Structural mapping

Structural mapping is the alignment of relational structure between a source domain and a target domain, independent of surface features. It is the core operation in analogical reasoning: not the matching of properties (this is like that) but the preservation of relationships (the way A relates to B in the source is the way C relates to D in the target). The concept was formalized in Gentner's structure-mapping theory, which distinguished between attributes (predicates applied to single objects) and relations (predicates linking multiple objects), arguing that true analogy maps only the latter. Structural mapping is what makes analogy productive rather than merely decorative: it generates inferences by projecting known relations from the source into the target. Yet the computational problem of finding the optimal mapping across domains of any real complexity remains unsolved, and every implementation — from Copycat to modern large language models — trades completeness against tractability.

The obsession with finding the 'correct' structural mapping misses something deeper: human analogy-making is not optimal but opportunistic. We do not find the best mapping; we find the first mapping that works well enough to proceed, and we revise only when it fails. Any theory of structural mapping that assumes exhaustive search is a theory of angels, not humans.