Mathematical cognition research has largely emphasized concepts that can be directly perceived or grounded in visuospatial referents. These include concrete number systems like natural numbers, integers, and rational numbers. Here, we investigate how a more abstract number system, the irrationals denoted by radical expressions like the square root…

Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of…

This article proposes a new model of human concept learning that provides a rational analysis of learning feature-based concepts. This model is built upon Bayesian inference for a grammatically structured hypothesis space--a concept language of logical rules. This article compares the model predictions to human generalization judgments in several…

Challenges Smolensky's theory that human intuitive/nonconscious cognitive processes can only be accurately explained in terms of subsymbolic computations in artificial neural networks. Symbolic learning models of two cognitive tasks involving nonconscious acquisition of information are presented: learning production rules and artificial finite…

Summarizes an initial foray in tackling artificial intelligence problems using a connectionist approach. The task chosen is visual recognition of Origami objects, and the questions answered are how to construct a connectionist network to represent and recognize projected Origami line drawings and the advantages such an approach would have. (30…

Reports results of studies with an unsupervised learning paradigm called competitive learning which is examined using computer simulation and formal analysis. When competitive learning is applied to parallel networks of neuron-like elements, many potentially useful learning tasks can be accomplished. (Author)