  We present a discovery-based, first version, explicit model of social
interaction that provides a basis for measuring the quality of interaction of a
human user with a social robot. The two core elements of the social interaction
model are engagement and co-regulation. Engagement emphasizes the
\textit{qualitative nature} of social interaction and the fact that a user
needs to be drawn into the interaction with the robot. Co-regulation emphasizes
the interaction process and the fact that a user and a robot need to be acting
together. We argue that the quality of social interaction with a robot can be
measured in terms of how efficiently engagement and co-regulation are
established and maintained during the interaction and how satisfied the user is
with the interaction.
