We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a model-theoretic characterization of the learning type InfEx≅, consisting of the structures whose isomorphism types can be learned in the limit. We show that a family of structures is InfEx≅-learnable if and only if the structures can be distinguished in terms of their Σ2inf-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.
Learning families of algebraic structures from informant
San Mauro L.
2020-01-01
Abstract
We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a model-theoretic characterization of the learning type InfEx≅, consisting of the structures whose isomorphism types can be learned in the limit. We show that a family of structures is InfEx≅-learnable if and only if the structures can be distinguished in terms of their Σ2inf-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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.