Evaluating the Interpretability of Threshold Operators

Weighted Threshold Operators are n-ary operators that compute a weighted sum of their arguments and verify whether it reaches a certain threshold. They have been extensively studied in the area of circuit complexity theory, as well as in the neural network community under the name of perceptrons. In Knowledge Representation, they have been introduced in the context of standard Description Logics (DL) languages by adding a new concept constructor, the Tooth operator (∇∇ ). Tooth expressions can provide a powerful yet natural tool to represent local explanations of black box classifiers in the context of Explainable AI. In this paper, we present the result of a user study in which we evaluated the interpretability of tooth expressions, and we compared them with Disjunctive Normal Forms (DNF). We evaluated interpretability through accuracy, response time, confidence, and perceived understandability by human users. We expected tooth expressions to be generally more interpretable than DNFs. In line with our hypothesis, the study revealed that tooth expressions are generally faster to use, and that they are perceived as more understandable by users who are less familiar with logic. Our study also showed that the type of task, the type of DNF, and the background of the respondents affect the interpretability of the formalism used to represent explanations.