  Explainability in Artificial Intelligence has been revived as a topic of
active research by the need of conveying safety and trust to users in the `how'
and `why' of automated decision-making. Whilst a plethora of approaches have
been developed for post-hoc explainability, only a few focus on how to use
domain knowledge, and how this influences the understandability of global
explanations from the users' perspective. In this paper, we show how ontologies
help the understandability of global post-hoc explanations, presented in the
form of symbolic models. In particular, we build on Trepan, an algorithm that
explains artificial neural networks by means of decision trees, and we extend
it to include ontologies modeling domain knowledge in the process of generating
explanations. We present the results of a user study that measures the
understandability of decision trees using a syntactic complexity measure, and
through time and accuracy of responses as well as reported user confidence and
understandability. The user study considers domains where explanations are
critical, namely, in finance and medicine. The results show that decision trees
generated with our algorithm, taking into account domain knowledge, are more
understandable than those generated by standard Trepan without the use of
ontologies.
