Martin Cooper

Martin Cooper, Leila Amgoud

Abductive explanations (AXp's) are widely used for understanding decisions of classifiers. Existing definitions are suitable when features are independent. However, we show that ignoring constraints when they exist between features may lead to an explosion in the number of redundant or superfluous AXp's. We propose three new types of explanations that take into account constraints and that can be generated from the whole feature space or from a sample (such as a dataset). They are based on a key notion of coverage of an explanation, the set of instances it explains. We show that coverage is powerful enough to discard redundant and superfluous AXp's. For each type, we analyse the complexity of finding an explanation and investigate its formal properties. The final result is a catalogue of different forms of AXp's with different complexities and different formal guarantees.

Leila Amgoud, Martin Cooper

Explaining autonomous and intelligent systems is critical in order to improve trust in their decisions. Counterfactuals have emerged as one of the most compelling forms of explanation. They address ``why not'' questions by revealing how decisions could be altered. Despite the growing literature, most existing explainers focus on a single type of counterfactual and are restricted to local explanations, focusing on individual instances. There has been no systematic study of alternative counterfactual types, nor of global counterfactuals that shed light on a system's overall reasoning process. This paper addresses the two gaps by introducing an axiomatic framework built on a set of desirable properties for counterfactual explainers. It proves impossibility theorems showing that no single explainer can satisfy certain axiom combinations simultaneously, and fully characterizes all compatible sets. Representation theorems then establish five one-to-one correspondences between specific subsets of axioms and the families of explainers that satisfy them. Each family gives rise to a distinct type of counterfactual explanation, uncovering five fundamentally different types of counterfactuals. Some of these correspond to local explanations, while others capture global explanations. Finally, the framework situates existing explainers within this taxonomy, formally characterizes their behavior, and analyzes the computational complexity of generating such explanations.

Joao Marques-Silva, Thomas Gerspacher, Martin Cooper et al.

In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction. Despite comprehensive efforts on learning monotonic classifiers, dedicated approaches for explaining monotonic classifiers are scarce and classifier-specific. This paper describes novel algorithms for the computation of one formal explanation of a (black-box) monotonic classifier. These novel algorithms are polynomial in the run time complexity of the classifier and the number of features. Furthermore, the paper presents a practically efficient model-agnostic algorithm for enumerating formal explanations.