Theoretical Framework
Proposed by Peter Gärdenfors, Conceptual Spaces represent information geometrically. Data is organized into quality dimensions (e.g., color, weight, time), where concepts are modeled as convex regions. This approach provides a mathematical bridge between symbolic and sub-symbolic systems.
Levels of Representation
- Symbolic Level: High-level logic and linguistic tokens.
- Conceptual Level: Geometric spaces where similarity is defined by distance metrics.
- Sub-symbolic Level: High-dimensional neural network activation vectors.
Theoretical Precursors & Related Ideas
- Prototype Theory (Eleanor Rosch): The psychological foundation for Gärdenfors' work, stating that some members of a category are more central than others.
- Image Schemas (Lakoff & Johnson): Fundamental recurring patterns of our sensory-motor experience that structure our conceptual understanding.
- Force Dynamics (Talmy): A linguistic framework describing how entities interact with respect to force, providing a geometric basis for causal reasoning.
- Frame Semantics: A theory of linguistic meaning that relates words to the background knowledge required to understand them.
Operational Utility
Conceptual spaces enable Semantic Reasoning that is more flexible than classical logic. By utilizing Voronoi diagrams and prototypical representations, agents can reason about vague or evolving concepts while maintaining structural consistency.
Implementation Paths
Research involves the mapping of Conceptual Spaces into Vector Symbolic Architectures. This enables the execution of geometric reasoning tasks using bitwise operations on CPU hardware.