  Recent years have witnessed a renewed interest in Boolean function in
explaining binary classifiers in the field of explainable AI (XAI). The
standard approach of Boolean function is propositional logic. We present a
modal language of a ceteris paribus nature which supports reasoning about
binary input classifiers and their properties. We study a family of classifier
models, axiomatize it as two proof systems regarding the cardinality of the
language and show completeness of our axiomatics. Moreover, we prove that
satisfiability checking problem for our modal language is NEXPTIME-complete in
the infinite-variable case, while it becomes polynomial in the finite-variable
case. We furthermore identify an interesting NP fragment of our language in the
infinite-variable case. We leverage the language to formalize counterfactual
conditional as well as a variety of notions of explanation including abductive,
contrastive and counterfactual explanations, and biases. Finally, we present
two extensions of our language: a dynamic extension by the notion of assignment
enabling classifier change and an epistemic extension in which the classifier's
uncertainty about the actual input can be represented.
