Learning logical concepts

This dissertation is a collection of various studies situated at the intersection of Logic and Artificial Intelligence (AI).
We examine the conditions of possibility and the computational complexity of learning logical concepts within Angluin’s model of exact learning. Such algorithms can subsequently be employed to learn a logical description of the (local) behaviour of a black-box system. For example, we show that the minimal representation of all Horn consequences of an arbitrary Boolean function (the so-called 'Horn envelope' of that function) is learnable, and we study the possibility of efficiently computing a semantically-complete characteristic set of examples, for a broad range of description logics that are freely generated from a set of logical connectives.
Another line of research investigates the logical structure of `knowledge base embeddings', that is, methods for embedding graph structures with an associated ontology into a higher-dimensional real space. We analyse various embedding methods from the literature and systematically explore which knowledge bases can or cannot be continuously represented by these methods, and whether this can be achieved in a way that reflects the classical semantics.
Finally, we investigate a recently introduced dependence logic, LFD, and demonstrate that this logic can be translated into the Guarded Fragment (GF) of first-order logic, and vice versa. In doing so, we establish new properties of LFD, strengthen existing connections, and reflect on the general transferability of logical properties under different conditions on translations.