有限结构极限的对偶理论视角：扩展版
A duality theoretic view on limits of finite structures: Extended version
AI总结：
本文通过Stone-Priestley对偶和概率算子扩展一阶逻辑，构建更细粒度测度空间，揭示结构极限理论的逻辑本质，并连接半环量词研究。
摘要：
Nesetril和Ossona de Mendez已经发展了一套关于有限模型结构极限的系统理论。该理论基于这样的洞见：有限结构的集合可以通过他们称为Stone配对的一个映射嵌入到一个测度空间中，在那里可以计算出所需的极限。我们表明，通过Stone-Priestley对偶和模型论中的类型概念，通过用某些“概率算子”丰富一阶逻辑的表达能力，会出现一个密切相关但更细粒度的（有限可加）测度空间。我们为这种扩展逻辑提供了一个可靠且完备的演算，并揭示了这一构造的函子性质。其后果是双重的。一方面，我们识别了结构极限理论的逻辑要旨。另一方面，我们的构造表明，Stone配对的对偶理论变体捕捉了量词层的添加，从而与最近关于逻辑中词上半环量词的工作建立了强有力的联系。在此过程中，我们将模型论中的类型概念识别为这一联系背后的统一概念。这些结果有助于弥合计算机科学中逻辑的两个分支，即分别侧重于语义和更侧重于算法及复杂性相关领域的逻辑分支。
英文摘要：
A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a space of measures, where the desired limits can be computed. We show that a closely related but finer grained space of (finitely additive) measures arises -- via Stone-Priestley duality and the notion of types from model theory -- by enriching the expressive power of first-order logic with certain "probabilistic operators". We provide a sound and complete calculus for this extended logic and expose the functorial nature of this construction. The consequences are two-fold. On the one hand, we identify the logical gist of the theory of structural limits. On the other hand, our construction shows that the duality theoretic variant of the Stone pairing captures the adding of a layer of quantifiers, thus making a strong link to recent work on semiring quantifiers in logic on words. In the process, we identify the model theoretic notion of types as the unifying concept behind this link. These results contribute to bridging the strands of logic in computer science which focus on semantics and on more algorithmic and complexity related areas, respectively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
