  Until now, most studies carried onto social or semantic networks have
considered each of these networks independently. Our goal here is to bring a
formal frame for studying both networks empirically as well as to point out
stylized facts that would explain their reciprocal influence and the emergence
of clusters of agents, which may also be regarded as ''cultural cliques''. We
show how to apply the Galois lattice theory to the modeling of the coevolution
of social and conceptual networks, and the characterization of cultural
communities. Basing our approach on Barabasi-Albert's models, we however extend
the usual preferential attachment probability in order to take into account the
reciprocal influence of both networks, therefore introducing the notion of dual
distance. In addition to providing a theoretic frame we draw here a program of
empirical tests which should give root to a more analytical model and the
consequent simulation and validation. In a broader view, adopting and actually
implementing the paradigm of cultural epidemiology, we could proceed further
with the study of knowledge diffusion and explain how the social network
structure affects concept propagation and in return how concept propagation
affects the social network.
