The present invention relates to a general-purpose analogical reasoning system. More specifically, the present invention relates to a high-performance, semantic-based hybrid architecture for analogical reasoning, capable of finding correspondences between a novel situation and a known situation using relational symmetries, object similarities, or a combination of the two. The system is a high-performance symbolic connectionist model which multiplexes activation across a non-temporal dimension and uses controlled activation flow based on an analogical network structure. The system uses incremental inference to stop inference early for object correspondence, uses initial mappings to constrain future mappings, uses inferred mappings to synchronize activation, and independent mapping based on roles, superficial similarity, or composites.