  One of the most pressing issues in AI in recent years has been the need to
address the lack of explainability of many of its models. We focus on
explanations for discrete Bayesian network classifiers (BCs), targeting greater
transparency of their inner workings by including intermediate variables in
explanations, rather than just the input and output variables as is standard
practice. The proposed influence-driven explanations (IDXs) for BCs are
systematically generated using the causal relationships between variables
within the BC, called influences, which are then categorised by logical
requirements, called relation properties, according to their behaviour. These
relation properties both provide guarantees beyond heuristic explanation
methods and allow the information underpinning an explanation to be tailored to
a particular context's and user's requirements, e.g., IDXs may be dialectical
or counterfactual. We demonstrate IDXs' capability to explain various forms of
BCs, e.g., naive or multi-label, binary or categorical, and also integrate
recent approaches to explanations for BCs from the literature. We evaluate IDXs
with theoretical and empirical analyses, demonstrating their considerable
advantages when compared with existing explanation methods.
