Exploring the Logic of Counterfactuals for Explaining Algorithmic Decisions

Abstract Interpretable machine learning (ML) is crucial for gaining insight into complex ML models. Among its most valuable tools are counterfactual explanations, identifying changes to input features that would alter an ML prediction. However, the reliability and usefulness of these explanations depend fundamentally on their logical foundation — a critical aspect that has largely been overlooked in the ML literature. This paper addresses this gap by establishing normative desiderata for a counterfactual logic specifically designed for explaining algorithmic decisions. We analyse and argue for the validity of logical properties such as simplification of disjunctive antecedents and modus ponens , while demonstrating the unsuitability of others such as antecedent strengthening and conjunction conditionalisation . To evaluate existing solutions, we critically compare three prominent counterfactual semantics — similarity, strict conditional, and interventionist — against these desiderata. Our findings reveal that none of these standard frameworks fully satisfy the requirements, highlighting the urgent need for alternative frameworks.