  Federated learning (FL) is an emerging approach for training machine learning
models collaboratively while preserving data privacy. The need for privacy
protection makes it difficult for FL models to achieve global transparency and
explainability. To address this limitation, we incorporate logic-based
explanations into FL by proposing the Logical Reasoning-based eXplainable
Federated Learning (LR-XFL) approach. Under LR-XFL, FL clients create local
logic rules based on their local data and send them, along with model updates,
to the FL server. The FL server connects the local logic rules through a proper
logical connector that is derived based on properties of client data, without
requiring access to the raw data. In addition, the server also aggregates the
local model updates with weight values determined by the quality of the
clients' local data as reflected by their uploaded logic rules. The results
show that LR-XFL outperforms the most relevant baseline by 1.19%, 5.81% and
5.41% in terms of classification accuracy, rule accuracy and rule fidelity,
respectively. The explicit rule evaluation and expression under LR-XFL enable
human experts to validate and correct the rules on the server side, hence
improving the global FL model's robustness to errors. It has the potential to
enhance the transparency of FL models for areas like healthcare and finance
where both data privacy and explainability are important.
