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Learning Families of Algebraic Structures from Text

Logic 2024-02-09 v1

Abstract

We adapt the classical notion of learning from text to computable structure theory. Our main result is a model-theoretic characterization of the learnability from text for classes of structures. We show that a family of structures is learnable from text if and only if the structures can be distinguished in terms of their theories restricted to positive infinitary Σ2\Sigma_2 sentences.

Keywords

Cite

@article{arxiv.2402.05744,
  title  = {Learning Families of Algebraic Structures from Text},
  author = {Nikolay Bazhenov and Ekaterina Fokina and Dino Rossegger and Alexandra Soskova and Stefan Vatev},
  journal= {arXiv preprint arXiv:2402.05744},
  year   = {2024}
}
R2 v1 2026-06-28T14:43:00.565Z