An Objective Metric for Explainable AI: How and Why to Estimate the Degree of Explainability

Numerous government initiatives (e.g. the EU with GDPR) are coming to the conclusion that the increasing complexity of modern software systems must be contrasted with some Rights to Explanation and metrics for the Impact Assessment of these tools, that allow humans to understand and oversee the output of Automated Decision Making systems. Explainable AI was born as a pathway to allow humans to explore and understand the inner working of complex systems. But establishing what is an explanation and objectively evaluating explainability, are not trivial tasks. With this paper, we present a new model-agnostic metric to measure the Degree of eXplainability of correct information in an objective way, exploiting a specific model from Ordinary Language Philosophy called the Achinstein's Theory of Explanations. In order to understand whether this metric is actually behaving as explainability is expected to, we designed a few experiments and a user-study on two realistic AI-based systems for healthcare and finance, involving famous AI technology including Artificial Neural Networks and TreeSHAP. The results we obtained are very encouraging, suggesting that our proposed metric for measuring the Degree of eXplainability is robust on several scenarios and it can be eventually exploited for a lawful Impact Assessment of an Automated Decision Making system.