Learning recursive functions: A survey

TL;DR: The Simplicity Principle allows learning from positive evidence alone, given quite weak assumptions, in apparent contrast to results on language learnability in the limit, which has been at the center of theoretical debate in research on language acquisition and linguistics.

TL;DR: The survey at hand picks out important studies on learning indexed families of recursive languages (including basic as well as recent research), summarizes and illustrates the corresponding results, and points out links to related fields such as grammatical inference, machine learning, and artificial intelligence in general.

TL;DR: This work proposes a rigorous approach of this kind on the basis of algorithmic information theory, based on a single postulate: that universal induction determines the chances of what any observer sees next, and shows that objective reality is not assumed on this approach but rather provably emerges as an asymptotic statistical phenomenon.

TL;DR: Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis.

TL;DR: The topics in LNAI include automated reasoning, automated programming, algorithms, knowledge representation, agent-based systems, intelligent systems, expert systems, machine learning, natural-language processing, machine vision, robotics, search systems, knowledge discovery, data mining, and related programming languages.