Transcript The City of Wood: The Spatial Representation of Knowledge

The City of Wood
Steven Tripp
Center for Language Research
University of Aizu
The Spatial Representation of
Knowledge
• Gärdenfors, P., Conceptual spaces: The
geometry of thought.: MIT Press,
Cambridge, 2000.
• Fauconnier, G., Mappings in thought and
language. Cambridge University Press,
Cambridge, 1997.
• Fauconnier, G., Mental Spaces. Cambridge
University Press, Cambridge, 1994.
Gärdenfors
• Theory of Conceptual Spaces
• Domains: spatial, color, kinship, sound, etc.
• Quality Dimensions: temperature, weight,
hardness, pitch, height, etc.
– Distance=similarity
– Discrete dimensions: species, kinship
Discrete Dimensions
Animals
Mammals
Cow
Reptiles
Horse
Fish
Taste Quality Space
• Tastes are
combinations of three
primaries
• Tastes can only be
represented on planes.
Saline
Sweet
Sour
Bitter
Multidimensional Scaling
• MDS
• Dimension Reduction
• Stress function measures misfit between
data and reduced space
• No guarantee that the dimensions have a
psychological interpretation
MDS Mammals
• Perceived
similarities
• Experts
Help
Colo r
Mous e
Box
Iter
Undo
Spi n
Home
Rock
Clip
Dim3
Zo om
Raccoo n
Opos sum
Fe rret
Koa la
Kan garoo
Dim2
Li on
Dim1
Up/Dn
C/CC
L/R
Spe ed
MDS Mammals
Help
Colo r
Mous e
Box
Iter
Undo
Spi n
• Perceived
similarities
• Novices
Home
Rock
Kan garoo
Clip
Rabb it
Dim2
Hedg ehog
Zo om
Dim1
Dim3
Mana tee
Pla typus
Bea ve r
Up/Dn
C/CC
L/R
Spe ed
Domain
• A set of integral (correlated) dimensions
• Separable dimensions (color and weight)
• A conceptual space is a set of correlated
domains
• A property is a region of a domain
Three Levels of
Representation
• Symbolic (names and rules)
• Conceptual (maps)
• Associationist (paths)
• Problem: How should concepts be
modeled?
Fauconnier’s Mental Spaces
• Cognitive Linguistics
– Language is a set of instructions for
constructing interconnected domains
• Mappings
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Analogy (computer virus)
New conceptual structure ( a new virus)
Projected Structure (disinfectant)
Blending (both computers and organisms)
Domains
• Different domains (beliefs, images,
couterfactuals, scenarios, etc.) have similar
structures.
• A limited set of principles allow structure
projection between domains.
Space Projection
• Maybe Romeo is in
love with Juliet.
• Maybe signals a
possibility space
b
a
A: name Romeo
B: name Juliet
I
Base Space B
I
love a’b’
relative
b’
a’
New Space M
WordNet
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G. Miller (Magic Number 7±2)
Hierarchically linked dictionary
http://www.cogsci.princeton.edu/~wn/
Nine starters
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{ entity, something, (anything having existence (living or nonliving)) }
{ psychological_feature, (a feature of the mental life of a living organism) }
{ abstraction, (a general concept formed by extracting common features from specific examples) }
{ state, (the way something is with respect to its main attributes; ") }
{ event, (something that happens at a given place and time) }
{ act, human_action, human_activity, (something that people do or cause to happen) }
{ group, grouping, (any number of entities (members) considered as a unit) }
{ possession, (anything owned or possessed) }
{ phenomenon, (any state or process known through the senses rather than by intuition or
reasoning) }
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Kinds of Nouns
• Table 1 List of 25 unique beginners for
WordNet nouns
{act, action, activity
{natural object
{animal, fauna
{natural phenomenon
{artifact
{person, human being
{attribute, property
{plant, flora
{body, corpus
{possession
{cognition, knowledge
{process
{communication
{quantity, amount
{event, happening
{relation
{feeling, emotion
{shape
{food
{state, condition
{group, collection
{substance
{location, place
{time
{motive
Sample Hierarchy
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Oak
Sense 1
oak -- (the hard durable wood of any oak; used especially for furniture and flooring)
=> wood -- (the hard fibrous lignified substance under the bark of trees)
=> plant material -- (material derived from plants)
=> material, stuff -- (the tangible substance that goes into the makeup of a physical object; "coal is a hard black material"; "wheat
is the stuff they use to make bread")
=> substance, matter -- (that which has mass and occupies space; "an atom is the smallest indivisible unit of matter")
=> object, physical object -- (a physical (tangible and visible) entity; "it was full of rackets, balls and other objects")
=> entity, something -- (anything having existence (living or nonliving))
Sense 2
oak, oak tree -- (a deciduous tree of the genus Quercus; has acorns and lobed leaves; "great oaks grow from little acorns")
=> tree -- (a tall perennial woody plant having a main trunk and branches forming a distinct elevated crown; includes both
gymnosperms and angiosperms)
=> woody plant, ligneous plant -- (a plant having hard lignified tissues or woody parts especially stems)
=> vascular plant, tracheophyte -- (green plant having a vascular system: ferns, gymnosperms, angiosperms)
=> plant, flora, plant life -- (a living organism lacking the power of locomotion)
=> life form, organism, being, living thing -- (any living entity)
=> entity, something -- (anything having existence (living or nonliving))
Meronyms of Oak Tree
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oak, oak tree -- (a deciduous tree of the genus Quercus; has acorns and lobed leaves; "great oaks grow from little
acorns")
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HAS SUBSTANCE: oak -- (the hard durable wood of any oak; used especially for furniture and flooring)
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HAS PART: acorn -- (fruit of the oak tree: a smooth thin-walled nut in a woody cup-shaped base)
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HAS PART: cupule, acorn cup -- (cup-shaped structure of hardened bracts at the base of an acorn)
=> tree -- (a tall perennial woody plant having a main trunk and branches forming a distinct elevated crown; includes
both gymnosperms and angiosperms)
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HAS SUBSTANCE: sapwood -- (newly formed outer wood lying between the cambium and the heartwood of a
tree or woody plant; usually light colored; active in water conduction)
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HAS SUBSTANCE: heartwood, duramen -- (the older inactive central wood of a tree or woody plant; usually
darker and denser than the surrounding sapwood)
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HAS PART: stump, tree stump -- (the base part of a tree that remains standing after the tree has been felled)
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HAS PART: crown, capitulum, treetop -- (the upper branches and leaves of a tree)
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HAS PART: tree branch -- (a branch arising from the trunk or a bough of a tree)
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HAS PART: trunk, tree trunk, bole -- (the main stem of a tree; usually covered with bark; the bole is usually the
part that is commercially useful for lumber)
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HAS PART: bark -- (tough protective covering of the woody stems and roots of trees and other woody plants)
The Image of the City
• Kevin Lynch, 1960
• Interviews about
mental maps
• Features
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Paths
Edges
Districts
Nodes
Landmarks
Map
Tokyo Subway
Wood Samples
Wood Classification
Rings
Disti nct
Wood
Ident if icat ion
Primary Color
Whit ish
Yellowish
Purplish or
crimson
Reddish or pinkish
Brownish
ash
lacewood
plane
padouk
agba
af rormo sia
maple, bird' s
eye
oak
bubinga cedar, west ern red
cedar of lebanon
pine,
poderosa
Blackish or
grey ish
cherry
elm
iroko
oak, brown
t eak
walnut , black
american
walnut , circassian
Obscure
Poplar
Av odire
syc amor e
maple
zebrawood
ant iaris
birch
lime
sat inwood
purpleheart
mahogony, af rican
beech
mahogony,
honduras
pearwood
walnut ,austr alian
ebony
paldao
Navigation
• Animal Navigation
• Complex and Varied
• Two General Types
– Egocentric (path, homing, DR)
– Allocentric (Cognitive Maps)
• Novel routes
• Short Cuts
• Multiple starting points
Brain Studies
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Hippocampus
Episodic Memory (egocentric?)
Semantic memory (allocentric?)
Brain damage
– Damage to the hippocampus causes loss of
navigational ability in rodents and birds
– Damage in humans causes anterograde amnesia
Navigation In Information
Space
P.P. Maglio and T. Matlock, The Conceptual Structure of Information Space, in A.J.
Munro, K. Höök, and D. Benyon, eds., Social Navigation of Information Space,
Springer, London, 1999.
People using internet browsers conceive
of cognitive space as physical space and
construct cognitive maps of that space.
Senses of Wood
Wood
plant material
forest
woodwind
meronym
substance
meronym
member
meronym
part
lignin
underbrush
tree
fingerhole
thumbhole
bell
mouthpiece
golf club
Hyponyms of Wood
Wood
plant
forest
woodwind
pine
oak
...
many more
grove
old growth
second growth
flute
clarinet
golf
Hypernyms of Wood
Entity
Object
substance
artifact
material
instrumentality
plant material
wood
device
equipment
instrument
sports equipment
musical instrument
golf equipment
wind instrument
golf club
woodwind
wood
Treemaps
Shneiderman, B. (2000).
Treemaps for Space Constrained Visualization of Hierarchies,
http://www.cs.umd.edu/hcil/treemaps/.
The Problem
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Representing Information Visually
Two-dimensional interface
Lack of space and resolution
Visual complexity is no solution
TreeMap Structure
• Representing:
• Hierarchy
• Values
Disk Contents
Stock Market data
Sports Statistics
Decision-Making Tool
Curriculum Structure
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Major and Minor Topics
Time Structure (weekly schedule)
Difficulty
Test Weight
Minutes of Lecture
Other?
Semantic Navigator
Semantic Navigator
Semantic Hierarchy