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Learning Aggregate Queries Defined by First-Order Logic with Counting

Authors Steffen van Bergerem , Nicole Schweikardt

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Author Details

Steffen van Bergerem
  • Humboldt-Universität zu Berlin, Germany
Nicole Schweikardt
  • Humboldt-Universität zu Berlin, Germany

Funding

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - project number 541000908 (gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 541000908).

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Steffen van Bergerem and Nicole Schweikardt. Learning Aggregate Queries Defined by First-Order Logic with Counting. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICDT.2025.4

Abstract

In the logical framework introduced by Grohe and Turán (TOCS 2004) for Boolean classification problems, the instances to classify are tuples from a logical structure, and Boolean classifiers are described by parametric models based on logical formulas. This is a specific scenario for supervised passive learning, where classifiers should be learned based on labelled examples. Existing results in this scenario focus on Boolean classification. This paper presents learnability results beyond Boolean classification. We focus on multiclass classification problems where the task is to assign input tuples to arbitrary integers. To represent such integer-valued classifiers, we use aggregate queries specified by an extension of first-order logic with counting terms called FOC₁.
Our main result shows the following: given a database of polylogarithmic degree, within quasi-linear time, we can build an index structure that makes it possible to learn FOC₁-definable integer-valued classifiers in time polylogarithmic in the size of the database and polynomial in the number of training examples.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database theory
  • Theory of computation → Logic
  • Theory of computation → Finite Model Theory
  • Computing methodologies → Logical and relational learning
  • Computing methodologies → Supervised learning
Keywords
  • Supervised learning
  • multiclass classification problems
  • counting logic

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