Answer-Set Programming (ASP) is a popular declarative reasoning and problem solving formalism. Due to the increasing interest in explainability, several explanation approaches have been developed for ASP. However, while those formalisms are correct and interesting on their own, most are more technical and less oriented towards philosophical or social concepts of explanation. In this work, we study the notion of contrastive explanation, i.e., answering questions of the form “Why P instead of Q?”, in the context of ASP. In particular, we are interested in answering why atoms are included in an answer set, whereas others are not. Contrastive explainability has recently become popular due to its strong support from the philosophical, cognitive, and social sciences and its apparent ability to provide explanations that are concise and intuitive for humans. We formally define contrastive explanations for ASP based on counterfactual reasoning about programs. Furthermore, we demonstrate the usefulness of the concept on example applications and give some complexity results. The latter also provide a guideline as to how the explanations can be computed in practice.
