Quantitative Concept Analysis

Computer modeling of activities such as concept-learning, conceptual blending, discovery, analogy and creativity has greatly expanded our understanding of possible mechanisms of conceptualization. Unfortunately, it has also meant that theoretical assessment of conceptual possibilities has become problematic. Determining what concepts can be constructed by what mechanisms in what contexts is far from straightforward. In this paper, a task analysis is developed which addresses the problem. This focuses on the combinatorial properties of conceptualization, dividing the space of concept-combination mechanisms into distinct prototypes and assessing the generative properties of each. Complexity formulae are presented which characterize the number of constructs which can be formed by a range of combinatorial strategies. The way in which such processes lead to the generation of distinct conceptual structures and spaces is mapped out. The analysis is then used to clarify the relationships between a range of concept-formation models and to address some issues of human conceptualization.