This paper proposes a new accountability and transparency evaluation framework (AccTEF) for ontology-based systems (OSysts). AccTEF is based on an analysis of the relation between a set of widely accepted data governance principles, i.e. findable, accessible, interoperable, reusable (FAIR) and accountability and transparency concepts. The evaluation of accountability and transparency of input ontologies and vocabularies of OSysts are addressed by analyzing the relation between vocabulary and ontology quality evaluation metrics, FAIR and accountability and transparency concepts. An ontology-based knowledge extraction pipeline is used as a use case in this study. Discovering the relation between FAIR and accountability and transparency helps in identifying and mitigating risks associated with deploying OSysts. This also allows providing design guidelines that help accountability and transparency to be embedded in OSysts. We found that FAIR can be used as a transparency indicator. We also found that the studied vocabulary and ontology quality evaluation metrics do not cover FAIR, accountability and transparency. Accordingly, we suggest these concepts should be considered as vocabulary and ontology quality evaluation aspects. To the best of our knowledge, it is the first time that the relation between FAIR and accountability and transparency concepts has been found and used for evaluation.