Subjective Complexity of Categories Defined over Three-Valued Features
Cordelia D. Aitkin, Jacob Feldman · eScholarship (California Digital Library) · 2006
Many studies in the last four decades have investigated the relative difficulty in learning of concepts defined by various logical forms.Historically, most such studies have used Boolean concepts, that is, categories formed by logical combinations of binary-valued variables.In previous work, we have found that in such categories subjective difficulty is well predicted by Boolean complexity, that is, the length of the shortest propositional formula equivalent to the concept.However, this formalization does not extend easily to concepts defined using features with more than two values.Such categories are of particular interest because they are not easily handled by any contemporary theories based on continuous metric spaces.In more recent work, we have developed a representational formalism suitable for representing such categories.This theory provides a measure of conceptual complexity for such categories, called algebraic complexity.Here we report an experiment testing the learnability of a set of a set of categories defined over two three-valued features.The results show that algebraic complexity gives a good account of the subjective learnability of these concepts.