concepts and categories - open computing...
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Concepts and Categories
Lecture 21
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Learning, Perception, and Memory
Rely on Thinking
• Learning
– Classical Conditioning
• How can I predict some event?
– Instrumental Conditioning
• How can I control that event?
• Perception
– What is out there? Where is it? What is it doing?
• Memory
– What happened in the past?
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“Every act of perception
is an act of categorization”Bruner (1957) [paraphrase]
• Fundamental Cognitive Process
– Perceptual Identification...
• Of Individual Object
– Categorization...
• As Belonging in Same Class as Other Objects
• Categorical Knowledge is Part of Semantic
Memory
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Categories and Concepts
• Enumeration
• Rule
• Attributes
– Perceptual
– Functional
– Relational
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Classical View of CategorizationAristotle, Categories (in the Organon, 4th C. BCE)
Categories are Proper Sets
• Defining Features
– Singly Necessary
– Jointly Sufficient
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Defining Features
• Geometrical Figures
– Triangles
• 2 Dimensions, 3 Sides, and 3 Angles
– Quadrilaterals
• 2 Dimensions, 4 Sides, and 4 Angles
• Animals
– Birds
• Vertebrate, Warm-Blooded, Feathers, Wings
– Fish
• Vertebrate, Cold-Blooded, Scales, Fins
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Categories as Proper SetsAristotle, On Categories, etc.
• Defining Features
• Vertical Arrangement into Hierarchies
– Perfect Nesting
• Superordinate (Supersets)
• Subordinate (Subsets)
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Geometric Figures
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Subcategories of Triangles
• Classified by Length of Sides
– Equilateral
– Isosceles
– Scalene
• Classified by Internal Angles
– Right
– Oblique
• Obtuse
• Acute
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Subcategories of Quadrilaterals
• Trapeziums
• Trapezoids
• Parallelograms
– Rhomboids
• Rhombuses
– Rectangles
• Squares
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Biological TaxonomyLinnaeus (1758)
• Kingdom
• Phylum
• Class
• Order
• Family
• Genus
• Species
• Subspecies
• Animalia
• Chordata
• Mammalia
• Primates
• Hominidae
• Homo
• Sapiens
• Sapiens
Pioneer 10
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Categories as Proper SetsAristotle, On Categories, etc.
• Defining Features
• Vertical Arrangement into Hierarchies
• Horizontal Relations
– “All or None”
– Sharp Boundaries
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Geometrical Figures
Point Line Plane Solid
Triangle Quadrilateral (etc.)
Equilateral Isosceles Scalene Trapezium Trapezoid Parallelogram
Right Oblique
Acute Obtuse
Rhomboid Rectangle
Square Not-Square
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Categories as Proper SetsAristotle, On Categories, etc.
• Defining Features
• Vertical Arrangement into Hierarchies
• Horizontal Relations “All or None”
• Homogeneous Internal Structure
– All Instances Are Equally Good
• All Share Same Set of Defining Features
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QuadrilateralsWikipedia
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Algorithms for Categorization
• Defining a Category
– Determine Defining Features
• Shared by All Members
• Categorize an Object
– Analyze Features of Object
• Perception
– Retrieve Defining Features of Category
• Memory
– Match Object Features to Defining Features
• If Match, Assign Object to Category
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Problems with Classical View of
Categories as Proper Sets
• Disjunctive Categories
– Baseball Strike
• Swing and Miss
• Pitch in Strike Zone
• Foul Ball
• Called Strike
– Jazz
• Blues
• Swing (Standards)
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Problems with Classical View of
Categories as Proper Sets
• Disjunctive Categories
• Unclear Category Membership
– Is a Rug an Article of Furniture?
– Is a Pickle a Vegetable?
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Is a Tomato a Fruit or a Vegetable?Nix v. Hedden (1893)
• Tariff Act of 1883
– Duty on Vegetables “In Natural State”
– No Duty on Fruits
• Customs Collector for Port of New York
– Declared Tomatoes to be Vegetables
• International Tomato Cartel
– Sued, Took Case to US Supreme Court
• Justice Gray, for a Unanimous Court
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Problems with Classical View of
Categories as Proper Sets
• Disjunctive Categories
• Unclear Category Membership
• Difficult to Specify Defining Features
– Required to Define Category
– Required to Assign Category Membership
The Concept of GAME(Wittgenstein (1953)
Eyes of Santa Clara
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Problems with Classical View of
Categories as Proper Sets
• Disjunctive Categories
• Unclear Category Membership
• Difficult to Specify Defining
Features
• Imperfect Nesting
– “Tangled Hierarchy”
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Category VerificationSmith, Shoben, & Rips (1973)
0
0.25
0.5
0.75
1
1.25
1.5
1.75
Sparrow/Chicken Dog/Pig
Resp
on
se L
ate
ncy (
secs)
Bird/Mammal Animal
Animal
Sparrow
MammalBird
Chicken Dog Pig
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Problems with Classical View of
Categories as Proper Sets
• Disjunctive Categories
• Unclear Category Membership
• Difficult to Specify Defining Features
• Imperfect Nesting
• Variations in Typicality
– Birds: Sparrow vs. Chicken
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“Typicality” RatingsRosch (1975)
• Furniture
Chair, 1.10
Desk, 1.54
Rug, 5.0
Ashtray, 6.35
• Vegetable
Pea, 1.07
Corn, 1.55
Tomato, 2.23
Pickle, 4.57
• Bird
Sparrow, 1.18
Owl, 2.96
Chicken, 4.02
Penguin, 4.53• Fruit
Orange, 1.07
Cherry, 1.82
Pickle, 4.57
Tomato, 5.58
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“Typicality” RatingsArmstrong, Gleitman, & Gleitman (1983)
• Female
Mother, 1.7
Housewife, 2.4
Princess, 3.0
Policewoman, 3.9
• Plane Geometry Figure
Square, 1.3
Rectangle, 1.9
Circle, 2.1
Ellipse, 3.4
• Even Number
4, 1.1
10, 1.7
18, 2.6
106, 3.9
• Odd Number
3, 1.6
23, 2.4
501, 3.5
447, 3.7
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Typicality Effects in CategorizationSmith, Rips, & Shoben (1974)
400
450
500
550
600
650
700
High Medium Low
Resp
on
se L
ate
ncy (
msec)
Typicality
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Implications of Problems with
Classical View of Categories
• These problems would not occur if
categories were represented as proper
sets
• Therefore, people must do something
else when they induce concepts or
deduce category membership
• Apparently, concepts are not structured
like proper sets after all!
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“Prototype” View: Categories as Fuzzy SetsRosch (1975)
• No Defining Features
– Probabilistic Relationship
• Central vs. Peripheral
• Family Resemblance
• Category Based on Similarity to Prototype
– Many Features Central to Category Membership
– Few Features Central to Membership in
Contrasting Categories
• Permits Heterogeneity Within Category
– Typicality Effects
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Problems with
the Classical View of Categories
Solved by the Prototype ViewRosch & Mervis (1975); Rosch et al. (1976)
• Disjunctive Categories
• Unclear Category Membership
• Difficult to Specify Defining Features
• Imperfect Nesting
• Variations in Typicality
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Alternative “Exemplar” ViewMedin & Schaffer (1978)
• Abandons Features
– No Defining or Characteristic Features
• Concept as List of Members
– Salient Examples of Category
• Compare Object to List of Exemplars
– Categorization Still Based on Similarity
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Problems with SimilarityAfter Medin & Shoben (1988); see also Medin et al. (1993)
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gsx.com; madiganillustration.com
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The Theory (Knowledge-Based) ViewMurphy & Medin (1985); Murphy (2002)
Concept : Instance :: Theory : Data
• Instances Not Bound Together by Similarity
– At Very Least, “Similarity” is Flexible
– Categorization Explains Similarity Judgments
• Concepts Organized by Theory of Domain
– “Explanatory Relationship” Between Concept, Instance
• Categorization Based on Knowledge, Not Similarity
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Implications of Categorization
• Logically, Categories are Structured as Proper Sets
– Represented by Defining Features
• Psychologically, Categories are Structured as “Fuzzy” Sets
– Represented by Prototypes, Exemplars
– Representations Differ by Expertise
• Principles of Reasoning Do Not Necessarily Follow the Principles of Formal Logic
– Cannot be Discovered by Reason Alone