  In recent years, the impact of machine learning (ML) and artificial
intelligence (AI) in society has been absolutely remarkable. This impact is
expected to continue in the foreseeable future. However,the adoption of AI/ML
is also a cause of grave concern. The operation of the most advances AI/ML
models is often beyond the grasp of human decision makers. As a result,
decisions that impact humans may not be understood and may lack rigorous
validation. Explainable AI (XAI) is concerned with providing human
decision-makers with understandable explanations for the predictions made by ML
models. As a result, XAI is a cornerstone of trustworthy AI. Despite its
strategic importance, most work on XAI lacks rigor, and so its use in high-risk
or safety-critical domains serves to foster distrust instead of contributing to
build much-needed trust. Logic-based XAI has recently emerged as a rigorous
alternative to those other non-rigorous methods of XAI. This paper provides a
technical survey of logic-based XAI, its origins, the current topics of
research, and emerging future topics of research. The paper also highlights the
many myths that pervade non-rigorous approaches for XAI.
