Linear separability and concept learning: Context, relational properties, and concept naturalness

Four experiments were designed to determine if the ease with which abstract category structures are learned interacts with the specific type of knowledge that is applied to the task. Participants were tested on category structures that were or were not linearly separable, and different knowledge structures were induced by manipulating the context of the stimulus information (behavioral characteristics, descriptions of objects, occupational descriptions, and lists of preferences) and the instructions (e.g., think of the following objects in terms of their utility as a hammer). Linearly separable (LS) categories are categories that can be perfectly partitioned on the basis of a weighted, additive combination of component information. Independent cue models (e.g., prototype theories) predict that the linearly separable categories used in the experiments should be easier to learn than the nonlinearly separable (NLS) categories across conditions, whereas interactive cue models (e.g., the context model) make the opposite prediction. The experiments revealed a strong interaction between abstract category structure and knowledge structures: When the knowledge structures induced coding compatible with LS categories, the LS categories were easier to learn than the NLS categories; but when the knowledge structures induced coding compatible with NLS structures, the reverse was true. The implications of the results for classification models and constraints on category formation are discussed in terms of the form of relational coding that is induced by different knowledge structures. Independent cue and interactive cue models may only account for a narrow range of interproperty coding.