有限结构极限的对偶理论观点
A duality theoretic view on limits of finite structures
摘要：
Nesetril和Ossona de Mendez发展了有限模型结构极限的系统理论。它是基于这样的见解，即有限结构的集合可以通过他们称为Stone配对的映射嵌入到测量空间中，在那里可以计算出所需的限制。我们表明，一个密切相关的，但更细粒度的措施空间出现--通过斯通-普里斯特利对偶和模型理论的类型的概念--通过丰富的表达能力的一阶逻辑与某些“概率算子”。我们提供了一个健全的和完整的演算，这个扩展的逻辑，并揭示了这个建设的函子性质。其后果是双重的。一方面，我们确定了结构极限理论的逻辑依据。另一方面，我们的建设表明，二重性理论的斯通配对的变体捕获添加一层量词，从而使一个强有力的链接到最近的工作半环量词在逻辑上的话。在这个过程中，我们将类型的模型论概念确定为这一联系背后的统一概念。这些结果有助于弥合链的逻辑在计算机科学侧重于语义和算法和复杂性相关的领域，分别。
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 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.
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