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This article introduces a computational model which illustrates how a population of agents can coordinate a vocabulary for goal oriented behavior through repeated local interactions, called “Action Games”. Using principles of self organization and specific assumptions on their behavior, the agents learn the goals and a vocabulary for them. It is shown that the proposed model can be used to investigate the coordination of vocabularies for goal oriented behavior both in a vertical (e.g. between a single teacher and student) and in a horizontal (e.g. in a population of agents which have no a priori repertoire of goals and no vocabularies) transmission scheme. Furthermore, it is shown that in this model shared vocabularies can only be learned from multiple demonstrations consisting of exactly these actions that are strictly required to reach the goal. Keywords: robot imitation; self organization; vocabularies