Conceptual spacesCSCTR – Session 6

Dana Retová

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

Conceptual spaces (Gärdenfors)

Innate – hardwired in nervous system Learned

◦ Learning involves expanding conc. Space with new quality dimensions

Culturally dependent◦ Time

Scientific◦ Weight vs. mass

Dimensions

In our culture and in science◦ One-dimensional structure isomorphic to the line

of real numbers In other cultures

◦ Circular structure

Dimension of ‘time’

1-D structure from low tones to high Logarithmic scale Acoustic frequency is spatially coded in

chochlea

Dimension of ‘pitch’

Hue Brightness Color

Color space

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”

Contrast classes

Similarity - defined via distance between representing points

Object – point in a conceptual space Property /Concept – region of a

conceptual space

Conceptual spaces

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

Metaphors in conceptual space

Predicates are assigned regions of space (red)

Secondary properties (tall)◦ “Parasitical” on other properties

“Big chihuahua”

Primary and secondary properties

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

Marr (1982)

Spatio-temporal patterns of forces that generate the movement

Action space

Function of an object can be analysed◦ Actions it affords

Functional concept = convex region in action space

Functional concepts

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”

Conceptual spaces

Questions?