The paper examines the problem of learning socio-linguistic skills through imitation when those skills involve both observable motor patterns and internal unobservable cognitive operations. This approach is framed in a research program trying to investigate novel links between context-dependent motor learning by imitation and language acquisition. More precisely, the paper presents an algorithm allowing a robot to learn how to respond to communicative/linguistic actions of one human, called an interactant, by observing how another human, called a demonstrator, responds. As a response to 2 continuous communicative hand signs of the interactant, the demonstrator focuses on one out of three objects, and then performs a movement in relation to the object focused on. The response of the demonstrator, which depends on the context, including the hand signs produced by the interactant, is assumed to be appropriate and the robotic imitator uses these observations to build a general policy of how to respond to interactant actions. In this paper the communicative actions of the interactant are based on hand signs. The robot has to learn several things at the same time: 1) Weather it is the first sign or the second sign that specifies the object to focus on (that is, requests an internal cognitive operation), and the same for the request of a movement type. 2) How many hand signs there are and how to recognize them. 3) How many movement types there are and how to reproduce them in different contexts. 4) How to assign specific interactant hand signs to specific internal operations and specific movements. An algorithm is proposed based on a similarity metric between demonstrations, and an experiment is presented where the unseen ''focus on object" operation and the hand movements are successfully imitated, including in situations not observed during the demonstrations.