Conceptual Ternary Diagrams for Shape Perception: A Preliminary Step

This work-in-progress provides a preliminary cognitive investigation of how the external visualization of the ‘Ternary diagram’ (TD) might be used as an underlying model for exploring the representation of simple 3D cuboids according to the theory of Conceptual Spaces. Gärdenfors introduced geometrical entities, known as conceptual spaces, for modeling concepts. He considered multidimensional spaces equipped with a range of similarity measures (such as metrics) and guided by criteria and mechanisms as a geometrical model for concept formation and management. Our work is inspired by the conceptual spaces approach and takes ternary diagrams as its underlying conceptual model. The main motivation for our work is twofold. First, Ternary Diagrams are powerful conceptual representations that have a solid historical and mathematical foundation. Second, the notion of overlaying an ‘InformationEntropy’ function on a ternary diagram can lead to new insights into applications of reasoning about shape and other cognitive processes.