This paper presents an analytical model of an agent about the capabilities of a learner for CSCL environments in DLV based on the ASP (Answer Sets Programming) formalism. The complete model is formally presented in the declarative language of DLV, a logic programming language for implementing ASP models. The model proposed provides a representation of the structural knowledge frontier and the social knowledge frontier of the learner, which are the components for the definition of the learner's zone of proximal development (zpd). Based on the zpd of its learner the agent can propose her a learning task and maintain the zpd for the learner in the group. The analytical model, as presented in the paper, runs using the DLV system that can be easily downloaded from the internet.