(Agnostic) PAC learning concepts in higher-order logic

This paper studies the PAC and agnostic PAC learnability of some standard function classes in the learning in higher-order logic setting introduced by Lloyd et al. In particular, it is shown that the similarity between learning in higher-order logic and traditional attributevalue learning allows many results from computational learning theory to be 'ported' to the logical setting with ease. As a direct consequence, a number of non-trivial results in the higher-order setting can be established with straightforward proofs. Our satisfyingly simple analysis provides another case for a more in-depth study and wider uptake of the proposed higher-order logic approach to symbolic machine learning.