Analogical Transfer of Non-Isomorphic Source Problems

In analogical problem solving, non-isomorphic source/target relations are typically only investigated in contrast to the ideal case of isomorphism. We propose to give a closer look to different types of non-isomorphic source/target relations and varying degrees of structural overlap. We introduce a measure of graph distance which captures the “size” of partial isomorphism between two structures and we present two experiments investigating the influence of different non-isomorphic relations on analogical transfer. In the first experiment we contrast transfer performance for isomorphic vs. source inclusive problems with high vs. low superficial similarity. In the second experiment we explore different types of partial isomorphisms: source inclusiveness, target exhaustiveness, and different degrees of source/target overlap. The results indicate that (1) transfer of isomorphs is not significantly influenced by superficial similarity but transfer of partial isomorphs is, and (2) partial isomorphs can be transferred successfully if the amount of structural overlap is at least as high as structurally differences. The experiments were inspired by some open design questions for the analogy module of IPAL (a computational model integrating problem solving and learning).