Quantifiers Closed Under Partial Polymorphisms

Authors Anuj Dawar , Lauri Hella



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Author Details

Anuj Dawar
  • Department of Computer Science and Technology, University of Cambridge, UK
Lauri Hella
  • Faculty of Information Technology and Communication Sciences, Tampere University, Finland

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Anuj Dawar and Lauri Hella. Quantifiers Closed Under Partial Polymorphisms. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CSL.2024.23

Abstract

We study Lindström quantifiers that satisfy certain closure properties which are motivated by the study of polymorphisms in the context of constraint satisfaction problems (CSP). When the algebra of polymorphisms of a finite structure 𝔅 satisfies certain equations, this gives rise to a natural closure condition on the class of structures that map homomorphically to 𝔅. The collection of quantifiers that satisfy closure conditions arising from a fixed set of equations are rather more general than those arising as CSP. For any such conditions 𝒫, we define a pebble game that delimits the distinguishing power of the infinitary logic with all quantifiers that are 𝒫-closed. We use the pebble game to show that the problem of deciding whether a system of linear equations is solvable in ℤ / 2ℤ is not expressible in the infinitary logic with all quantifiers closed under a near-unanimity condition.

Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
Keywords
  • generalized quantifiers
  • constraint satisfaction problems
  • pebble games
  • finite variable logics
  • descriptive complexity theory

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