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.

翻译：二值分类器传统上由命题逻辑（PL）研究。PL只能将其表示为白箱，假设底层布尔函数完全已知。然而，实际应用中使用且通过机器学习训练的二值分类器是不透明的，通常被描述为黑箱。本文提出一种乘积模态逻辑PLC（用于二值输入分类器的乘积模态逻辑），其中“黑箱”概念被解释为对一组分类器的不确定性。我们给出了该逻辑的公理化及可满足性判定复杂度的结果。此外，我们还提出一种动态扩展，可表示获取关于实际分类器新信息的过程。