CSCTR Session 6 Dana Retov á Consist of a number of quality dimensions Building blocks of representations Weight temperature brightness pitch height width depth Abstract nonsensory dimensions ID: 552707
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Slide1
Conceptual spaces
CSCTR – Session 6
Dana
Retov
áSlide2
Consist of a number of quality dimensionsBuilding blocks of
representations
Weight, temperature, brightness, pitch, height, width, depthAbstract non-sensory dimensionsRepresent various qualities of objectsIndependent of symbolic representations (language)Abstract representation for modelingDo not claim to have any immediate physical realization
Conceptual spaces (G
ärdenfors
)Slide3
Innate – hardwired in nervous systemLearnedLearning involves expanding conc. Space with new quality dimensionsCulturally dependent
T
imeScientificWeight vs. massDimensionsSlide4
In our culture and in scienceOne-dimensional structure isomorphic to the line of real numbersIn other culturesCircular structure
Dimension of ‘time’Slide5
1-D structure from low tones to highLogarithmic scaleAcoustic frequency is spatially coded in chochlea
Dimension of ‘pitch’Slide6
HueBrightnessColor
Color spaceSlide7
Skin colorPossible colors are the subset of the full color spaceCan be irregular
Subset “stretched” to form a space with the same
topologyColor terms can be used even if they do not correspond to the original hues“Metaphor”Contrast classesSlide8
Similarity - defined via distance between representing pointsObject – point in a conceptual space
Property
/Concept – region of a conceptual spaceConceptual spacesSlide9
A metaphor expresses a similarity in topological or metrical structure between different quality dimensionsA 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 anotherE.g. space mapped to timeMetaphors in conceptual spaceSlide10
Predicates are assigned regions of space (red)Secondary properties (tall)“Parasitical” on other properties
“Big
chihuahua”Primary and secondary propertiesSlide11
Cylinders
Length
WidthAngle between the dominating and the other onePosition of the added cylinder Prototypical vector for an object – image schema Subordinate cat. –
subregions
of the convex region
Marr (1982)Slide12
Spatio-temporal patterns of forces that generate the movement
Action spaceSlide13
Function of an object can be analysedActions it affords
Functional concept = convex region in action space
Functional conceptsSlide14
Ideal to representConcepts on basic level of conceptualizationSpatial-relations conceptsRules follow from the topological structure
For example:
A point in a conceptual space will always have an internally consistent set of propertiesSomething cannot be blue and yellow at the same timeEverything that is green is also coloredNothing is in the same place in the same timeTransitivity – as in “earlier than”
Conceptual spacesSlide15
Questions?