1. INTRODUCTION TO ARTIFICIAL INTELLIGENCE
Massimo Poesio LECTURE 7 Psychological theories of concepts: Prototype theory, Image schemas

2. Evidence for the taxonomic theory of concepts
Collins & Quillian, 1969, 1970
Evidence: When people do a semantic verification task, you see evidence of a hierarchy (response times are correlated with the number of links).
Superset (category):
Property:
Number of links:
A canary is a canary (S0)
A canary can sing (P0)
A canary is a bird (S1)
A canary can fly (P1) 1
A canary is an animal (S2)
A canary has skin (P2) 2

3. Semantic networks Collins & Quillian, 1970:
Collins & Quillian (1970, p. 306; reporting data from Collins & Quillian, 1969)

4. Semantic network models (Collins & Quillian, 1970)
Concepts are organized as a set of nodes and links between those nodes.
Nodes hold concepts. For example, you would have a node for RED, FIRE, FIRETRUCK, etc. Each concept you know would have a node.
Links connect the nodes and encode relationships between them. Two kinds:
Superset/subset: Essentially categorize. For example, ROBIN is a subset of BIRD.
Property: Labeled links that explain the relationship between various properties and nodes. For example, WINGS and BIRD would be connected with a “has” link.

5. Semantic network models
Collins & Quillian (1970, p. 305)

6. Semantic network models
The nodes are arranged in a hierarchy and distance (number of links traveled) matters. The farther apart two things are, the less related they are. This is going to be important in predicting performance.
The model has a property called cognitive economy. Concepts are only stored once at the highest level to which they apply (e.g., BREATHES is stored at the ANIMAL node instead of with each individual animal). This was based on the model’s implementation on early computers and may not have a brain basis. Also, not necessarily crucial for the model.

7. PROBLEMS FOR THE CLASSICAL THEORY OF CONCEPTS
The view dominant since Aristotle that knowledge is organized around concepts whose definitions provide necessary and sufficient conditions in terms of genus and differentia (ie in terms of a taxonomic organization) has been challenged first from within Philosophy, then from within Psychology

8. PLATO’S PROBLEM
For many concepts, there simply aren’t any definitions” (LM p.14)
A theory that correctly describes the behavior of perhaps three hundred words has been asserted to correctly describe the behavior of the tens of thousands of general names (Putnam)

9. WITTGENSTEIN’s EXAMPLE: ‘GAME’
What is common to all games?
Are they all ‘amusing’?
Cfr. chess
Or is there always winning and losing?
Counterex: child throwing his ball at the wall
Look at the parts played by skill and luck
“I can think of no better expression that FAMILY RESEMBLANCE”
‘games form a family’

10. PUTNAM
the term ‘lemon’ not definable by simply conjoining its ‘definining characteristics’ yellow color / tart taste / a certain kind of peel
Abnormal members (green lemon)
Three legged tiger (Also: three-legged chair, see below)

11. THE VIEW FROM PSYCHOLOGY
Early psychological work seems to support the traditional taxonomic view
But evidence from the mid-70’s raised a number of questions

12. PROBLEMATIC EVIDENCE FROM PSYCHOLOGY
Typicality effects
Is a tomato a vegetable or a fruit?
‘Is this art?’
Evidence that IS-A may have different properties – eg., failures of transitivity
If A is a B and B is a C, is A a C?
Evidence that categorization may not be based on necessary and sufficient conditions
Basic level effects

13. Typicality effects
The ease with which people judge CATEGORY MEMBERSHIP depends on typicality
Rips, Shoben and Smith (1973): Fast to affirm that a robin is a bird; not so fast to affirm that a chicken is a bird
Posner & Keele: similarity to visual pattern
Learning: typical items learned before atypical ones (Rosch Simpson & Miller 1976)
Learning is faster if subjects are taught on typical items
Typicality affects speed of inference
Rips 1975:
Garrod & Sanford 1977: faster reading time for “The bird came in through the front door” when ROBIN than when GOOSE

14. Typicality effects
Rips, Shoben & Smith (1973): Typicality seems to influence responses.
Technically, “a robin is a bird” and “a chicken is a bird” are each one link. But, the robin is more typical. What is that in the network? Shows up in reaction times as well.

15. Typicality ratings
Smith, Shoben, & Rips (1974, p. 218)

16. Typicality effects
With the hierarchy: “A horse is an animal” is faster than “A horse is a mammal” which violates the hierarchy.
A chicken is more typical of animal than a robin, a robin is more typical of bird than a chicken. How can a network account for this (Smith, Shoben, & Rips, 1974)?

17. Typicality effects
Answering “no”: You know the answer to a questions is “no” (e.g., “a bird has four legs”) because the concepts are far apart in the network. But, some “no” responses are really fast (e.g., “a bird is a fish”) and some are really slow (e.g., “a whale is a fish”). The reason for this isn’t obvious in the model.
“Loosely speaking, a bat is a bird” is true, but how does a network model do it (Smith, Shoben, & Rips, 1974)?

18. Agreement on typicality judgments
(‘think of a fish, any fish’)
Rosch (1975): very high correlation (.97) between subjects’s typicality rankings for 10 categories

19. TYPICALITY JUDGMENTS 1 chair 1 sofa 3 couch 3 table 5 easy chair
6 dresser
6 rocking chair
8 coffee table
9 rocker
10 love seat
11 chest of drawers
12 desk
13 bed
...
...
22 bookcase
27 cabinet
29 bench
31 lamp
32 stool
35 piano
41 mirror
42 tv
44 shelf
45 rug
46 pillow
47 wastebasket
49 sewing machine
50 stove
54 refrigerator
60 telephone

20. Other typicality effects
Learning: typical items learned before atypical ones (Rosch Simpson & Miller 1976)
Learning is faster if subjects are taught on typical items
Typicality affects speed of inference
Rips 1975:
Garrod & Sanford 1977: faster reading time for “The bird came in through the front door” when ROBIN than when GOOSE

21. apples, carrots, tomatoes, cauliflower, oranges, pumpkin, cucumber?
Divide the following items into the category of fruits and the category of vegetables:
apples, carrots, tomatoes, cauliflower, oranges, pumpkin, cucumber

22. Feature models Smith, Shoben, & Rips, 1974:
Concepts are clusters of semantic features. There are two kinds:
Distinctive features: Core parts of the concept. They must be present to be a member of the concept, they’re the defining features. For example, WINGS for BIRD.
Characteristic features: Typically associated with the concept, but not necessary. For example, CAN FLY for BIRD.

23. Feature models
Smith, Shoben, & Rips (1974, p. 216)

24. Feature models Some examples: BIRD MAMMAL Distinctive Wings Feathers…
Nurses-young
Warm-blooded
Live-birth…
Characteristic
Flies
Small…
Four-legs…
ROBIN
WHALE
Swims
Live-birth
Nurses-young…
Red-breast
Large

25. Feature models
Why characteristic features? Various evidence, such as hedges:
Smith, Shoben, & Rips (1974, p. 217)

26. Feature models
Why characteristic features? Various evidence, such as hedges:
OK:
A robin is a true bird.
Technically speaking, a chicken is a bird.
Feels wrong:
Technically speaking, a robin is a bird.
A chicken is a true bird.
The answer depends on the kinds of feature overlap.

27. Feature models
Answering a semantic verification question is a two-step process.
Compare on all features. If there is a lot of overlap it’s an easy “yes.” If there is almost no overlap, it’s an easy “no.” In the middle, go to step two.
Compare distinctive features. This involves an extra stage and should take longer.

28. Smith, Shoben, & Rips (1974, p. 222)

29. Feature models Some questions: Easy “yes” Easy “no” Hard “yes”
Hard “no”
A robin is a bird
A robin is a fish
A whale is a mammal
A whale is a fish

30. Feature models Can account for:
Typicality effects: One step for more typical members, two steps for less typical members, that explains the time difference.
Answering “no”: Why are “no” responses different? Depends on the number of steps (feature overlap).
Hierarchy: Since it isn’t a hierarchy but similarity, we can understand why different types of decisions take different amounts of time.

31. Feature models Problem: How do we get the distinctive features?
What makes something a game? What makes someone a bachelor? How about cats?
How many of the features of a bird can you lose and still have a bird?
The distinction between defining and characteristic features addresses this somewhat, but it is still a problem in implementation.

32. FEATURE NORMS
Psychologists have been collecting concept features from subjects at least since Rosch and Mervis (1975)
Different methodologies used (from free association to very tightly controlled)
Three such databases currently available
Garrard et al (2001) - GA
Vinson and Vigliocco (2004) - VV
McRae et al (2005) – MCRA - the largest, also classified

33. SPEAKER-GENERATED FEATURES (VINSON AND VIGLIOCCO)

34. SPEAKER-GENERATED FEATURES (MCRAE)

35. FEATURE NORMS (GARRARD)

36. What makes an item typical? Rosch & Mervis 1975
Items are typical when they have HIGH FAMILY RESEMBLANCE with members of the category:
Typical items have many of the attributes of members
Do not have properties of nonmembers
Irrespective of frequency: ORIOLE vs CHICKEN
Evidence 1: checked that subjects agree on typicality for several natural categories
Asked subjects to list attributes (actually, check)
Weighed each attribute by how many items it occurred with within the category
‘SCORE’ indicates how many common features
Found that score highly predictive of typicality ( )
Five most typical ‘furniture’ (CHAIR, SOFA, TABLE, DRESSER, DESK) have 13 features in common
Five least typical (CLOCK, PICTURE, CLOSET, VASE, TELEPHONE) had 2 attributes in common
Cfr. Wittgenstein

37. Rosch and Mervis 1975 (2)
Evidence 2: non-typical elements have more features in common with other categories
Evidence 3: speed of learning with artificial stimuli belonging to 2 classes
Items with more features in common with family easier to learn
Items with more features in common with contrast category harder to learn

38. ‘Fuzzy’ or ‘graded’ categorization
A necessary and sufficient definition should pick up all the category members and none of the non-members
But this is not what happens:
Hampton (1979): no clear division between members and non-members of 8 categories
Kitchen utensils: SINK? SPONGE?
Vegetables: TOMATOES? GOURDS?

39. CATEGORIES AS CLUSTERS
CHICKEN
GOOSE
ORIOLE
ROBIN
Focus of the research in this area almost entirely on the ML side; we believe there is room for improvements on the REPRESENTATION side – and that work like that discussed at this conference can help
OSTRICH

40. PROTOTYPE THEORY
The dominant theory of concepts in Psychology, developed by E. Rosch and collaborators in the ’70s

41. Prototype theory Wittgenstein’s examination of game
Generally necessary that all games be amusing, not sufficient since many things are amusing
Board games, ball games, card games, etc. have different objectives, call on different skills and motor routines
- categories normally not definable in terms of necessary and sufficient features

42. Prototypes and Multidimensional Concept Spaces
A Concept is represented by a prototypical item = central tendency (e.g. location P below)
A new exemplar is classified based on its similarity to the prototype

43. Is this a “cat”?
Is this a “chair”?
Is this a “dog”?

44. PROTOTYPE THEORY IN A NUTSHELL
We store in memory feature-based representations of concepts
For each category of objects we have a PROTOTYPE
To decide if an object is a chair or an armchair we compute the distance between that object and the typical chair / armchair

45. Prototype theory in a nutshell
Certain members of a category are prototypical – or instantiate the prototype
Categories form around prototypes; new members added on basis of resemblance to prototype
No requirement that a property or set of properties be shared by all members
Features/attributes generally gradable
Category membership a matter of degree
Categories do not have clear boundaries

46. Prototype theory
Certain members of a category are prototypical – or instantiate the prototype
Category members are not all equal
a robin is a prototypical bird, but we may not want to say it is the prototype, rather it instantiates (manifests) the prototype or ideal -- it exhibits many of the features that the abstract prototype does
“It is conceivable that the prototype for dog will be unspecified for sex; yet each exemplar is necessarily either male or female.” (Taylor)

47. Prototypes and typicality Effects
is robin a bird?
is dog a mammal?
is diamond a precious stone?
atypical
is ostrich a bird?
is a whale a mammal?
is turquoise a precious stone?
slower verification times for atypical items

48. Prototype theory
Categories form around prototypes; new members can be added on the basis of resemblance to the prototype
Categories may also be extended on the basis of more peripheral features
house for apartment

49. Prototype theory
3. No requirement that a property or set of properties be shared by all members -- no criterial attributes
Category where a set of necessary and sufficient attributes can be found is the exception rather than the rule
Labov household dishes experiment
Necessary that cups be containers, not sufficient since many things are containers
Cups can’t be defined by material used, shape, presence of handles or function
Cups vs. bowls is graded and context dependent

50. Graded Structure P Typical items are similar to a prototype
Typicality effects are naturally predicted
atypical P
typical

51. Problem with Prototype Models
All information about individual exemplars is lost
category size
variability of the exemplars
correlations among attributes
(e.g., only small birds sing)
Variability of exemplars
Rulers and pizza example
Most pizzas are 12 inches wide but can vary from 2 to 30 inches
Most rulers are 12 inches across and can vary much less than pizzas
Experiment: when participants are asked whether a new object 19 inches wide is a pizza or a ruler, most participants said it probably corresponded to a pizza. A prototype theory cannot explain this finding because 19 inches is equally distant to both the pizza and ruler prototype (both 12 inches). However, in an exemplar theory, the 19 inch overlaps with more pizza exemplars because there are more pizza exemplars experienced (and represented in memory) that are around 19 inches wide.

52. Exemplar Models
category representation consists of storage of a number of category members
New exemplars are compared to known exemplars – most similar item will influence classification the most
dog ??
cat
dog
dog
cat
dog
cat

53. Exemplar Models Model can explain
Prototype classification effects
Prototype is similar to most exemplars from a category
Graded typicality
How many exemplars is new item similar to?
Effects of variability
Overall, compared to prototype models, exemplar models better explain data from categorization experiments (Storms et al., 2000)

54. THE BASIC LEVEL HYPOTHESIS
Recent psychological evidence also challenges the taxonomic view developed in work on ontologies in another respect:
Not all levels the same

55. Superordinate Basic Subordinate Superordinate level Furniture
Preferred level
BASIC LEVEL
Basic
Chair
Subordinate level
Subordinate
Windsor

56. SUPERORDINATE, BASIC, SUBORDINATE
ANIMAL
MAMMAL
FISH
DOG
DEER
TROUT
TUNA
TERRIER
LABRADOR

57. NOT ALL LEVELS ARE THE SAME
Brown (1958): parents would call a sheepdog DOG or DOGGIE rather than ANIMAL or SHEEPDOG
Rosch et al (1976):
Subjects name more attributes for basic concepts (PANTS) than for superordinate (CLOTHING) or subordinate (JEANS)
Subjects are faster at verifying that a picture was a TABLE than it was a PIECE OF FURNITURE of a KITCHEN TABLE

58. Basic Level and Expertise
Dog and bird experts identifying dogs and birds at different levels
Experts make subordinate as quickly as basic categorizations

59. Models of categorization: Classical vs Prototype / Exemplar
Classical model
Category membership determined on basis of essential features
Categories have clear boundaries
Category features are binary
Prototype model
Features that frequently co-occur lead to establishment of category
Categories are formed through experience with exemplars

60. (Image) Schemas
According to much research in child concept acquisition, children’s (and adults) conceptual knowledge is rooted into SCHEMAS
Regularities in our perceptual, motor and cognitive systems
Structure our experiences and interactions with the world.
May be grounded in a specific cognitive system, but are not situation-specific in their application (can apply to many domains of experience)
So where do image schemas fit into this?
--The idea is that there are regularities in our perceptual, motor and cognitive systems that structure our experiences and interactions in the world.
-- For spatial relations, these structural regularities are presumably the basis for semantic primitives. Image schemas describe these primitives, but in addition, primitive schemas can be combined to form more complex image schemas.
Image schemas are schematic in at least two ways
– though they may be grounded in a specific cognitive or perceptual system, they are not situation-specific in their application (i.e. can apply to many domains of experience, unlike many frames).
-- The entities that they apply to are only schematically specified, e.g. they do not apply only to specific shapes or types of objects.

61. Basis of Image schemas Perceptual systems Motor routines
Social Cognition
Image Schema properties depend on
Neural circuits
Interactions with the world
What sort of regularities are we talking about, and what is their basis?
Perceptual system: -- Visual system – edge-detecting and orientation-sensitive cells CHECK
-- Equilibrium – know orientation of head and body relative to gravity
-- Proprioceptic – we are sensitive to the changing tensions of muscles and tendons
-- We can sense contact and pressure on our skin
Motor routines, with their own structure often referred to as X-schemas [will hear more on this later in course]
Neural basis, e.g. generalization of input
-- different pathways in the brain – the so-called “what” and “where” pathways in the brain These may use different types of visual information (and for different purposes, e.g. object identification vs. location)
Interactions with the world -- affordances of objects, functional purpose of interaction (e.g motor control)
--Information from the primary visual cortex (located at the back of the head) is transmitted along two pathways -- the ventral stream to the temporal cortex (the so-called "what" system) and the dorsal stream to the parietal cortex (the "where" system).

62. Image schemas Trajector / Landmark (asymmetric)LM TR
Trajector / Landmark (asymmetric)
The bike is near the house
? The house is near the bike
Boundary / Bounded Region
a bounded region has a closed boundary
Topological Relations
Separation, Contact, Overlap, Inclusion, Surround
Orientation
Vertical (up/down), Horizontal (left/right, front/back)
Absolute (E, S, W, N)
bounded region
boundary

63. Boundary Schema Roles: Boundary Region A Region B Region A Region B
The idea here is that a continuous region of space can be divided into two sub-regions when there’s a difference in values for some property or properties.
In the drawing above, for example, the two regions are different colors, but we can differentiate areas on the basis of all sorts of properties, such as…???.
The three main roles of this schema have been labeled Boundary, Region A and Region B. In a full schema description we’d want to say more… we’d want to at least add the restriction that Region A is different from Region B in some perceivable way.
I’ve included drawings to help you understand the schemas, but a drawing always ends up specifying some things that aren’t actually specified by the schema. For example, the boundary here is shown as a straight line of a certain width and seems to be a separate object. But no separate boundary object need be present, nor does the boundary need to be of any particular shape.
Boundary

64. Bounded Region Roles: Boundary: closed Bounded Region
Background region
This is related to the Boundary schema, with the additional constraint that the boundary is a closed curve or surface.
Bounded objects are type of bounded region. They are perceived as a Figure, distinct from the surrounding background region.
Again though the drawing shows a circle, the bounded region could be of any shape.

65. Topological Relations
Separation
Two bounded regions or objects can have various topological relations. These relations don’t make distinctions about actual sizes, distances, or shapes., and stay constant under various kinds of deformations, e.g. stretching, twisting…
One such relation is separation -- no portion of either region, including the boundary, is immediately adjacent to or coincident with the other region. In the drawing here, each of the blue regions occupy different parts of space.
-- because the two regions are separate, they can be perceived as distinct entities even if they share all the same properties
-- separation is often bound to a proximal distal scale, allowing a distinction between objects which are very near to each other versus ones that are far apart.

66. Topological Relations
Separation
Contact
Contact is a relation where some portion of the boundary of each of the regions are immediately adjacent, with no space between them. But, the two regions – the blue region and the yellow region-- still occupy different parts of space.
-- When contact is perceived visually, it’s sometimes difficult to tell whether objects are actually contacting each other or whether they’re just very close to each other.
-- But for force, contact is more readily distinguished from proximity since the transmission of force generally requires actual contact rather than just close proximity. So, for example, when we sense that something is exerting pressure on our skin, contact is present.

67. Container Schema Roles: Interior: bounded region Exterior Boundary C
The container schema can be described in terms of the bounded region schema, with the roles:
…Interior, which is a bounded region
Exterior
Boundary
This schema basically represents containers as bounded regions in space, with no restrictions on the size or shape of this region.

68. Source-Path-Goal Constraints: initial = TR at Source
central = TR on Path
final = TR at Goal
To this point, the relations described have been static ones. But trajectors often move, and change location over time. The schema associated with moving Trajectors is the SPG
To represent this will need to add different time stages – initial, central final
And at each of these times the TR will be at a different location, e.g. TR starts at source, moves along Path and arrives at Goal.
Though the Path here is shown as straight, any shape is possible…
To make this meaningful, need to add one or more LMs in order to determine S P and/or G locations
Source
Path
Goal

69. SPG -- simple example She drove from the store to the gas station.
TR = she
Source = the store
Goal = the gas station
A very basic use of SPG
Basic inferences –
Initially she is closest to the store.
As time progresses, she is further to the store and closer to the gas station.
Once she is at the gas station, she has been at all the points on the path between the store and gas station.
The Source PathGoal schema, like the basic TR/LM schema, can combine with all sorts of other schemas….
Source
Path
Goal

70. SPG and Container She ran into the room.
SPG. Source ↔ Container.Exterior
SPG.Path ↔ Container.Portal
SPG. Goal ↔ Container.Interior
So for example, with SPG and container schema combined, can get She ran into the room.
The room is conceptualized as a container, with a boundary and an interior.
Initially, she is outside the room.
At the final state, she is in the room.
Somewhere in the central state, her path crossed the room boundaries (presumably through a door)

71. Language and Spatial Schemas
People say that they look up to some people, but look down on others because those we deem worthy of respect are somehow “above” us, and those we deem unworthy are somehow “beneath” us.
But why does respect run along a vertical axis (or any spatial axis, for that matter)? Much of our language is rich with such spatial talk.
Concrete actions such as a push or a lift clearly imply a vertical or horizontal motion, but so too can more abstract concepts.
Metaphors: Arguments can go “back and forth,” and hopes can get “too high.”

72. REFERENCES
E. Rosch & C. B. Mervis, Family resemblances. Cognitive Psychology, 7,
E. Rosch, C. B. Mervis, W. Gray, D. Johnson & P. Boyes-Braem, Basic objects in natural categories. Cognitive Psychology, 8,