This paper deenes a new computational model of inductive learning, called U-learnability (Universal Learnability), that is well-suited for rich representation languages, most notably for universal (Turing equivalent) representations. It is motivated by three observations. Firstly, existing computational models of inductive learning|the best known of which are identiication in the limit and PAC-...

We prove a new combinatorial characterization of polynomial learnability from equivalence queries, and state some of its consequences relating the learnability of a class with the learnability via equivalence and membership queries of its subclasses obtained by restricting the instance space. Then we propose and study two models of query learning in which there is a probability distribution on ...

There is much debate over the degree to which language learning is governed by innate language-specific biases, or acquired through cognition-general principles. Here we examine the probabilistic language acquisition hypothesis on three levels: We outline a novel theoretical result showing that it is possible to learn the exact generative model underlying a wide class of languages, purely from ...

Algorithmic learning theory traditionally studies the learnability of effective infinite binary sequences (reals), while recent work by [Vitányi and Chater, 2017] and [Bienvenu et al., 2014] has adapted this framework to the study of learnability of effective probability distributions from random data. We prove that for certain families of probability measures that are parametrized by reals, le...

In any learnability setting, hypotheses are conjectured from some hypothesis space. Studied herein are the eeects on learnability of the presence or absence of certain control structures in the hypothesis space. First presented are control structure characterizations of some rather speciic but illustrative learnability results. Then presented are the main theorems. Each of these characterizes t...