A principal requirement to achieve trustworthy AI is to consider ethical aspects in the design and development of AI systems. This is particularly challenging when it comes to automatic decision making and requires appropriate tools to incorporate these aspects in the decision process. One way to address this issue is to evaluate the available alternatives in terms of their adherence to AI-specific moral values, i.e. responsible-AI values. In this article, we propose a hierarchical model to incorporate responsible AI values as ethical criteria in the decision-making process. We adopt our framework on the problem of ranking several recommendation systems according to their adherence to responsible AI values. We use Answer Set Programming (ASP) to formally represent the implementation of our framework on this problem and derive a ranking of alternatives using logical reasoning.