Many concept formation systems construct disjoint-concept trees. However, a priori imposed tree structures may restrict the application of these systems in some domains. A joint concept formation scheme is thus proposed, which learns from observation, and constructs acyclic directed concept graphs (trees are a special case). We show that the joint concept formation system can avoid or alleviate some problems the disjoint concept formation system would face, such as the unique winner and oscillation problems. We also demonstrate that a joint concept formation system is able to generate a concept tree if such a regularity is found among the data. The experimental results are consistent with the expectations that the joint system is a generalized version of the disjoint system and improves the learning performance. Joint concept formation extends the classic works, such as COBWEB and ARACHNE.