A logical study of group-size based social network creation

This paper is part of an on-going research programme on the logical aspects of social network creation. In our proposed setting we make use of a notion of distance between agents, defined as the number of features distinguishing them. Following the ideas of the cognitive science literature, we build the social network by adopting a group-size approach: each agent's new social space will contain the λ agents that are closer to her. The paper studies the properties of the resulting networks, providing a sound and complete axiom system for a logical language which describes the changes that the social network creation operation brings about. This is done not only for the basic case in which the distance is relative to all basic features and the more general one in which the distance is relative to a given subset of them, but also for the more interesting scenario in which the distance is relative to a set of more complex social features.