此重新审视 λ-演算双范畴理论中的结果。
原文摘要(Abstract)

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 two-dimensional dynamic and static models: we connect the bicategory of thin concurrent games and strategies, based on event structures, to the bicategory of generalized species of structures, based on distributors.In the first part of the paper, we construct an oplax functor from (the linear bicategory of) thin concurrent games to distributors. This explains how to view a strategy as a distributor, and highlights two fundamental differences: 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 bicategorical theory of the λ-calculus.

链接与引用

DOI 原文 · PDF(开放获取) · DBLP

BibTeX
@inproceedings{ClairambaultOP23,
  title = {From Thin Concurrent Games to Generalized Species of Structures},
  author = {Pierre Clairambault and Federico Olimpieri and Hugo Paquet},
  booktitle = {LICS},
  year = {2023},
  doi = {10.1109/lics56636.2023.10175681}
}