conceptual spaces
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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 - PowerPoint PPT PresentationTRANSCRIPT
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Conceptual spacesCSCTR – Session 6
Dana Retová
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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)
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Innate – hardwired in nervous system Learned
◦ Learning involves expanding conc. Space with new quality dimensions
Culturally dependent◦ Time
Scientific◦ Weight vs. mass
Dimensions
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In our culture and in science◦ One-dimensional structure isomorphic to the line
of real numbers In other cultures
◦ Circular structure
Dimension of ‘time’
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1-D structure from low tones to high Logarithmic scale Acoustic frequency is spatially coded in
chochlea
Dimension of ‘pitch’
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Hue Brightness Color
Color space
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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
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Similarity - defined via distance between representing points
Object – point in a conceptual space Property /Concept – region of a
conceptual space
Conceptual spaces
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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
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Predicates are assigned regions of space (red)
Secondary properties (tall)◦ “Parasitical” on other properties
“Big chihuahua”
Primary and secondary properties
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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)
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Spatio-temporal patterns of forces that generate the movement
Action space
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Function of an object can be analysed◦ Actions it affords
Functional concept = convex region in action space
Functional concepts
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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
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Questions?