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Conceptual spaces

Conceptual spaces. CSCTR – Session 6 Dana Retov á. Conceptual spaces (G ärdenfors ). Consist of a number of quality dimensions Building blocks of representations Weight, temperature, brightness, pitch, height, width, depth Abstract non-sensory dimensions

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Conceptual spaces

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  1. Conceptual spaces CSCTR – Session 6 Dana Retová

  2. Conceptual spaces (Gärdenfors) • Consist of a number of quality dimensions • Building blocks of representations • Weight, temperature, brightness, pitch, height, width, depth • Abstract non-sensory dimensions • Represent various qualities of objects • Independent of symbolic representations (language) • Abstract representation for modeling • Do not claim to have any immediate physical realization

  3. Dimensions • Innate – hardwired in nervous system • Learned • Learning involves expanding conc. Space with new quality dimensions • Culturally dependent • Time • Scientific • Weight vs. mass

  4. Dimension of ‘time’ • In our culture and in science • One-dimensional structure isomorphic to the line of real numbers • In other cultures • Circular structure

  5. Dimension of ‘pitch’ • 1-D structure from low tones to high • Logarithmic scale • Acoustic frequency is spatially coded in chochlea

  6. Color space • Hue • Brightness • Color

  7. Contrast classes • Skin color • Possible colors are the subset of the full color space • Can be irregular • Subset “stretched” to form a space with the same topology • Color terms can be used even if they do not correspond to the original hues • “Metaphor”

  8. Conceptual spaces • Similarity - defined via distance between representing points • Object – point in a conceptual space • Property/Concept – region of a conceptual space

  9. Metaphors in conceptual space • A metaphor expresses a similarity in topological or metrical structure between different quality dimensions • A word that represent a particular structure in one quality dimension can be used as a metaphor to express a similar structure about another dimension • Metaphors transfer knowledge about one conceptual dimension to another • E.g. space mapped to time

  10. Primary and secondary properties • Predicates are assigned regions of space (red) • Secondary properties (tall) • “Parasitical” on other properties • “Big chihuahua”

  11. Marr (1982) • Cylinders • Length • Width • Angle between the dominating and the other one • Position of the added cylinder • Prototypical vector for an object – image schema • Subordinate cat. – subregions of the convex region

  12. Action space • Spatio-temporal patterns of forces that generate the movement

  13. Functional concepts • Function of an object can be analysed • Actions it affords • Functional concept = convex region in action space

  14. Conceptual spaces • Ideal to represent • Concepts on basic level of conceptualization • Spatial-relations concepts • Rules follow from the topological structure • For example: • A point in a conceptual space will always have an internally consistent set of properties • Something cannot be blue and yellow at the same time • Everything that is green is also colored • Nothing is in the same place in the same time • Transitivity – as in “earlier than”

  15. Questions?

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