Virtue theory is a natural approach towards the design of artificially intelligent systems, given that the design of artificial intelligence essentially aims at designing agents with excellent dispositions. This has led to a lively research programme to develop artificial virtues. However, this research programme has until now had a narrow focus on moral virtues in an Aristotelian mould. While Aristotelian moral virtue has played a foundational role for the field, it unduly constrains the possibilities of virtue theory for artificial intelligence. (...) This paper aims to remedy this limitation. Philosophers have developed a rich tradition investigating virtues, their normative domains and their structure. Drawing on this tradition, I propose a three-dimensional classification system of possible artificial virtues: virtues can be classified according to the domain in which virtue is an excellence, norm which makes a virtue an excellence, and mode how the virtue delivers the excellence. With this framework, we can discern gaps in the current theorising about artificial virtues. Additionally, it gives us a tool to evaluate the competences of extant artificially intelligent systems. (shrink)