Knowledge sharing in communities with partially focused identities requires formal representation of data, without precise common vocabulary. Differentiated vocabulary, in which specific terms inherit from shared general concepts, can meet this need. Concepts are defined with enriched case frames and constraints, and are organized by subsumption within ontologies. Ontologies are also organized by subsumption. Expressions represent knowledge as networks of instantiated concepts: ontologies appropriate to the problem context supply the vocabulary. An algorithm for comparing expressions builds mappings with one-to-one correspondences between nodes in the source and target expressions. Mappings can be used to answer queries in a differentiated vocabulary knowledge base.
A series of comparisons between expressions with varying degrees of differentiation in vocabulary and structure is implemented. High quality mappings are achieved with satisfactory time and space complexity. The results confirm our intuitions about the need for common language, demonstrate that differentiated vocabulary is feasible, and suggest that mappings can support a richly substantive dialogue between an intelligent coach and users.
A mapping between an expression in pond ecology ("increasing temperature causes dissolved oxygen to decrease") and an expression describing fizzy soda ("more degrees are associated with less carbonation").
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