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.

A duality theoretic view on limits of finite structures

ETAPS is a confederation of several conferences, each with its own Programme Committee and Steering Committee. ETAPS is the most important and visible annual European event related to software sciences. Altogether, more than 500 researchers participate in this event every year. The confederated conferences cover various aspects of software systems, ranging from theoretical foundations to programming language developments, compiler advancements, analysis tools, formal approaches to software engineering, and security.

A gather.town room will be open during the whole conference, which can be found here:

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Password: Luxembourg2021

This can be used to meet in the coffee breaks.

 PDF's of the papers are available on https://etaps.org/2021/programme