  Binary classifiers are traditionally studied by propositional logic (PL). PL
can only represent them as white boxes, under the assumption that the
underlying Boolean function is fully known. Binary classifiers used in
practical applications and trained by machine learning are however opaque. They
are usually described as black boxes. In this paper, we provide a product modal
logic called PLC (Product modal Logic for binary input Classifier) in which the
notion of "black box" is interpreted as the uncertainty over a set of
classifiers. We give results about axiomatics and complexity of satisfiability
checking for our logic. Moreover, we present a dynamic extension in which the
process of acquiring new information about the actual classifier can be
represented.
