从线人那里学习代数结构族
Learning families of algebraic structures from informant
摘要：
我们结合可计算结构理论和算法学习理论来研究代数结构族的学习。我们的主要结果是一个模型理论的性质的类$\mathbf{InfEx}_{\cong}$，其同构类型的结构组成，可以学习的限制。我们表明，一个家庭的结构$\mathfrak{K}$是$\mathbf{InfEx}_{\cong}$ -learnable当且仅当$\mathfrak{K}$的结构可以区分在他们的$Σ^{\mathrm{inf}}_2$ -理论。我们将此特征应用到熟悉的情况下，我们表明：有一个无限的家庭学习的分配格;没有一对布尔代数是可学习的;没有无限家庭的线性订单是可学习的。
英文摘要：
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 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 $Σ^{\mathrm{inf}}_2$-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.
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