A Thorough Formalization of Conceptual Spaces
arXiv:1706.06366 · doi:10.1007/978-3-319-67190-1_5
Abstract
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.
accepted at KI 2017 (http://ki2017.tu-dortmund.de/), final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-67190-1_5