The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After pointing out a problem with the convexity requirement, we propose a formalization of conceptual spaces based on fuzzy star-shaped sets. Our formalization uses a parametric definition of concepts and extends the original framework by adding means to represent correlations between different domains in a geometric way. Moreover, we define computationally efficient operations on concepts (intersection, union, and projection onto a subspace) and show that these operations can support both learning and reasoning processes.
CITATION STYLE
Bechberger, L., & Kühnberger, K. U. (2017). A Thorough Formalization of Conceptual Spaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10505 LNAI, pp. 58–71). Springer Verlag. https://doi.org/10.1007/978-3-319-67190-1_5
Mendeley helps you to discover research relevant for your work.