Conceptual Spaces 1 Flashcards
(20 cards)
What are Conceptual Spaces (Gärdenfors, 2000)?
A geometric framework representing concepts as convex regions in a multidimensional metric space defined by interpretable quality dimensions.
How do Conceptual Spaces differ from symbolic representations?
They ground concepts in a metric space via quality dimensions, enabling geometric modeling of similarity, typicality, and vagueness, unlike rule-based or logical symbol manipulation.
What is a quality dimension?
An axis representing a perceptual or psychological feature (e.g., hue, sweetness) along which entities have measurable values.
How are entities represented in Conceptual Spaces?
As points whose coordinates correspond to their values on each quality dimension.
How are concepts represented?
As convex regions; points closer to the region’s prototype center have higher membership.
How is similarity measured?
By geometric distance: entities with points closer in space are more similar.
What is typicality?
The degree to which an entity represents a concept, modeled by proximity to the region’s center.
How is vagueness handled?
Through graded (fuzzy) membership: soft boundaries allow entities to partially belong to concepts.
What is context-dependence?
Dimensions can be reweighted or rescaled based on context, shifting region shapes and similarity judgments.
How do Conceptual Spaces support generalisation?
Nearby points sharing properties suggest other nearby entities likely share those properties.
What is compositionality and its challenge?
Combining concept regions to form complex concepts; challenging because region intersection may not capture logical combinations simply.
Compare Conceptual Spaces with word embeddings.
CS use domain-specific, interpretable dimensions and distinct point vs. region representations; embeddings are global, learned, and have opaque axes.
Describe the traditional MDS-based learning approach.
Convert bag-of-words to distances, apply MDS to embed entities, then post-hoc identify dimensions via analysis.
List limitations of the traditional approach.
Poor scalability, manual dimension selection, no relational or hierarchical constraints, limited interpretability.
Outline modern learning methods.
Learn unified space with semantic-type subspaces, hierarchical constraints, space alignment using KG relations, and max-margin losses.
Name three advantages of Conceptual Spaces.
Interpretability, cognitive plausibility, and natural modeling of vagueness and typicality.
Name three limitations or challenges.
Scalability to large data, automated dimension discovery, and integration of relational structure with geometry.
Give four AI applications.
Plausible reasoning (induction), entity retrieval, ontology reasoning/KB completion, and category-based induction.
How to embed multi-type entities for similarity clustering?
Define type-specific dimensions/subspaces, represent entities as points in combined space, align subspaces into a unified metric, and compute distances.
Why is space alignment important?
It ensures meaningful cross-type distance comparisons by projecting subspaces into a common coordinate system.
