Project Groups

1
Project Groups

• Cognitive Modeling
• Fall 2003

2
Areas to consider

• Problem-solving
• Analogy
• Memory
• Attention
• Others?

3
Problem-solving

• Modeling problems with executive function (done
  last year)
• Tower of Hanoi task
• Geometry problems
• Mathematical problems
• Logic problems
• Many others
• Model ACT-R

4
Analogy

• Lots to choose from here
• Similarity comparisons
• Symmetry
• Metaphor (linguistic aspect?)
• Visual similarity
• Similarity and categorization
• Example project Analogy and constructivism

5
Memory

• New area for this course
• Retrieval
• Priming
• Other
• Models
• Shiffrin
• MAC/FAC (Gentner, Forbus Law)
• ACT-R

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Visual attention

• Preattentive factors
• Visual reasoning
• Interactions between attention and language
• Many, many others
• Models
• APEX/GOMS
• ACT-R
• Others?

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Feature-based models of representation

• Cognitive Modeling
• Fall 2003

8
Outline

• Features, symbols, and all that
• Computing with symbols
• Tverskys critique of MDS
• Tverskys contrast model
• Generativity of Contrast Model
• Basic level categories (Rosch)
• Salience imbalance model (Ortony)
• Do Cognitive Models Evolve?

9
Feature-based models Whats in a feature?

• Features, Symbols, Token/Types, Attributes,
  Keywords
• Intuition seems clears
• Still helpful to decompose assumptions behind
  features

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Pens and Chalk

• PEN
• Oblong
• Writing-instrument
• Marking-item
• Pointed
• Uses-ink
• Inexpensive
• Contains-cartridge
• Made-of-plastic

• CHALK
• Oblong
• Writing-instrument
• Marking-item
• Bipolar
• Made-of-chalk
• Inexpensive

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Pens and Chalk

• PEN
• Oblong
• Writing-instrument
• Marking-item
• Pointed
• Uses-ink
• Inexpensive
• Contains-cartridge
• Made-of-plastic

• CHALK
• Oblong
• Writing-instrument
• Marking-item
• Bipolar
• Made-of-chalk
• Inexpensive

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Advantages of feature sets

• Independence of features
• Can be manipulated via logical or set operations
• AND, OR, NOT, ?, ?.
• Divvies up conceptual space
• Keywords in library searches
• Canonicalization

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Problems with feature sets

• Assumption of independence isnt always true
• Some features cause others
• Some features are categorically related
• Some features are part of a closed set of
  alternatives
• MADE-OF-PLASTIC, MADE-OF-CHALK

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Symbols ? Words

• Attempt1
• above(A,B)
• Attempt2
• above(square-a,circle-b)
• Attempt 3
• above(a,b)
• square(a)
• circle(b)
• Symbol ROSE might or might not have same meaning
  as word Rose in English.

A
B
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Outline

• Features, symbols, and all that
• Computing with symbols
• Tverskys critique of MDS
• Tverskys contrast model
• Generativity of Contrast Model
• Basic level categories (Rosch)
• Salience imbalance model (Ortony)
• Do Cognitive Models Evolve?

16
Implementing symbols and feature matching

• The hard but efficient way
• Boolean vectors
• AND circuits
• The easy but inefficient way
• LISP symbol manipulation routines

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Pros/Cons of these approaches

• Very scalable
• Massively parallel
• Linear or constant time
• Thus neurologically plausible
• Cognition is both quick and massively parallel
• Hard to program complex systems
• Hard to add new knowledge
• Hard to interpret results
• Not very flexible
• For this, must turn to more intuitive system for
  handling symbols

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Symbols in Computer Languages

• Most languages have symbols
• Variable names LET X10
• Function names CALL CALC-SQUARE
• Not the same as strings
• LET FOOBAR Hello, World
• Symbols represent something specific, yet a
  symbol name is arbitrary from the programs
  perspective.
• Usually symbols are used rather than acted on in
  most languages
• Different than mostLISP!

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LISP

• LISt Processing language
• Lingua Franca of Artificial Intelligence
• Developed by John McCarthy at MIT during 50s and
  60s.
• Based on lambda calculus
• Since 1990s, an ANSI standard
• Object-oriented

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Writing LISP

• All functions (including built-in functions and
  added functions) are called using prefix
  notation
• Instead of F(x,y), use (F x y).
• (calc-square 20) gt 400
• ( 3 4 5) gt 12
• Function calls can contain other function calls
• (calc-square ( 3 4 5)) gt 144
• ( (calc-square 10) 15) gt 115

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Using symbols in Lisp

• Symbols and symbol lists are prefixed with
  quotes
• red
• (red white blue)
• Lisp handles symbol canonicality
• Strings Red and Red may not be equivalent
  (may be two separate copies).
• Strings red and red are always equivalent.
• Variables can point at symbols or lists of
  symbols
• (setq pencil-features (oblong
  writing-instrument marking-item))
• (setq chalk-features (oblong made-of-chalk
  dusty))

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Using symbols in Lisp

• (setq pencil-features (oblong writing-instrument
  marking-item))
• (setq chalk-features (oblong made-of-chalk
  dusty))
• (intersection pencil-features chalk-features)
• (oblong)
• (ldiff chalk-features pencil-features)
• (made-of-chalk dusty)

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Using symbols in Lisp

• Lisp provides a good language for manipulating
  symbols
• Key to AI programming
• Well cover more of Lisps abilities in future
  lectures
• Many basic knowledge representation structures
  (feature lists, association lists, frames) first
  implemented as list-based expressions in Lisp

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Summary Implementing symbols and feature-matching

• Lesson General complexity of feature and feature
  matching is quite low
• Good model for cognitive tasks that must be fast
  and handle lots of information (i.e., must
  scale).
• Often constant-time or linear complexity
• Actual implementations in symbolic languages
  still very fast, but do not scale as well
• Certainly not constant-time, often not linear
• Still, better for development purposes

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Outline

• Features, symbols, and all that
• Computing with symbols
• Tverskys critique of MDS
• Tverskys contrast model
• Generativity of Contrast Model
• Basic level categories (Rosch)
• Salience imbalance model (Ortony)
• Do Cognitive Models Evolve?

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Tverskys Axioms

• Minimality
• d(x,x) d(y,y) 0.
• Symmetry
• d(x,y) d(y,x).
• Triangle Inequality
• d(x,y)lt d(x,z)d(y,z)
• Tversky levels critique for each axiom

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Minimality

• d(x,x) d(y,y) 0.
• Everything is most similar (or proximate) to
  itself
• Each thing is as similar to itself as another
  item is similar to itself.
• Dog, Dog
• Freedom, Freedom
• George Washington, George Washington
• 1.23 , 1.23

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Problems with minimality

• Some things are more similar to themselves than
  others
• Example Cross-mapping experiment by Gentner
  Ratterman.

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Cross-Mapping Experiment (Gentner, Ratterman
Forbus 1993)
Sticker-finding task for 3, 4, 5 yr olds.
30
Younger children were aided by rich structure in
the literal similarity task.
Children were consistently worse on the
cross-mapping task for rich stimuli.
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Symmetry

• d(x,y) d(y,x).
• A is as similar to B as B is to A.
• d(Cuba, China) d(China, Cuba)
• d(butcher, surgeon) d(surgeon, butcher)
• Experiments
• Similarity of countries (Tversky)
• Similarity of good and bad forms (Tversky)
• Roschs A is essentially B study.

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Triangle Inequality

• d(x,y)lt d(x,z)d(y,z)
• d(atlanta,chicago) lt d(atlanta,indianapolis)
  d(indianapolis, chicago)
• d(goat,sheep) lt d(goat, pig) d(pig,
  sheep).

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Problems with Triangle Inequality

• Difficult to falsify, however
• s(watch,bracelet)s(watch,clock)gtgt s(bracelet,
  clock)
• s(box,barrel)s(box,toy-block) gtgt s(barrel,
  toy-block)

34
Outline

• Features, symbols, and all that
• Computing with symbols
• Tverskys critique of MDS
• Tverskys contrast model
• Generativity of Contrast Model
• Basic level categories (Rosch)
• Salience imbalance model (Ortony)
• Do Cognitive Models Evolve?

35
Tverskys Contrast Model
s(a,b) ?f(AB) ?f(A-B) ?f(B-A).
36
Does Tversky meet his own criticisms?

• Minimality
• Symmetry (or asymmetry)
• Triangle inequality

37
Additional characteristics of the Contrast Model

• Independence of features
• Conditions for symmetry/asymmetry in comparisons
• Distinction between difference and similarity
  judgments

38
Problems with feature sets

• Assumption of independence isnt always true
• Some features cause others
• Some features are categorically related
• Some features are part of a closed set of
  alternatives
• MADE-OF-PLASTIC, MADE-OF-CHALK

39
Pens and Chalk (redux)

• PEN
• Oblong
• Writing-instrument
• Marking-item
• Pointed
• Uses-ink
• Inexpensive
• Contains-cartridge
• Made-of-plastic

• CHALK
• Oblong
• Writing-instrument
• Marking-item
• Bipolar
• Made-of-chalk
• Inexpensive

40
Outline

• Features, symbols, and all that
• Computing with symbols
• Tverskys critique of MDS
• Tverskys contrast model
• Generativity of Contrast Model
• Basic level categories (Rosch)
• Salience imbalance model (Ortony)
• Do Cognitive Models Evolve?

41
Basic level categories
42
Ortonys Salience Imbalance metric

• Perhaps salience of features is not independence
• If features are salient in base but not in target
  domain, may lend metaphoricity to comparison
• Billboards are like placards.
• Billboards are like warts.
• This also lends greater explanatory power to
• That surgeon is a butcher.
• That butcher is a surgeon.

43
Roschs Basic-level categories

• Category Superordinate Basic Level
  Subordinate
• Musical inst. 1 8.3 8.7
• Fruit 3 8.3 9.5
• Tool 3 8.7 9.2
• Clothing 2 8.3 9.7
• Furniture 0 7.0 7.8
• Vehicle 1 11.7 16.8
• Table giving average number of shared features
  for each category item at the three category
  levels. From Rosch, et al., 1976. Table 2

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Evolution of representations for similarity
comparisons?

• MDS models
• One step above statistics
• Placement in an N-dimensional space
• Feature models (Contrast model)
• Instead of N-space, set of weighted features
• Salience imbalance
• Salience of features depends on context provided
  by object
• Salience imbalance indicates metaphoricity

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Next time Connectionist Networks