Keywords: binary classifier, decidability, interpretability
Interpretable machine learning and modeling (sometimes being referred to as “explainable”) generate some interest as of late.
In this paper, we are presenting some new results in this practical, new and industry-oriented direction in machine learning . Complementary to many well-known incarnations of trade-offs of machine learning such as bias and variance, model complexity and performance, we present yet another phenomenon.
Being just at a higher level of abstraction, it shows that we will not be able to create a rigorous decidable or axiomatizable (first-order) theory even for a binary classifier.
One then may argue (formally and informally) that, therefore, the very notion of interpretability is heuristics.
Keywords: Decidability, first order logic, binary classifier, interpretability