On the computational hardness of learning from structured symbolic data

We present general learnability results for structural representations, with applications to Description Logics. We first extend three existing Boolean formula classes to an arbitrary structural language, then propose a generalization of the PAC learnability model (Valiant 1984) in order to handle non Boolean formalisms. After showing the consistency of our definitions with the originals, we give properties on the extension language which are sufficient to ensure the learnability of the extended classes, and finally give a practical example by choosing Description Logics as the extension language.