A Thorough Formalization of Conceptual Spaces
This work provides an incremental improvement to the conceptual spaces framework, potentially benefiting researchers in knowledge representation and AI.
The authors tackled the problem of the convexity requirement in the conceptual spaces framework by proposing a formalization based on fuzzy star-shaped sets, which allows for representing correlations between domains and defines efficient operations for learning and reasoning.
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.