  In domains with high knowledge distribution a natural objective is to create
principle foundations for collaborative interactive learning environments. We
present a first mathematical characterization of a collaborative learning
group, a consortium, based on closure systems of attribute sets and the
well-known attribute exploration algorithm from formal concept analysis. To
this end, we introduce (weak) local experts for subdomains of a given knowledge
domain. These entities are able to refute and potentially accept a given
(implicational) query for some closure system that is a restriction of the
whole domain. On this we build up a consortial expert and show first insights
about the ability of such an expert to answer queries. Furthermore, we depict
techniques on how to cope with falsely accepted implications and on combining
counterexamples. Using notions from combinatorial design theory we further
expand those insights as far as providing first results on the decidability
problem if a given consortium is able to explore some target domain.
Applications in conceptual knowledge acquisition as well as in collaborative
interactive ontology learning are at hand.
