  A central quest in explainable AI relates to understanding the decisions made
by (learned) classifiers. There are three dimensions of this understanding that
have been receiving significant attention in recent years. The first dimension
relates to characterizing conditions on instances that are necessary and
sufficient for decisions, therefore providing abstractions of instances that
can be viewed as the "reasons behind decisions." The next dimension relates to
characterizing minimal conditions that are sufficient for a decision, therefore
identifying maximal aspects of the instance that are irrelevant to the
decision. The last dimension relates to characterizing minimal conditions that
are necessary for a decision, therefore identifying minimal perturbations to
the instance that yield alternate decisions. We discuss in this tutorial a
comprehensive, semantical and computational theory of explainability along
these dimensions which is based on some recent developments in symbolic logic.
The tutorial will also discuss how this theory is particularly applicable to
non-symbolic classifiers such as those based on Bayesian networks, decision
trees, random forests and some types of neural networks.
