A Logic of "Black Box" Classifier Systems

TL;DR

This paper introduces PLC, a product modal logic framework for representing and reasoning about opaque 'black box' classifiers, including a dynamic extension for modeling information acquisition.

Contribution

It develops a novel modal logic for black box classifiers and explores its axiomatic properties, complexity, and dynamic information update capabilities.

Findings

Axiomatic characterization of PLC logic

Complexity results for satisfiability checking

Dynamic extension for information acquisition

Abstract

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.