ABSTRACT
Some cognitive scientists have suggested that invariance plays a role in higher level cognition. This chapter introduces the notion of categorical invariance. Generalized invariance structure theory (GIST) uses the mathematical notion of categorical invariance to describe the kinds of patterns that humans are sensitive to in categorical stimuli. Categorical invariance theory (CIT) was developed primarily as a stimulus-oriented theory of conceptual behavior where the degree of concept-learning difficulty of categorical stimulus is modeled quantitatively as the ratio between its degree of categorical invariance and its size. The chapter proceeds with a discussion of Boolean derivative. The Boolean derivative was introduced by Reed in a discussion of error-correcting codes in electrical circuits. The goal is to measure the degree of qualitative invariance that is revealed by an application of the Boolean partial derivative operator on a Boolean category. To do this, the two new differential operators: the n-th logical manifold of a Boolean formula and the Boolean category Laplacian are introduced.
