# A Logic of "Black Box" Classifier Systems

arXiv: https://arxiv.org/abs/2210.07161 · HTML: https://mlsanity.com/paper/2210.07161/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2022.

## Built on by (most cited first, 5 of 5)

- [Logic-Based Explainability in Machine Learning](https://mlsanity.com/paper/2211.00541/) (2022)
- [Delivering Inflated Explanations](https://mlsanity.com/paper/2306.15272/) (2023)
- [Toward A Logical Theory Of Fairness and Bias](https://mlsanity.com/paper/2306.13659/) (2023)
- [Uncovering Bugs in Formal Explainers: A Case Study with PyXAI](https://mlsanity.com/paper/2511.03169/) (2025)
- [Efficient & Correct Predictive Equivalence for Decision Trees](https://mlsanity.com/paper/2509.17774/) (2025)

## Abstract (arXiv)

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.