A DUALITY THEORETIC VIEW ON LIMITS OF FINITE STRUCTURES


Type
Article
Change log
Authors
Gehrke, M 
Reggio, L 
Abstract

A systematic theory of structural limits for finite models has been developed by Nešetřil 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.

Description
Keywords
Stone duality, finitely additive measures, structural limits, finite model theory, formal languages, logic on words
Journal Title
Logical Methods in Computer Science
Conference Name
Journal ISSN
1860-5974
1860-5974
Volume Title
18
Publisher
Centre pour la Communication Scientifique Directe (CCSD)
Sponsorship
EPSRC (EP/T007257/1)