Learning Families of Algebraic Structures from Text

Nikolay Bazhenov, Ekaterina Fokina, Dino Rossegger, Alexandra Soskova, Stefan Vatev

Published 2024-02-08Version 1

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 $\Sigma_2$ sentences.