Rethinking Explanations: Formalizing Contrast in Description Logics

2026-05-02

AI Summary

This work addresses the lack of support for contrastive questions of the form “why P rather than Q?” in existing explanation methods for description logic knowledge bases. It introduces contrastive explanations to description logics for the first time, formally defining foil types based on individual or concept substitution. The paper systematically analyzes the theoretical properties of such explanations within the EL and ALC fragments. Corresponding reasoning algorithms are developed, and a prototype system capable of generating contrastive explanations is implemented. Empirical evaluation demonstrates the effectiveness and scalability of the proposed approach across knowledge bases of varying sizes.

Abstract

There has been a growing interest in explaining entailments over description logic (DL) knowledge bases. The existing explanation formalisms focus on justifications to explain true axioms, and abductive reasoning to explain missing axioms in a knowledge base. However, these formalisms only point out the reasoning steps behind a (missing) entailment and lack a user-centered approach as they do not consider an inquirer's needs, level of understanding, or prior knowledge. We propose contrastive explanations, aiming at answering "why an axiom P (fact) is true instead of another axiom Q (foil)" over description logic knowledge bases. The motivation arises from the observation that when a user discovers that P has occurred, they are often surprised because they anticipated the occurrence of another similar event Q. Furthermore, individual explanations for "why P" and "why not Q" are unsatisfactory since a user expects to see the difference between P and Q. In this work, we first present formal foundations of contrasting questions and then define contrastive explanations within description logics. To this end, facts include ABox assertions of the form C(x) for a concept C and individual x. Possible foils for such facts are assertions C(y) (contrasting against an individual y), or D(x) (contrasting against a concept D). Additionally, we explore the properties of contrastive explanations in the DL EL and ALC. We also provide an implementation of our definition and an experimental evaluation on KBs of varying sizes.

Problem

• contrastive explanations
• description logics
• knowledge base explanation
• foil
• user-centered explanation

Innovation

• contrastive explanations
• description logics
• knowledge base explanation
• foil-based reasoning
• formal foundations