Explainable Artificial Intelligence (XAI) is an area of AI that aims to make AI systems human-understandable by explaining their functions, knowledge and actions. However, it is difficult to define and quantify how well people actually understand machine explanations. This thesis investigates an operational approach to define and analyse the effects of machine explanations on human comprehension. We explore AI-human interactions where people are taught by AI. An AI ``teacher'' presents machine explanations and human ``students'' are evaluated on how accurately they can apply the taught knowledge on new materials. Notably, we show that explanations provided by AI can quantifiably boost human task performance and lead to the re-discovery of efficient computational algorithms by non-experts.

We present an assessment framework $E_{ex}$ to empirically quantify 1) both the beneficial and harmful effects of machine explanations and 2) the impacts of machine-human teaching curricula. This framework can evaluate machine explanations regardless of their representations. To demonstrate this framework, we examine explanations generated from logic theories learned via a Machine Learning approach called Inductive Logic Programming (ILP). These logic theories are computational logic statements learned by ILP systems from training examples. We describe a preliminary theoretical work that characterises the properties of logic theories and curricula for enhancing human task performance. We show that learning from a machine-learned logic theory that is informatively compact and less cognitively demanding improves human task performance. We also observe that teaching by building on simpler concepts benefits human task performance. When concepts with increasing complexity are explained, human novices can develop efficient computational algorithms.