Product configuration is one of the most important industrial applications of artificial intelligence. To enable customers to individualize complex products, usually logical configuration models are necessary. One challenge that exists here is the communication of product knowledge to the customer. This work deals with the situation of invalid customer requirements under given logical constraints. The goal is to explain why configurations are invalid and how they can be minimally changed to become valid again. This involves computing all minimal subsets of both constraints and requirements that make the configuration unsatisfiable. For this, we present a novel approach based on the declarative paradigm of Answer Set Programming. We empirically demonstrate its suitability for real-time configurators with thousands of features and constraints. The approach thus fills the gap of an easy-to-implement as well as high-performing conflict resolution component.