Learning families of algebraic structures from informant
Abstract
We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a modeltheoretic characterization of the class $\mathbf{InfEx}_{\cong}$, consisting of the structures whose isomorphism types can be learned in the limit. We show that a family of structures $\mathfrak{K}$ is $\mathbf{InfEx}_{\cong}$learnable if and only if the structures from $\mathfrak{K}$ can be distinguished in terms of their $\Sigma^{\mathrm{inf}}_2$theories. We apply this characterization to familiar cases and we show the following: there is an infinite learnable family of distributive lattices; no pair of Boolean algebras is learnable; no infinite family of linear orders is learnable.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 DOI:
 10.48550/arXiv.1905.01601
 arXiv:
 arXiv:1905.01601
 Bibcode:
 2019arXiv190501601B
 Keywords:

 Mathematics  Logic;
 68Q32;
 03C57
 EPrint:
 28 pages, 1 figure, forthcoming in Information and Computation