Properties of a PDP model 1. Network of units with activation values. 2.Communication between units is through connections, each associated with a weight.

Properties of a PDP model1. Network of units with activation values.

2. Communication between units is through connections, each associated with a weight.

3. Mental states are represented as a pattern of activation over these units.

4. Encoding corresponds to changing weights.

5. Memory traces are represented by the weights.

6. Memory traces are distributed.-- Each memory trace involves many connections.-- Each connection participates in many traces.

7. Retrieval involves pattern completion.

==> Representations of covariation of intensional components.

Properties of a symbol processor1. Generality of purpose.

-- can follow any well-specified symbolic instruction.

2. Systematicity-- ability to encode and reason about certain facts implies the

ability to encode and reason about others.

3. Productivity-- ability to encode an unbounded number of propositions.

4. Hence, compositionality (combinatorial syntax and semantics).

5. Processing is sequential.==> Representations of extensional relations

Hybrids1. PDP models that encode limited kinds of compositional

structure• Mapping part-whole structure into distributed representations

(e.g., Hinton)• Tensor products (Smolensky)• Relational representations (Hummel & Holyoak)

2. Models with a PDP component and a symbolic component (e.g., MAC-FAC).

3. Structured stochastic models• Part-whole structure• Causal structure

The Data

1. Categorization: How we stick things into urns.

FAMILY RESEMBLANCENo features are common to ALL members of a category. Rather, some features are common to some members, other features to other members. Any two members will always have something in common (successive overlap).

Mother Daughter Daughter Son

Height Tall Medium Short Medium

Eyes Brown Blue Brown Green

Hair Brown Brown Blond Blond

Knees Knobby Straight Straight Knobby

Converging operational definitions of category typicality

1. Reliable typicality of exemplar ratings.2. Typical exemplars have greater family

resemblance.3. Typical exemplars are verified faster in real and

artificial categories.4. Typical exemplars are learned faster and earlier

by children.5. Typical exemplars are produced earlier and more

reliably by adults.

Converging operational definitions of category typicality

1. Reliable typicality of exemplar ratings.2. Typical exemplars have greater family

resemblance.3. Typical exemplars are verified faster in real and

artificial categories.4. Typical exemplars are learned faster and earlier

by children.5. Typical exemplars are produced earlier and more

reliably by adults.

Converging operational definitions of category typicality cont’d

6. Linguistic hedges apply differentially to typical and atypical exemplars:

A penguin is technically a bird. (good)A robin is technically a bird. (bad)A penguin is a bird par excellence. (bad)

7. American Sign Language superordinates are constructed by concatenating 3 typical exemplars.

e.g., fruit = {apple, orange, banana}8. Asymmetry in similarity judgments.

Theories of prototype effects• Prototypes are actual representations in the mind

i. Typical exemplar (clusters of correlated features)

ii. Central tendency

iii. Best exemplar• Prototypes are generated on the spot

i. We represent all and only exemplars (e.g., Medin & Schaffer, 1978).

ii. Prototypes are the stimulus that the system is most responsive to (PDP).

The anti-similarity reaction

• Murphy & Medin: categorization is not just similarity-based. – a wide range of coherent categories exist like

"children, money, photo albums, pets"

• Category and exemplar linked via an explanatory relation

Evidence for dual structure (Rips)

• Procedure:1. How big is the smallest pizza you've come across? How big is the largest quarter you've come across?

Calculate average (X).

2. "I'm thinking of something X inches in diameter." a. Is it a pizza or a quarter? b. Is it more similar to a pizza or a quarter?

• Result: Systematically different answer for a. and b. Knowledge about variability acts as a core feature.

Keil’s discovery paradigm

• Natural kinds (e.g., horse/cow) vs. Artifacts (e.g., key penny): objects with internal features from one category and external features from another. What are they?

Categorization: Conclusions

1. Strong evidence for similarity-based processing.

2. Strong evidence that similarity-based processing can be overridden by explanatory rules.

Judgment heuristics and some consequent biases

• Similarity: Representativeness. The probability that object A belongs to class B or originates from process B is evaluated by the degree to which A resembles B.

– some examples of the conjunction fallacy– misconceptions of chance– Law of Small Numbers (people expect samples from a

given population or process to be more similar to one another than sampling theory predicts, at least for small samples).

– stereotypes

Conjunction Fallacy Attributable to Representativeness

Linda is 38 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

– Linda is a bank teller. (T)

– Linda is a bank teller and is active in the feminist movement. (T&F)

Conjunction Rule: Pr{A} ≥ Pr{A & B}

Conjunction Fallacy: Cases where people's probability estimates violate the conjunction rule.

Sides, Osherson, Bonini, VialeAsked late in 1999: Which would you prefer to bet on:A tax cut will be passed by Congress between Jan. 1 and Mar. 31, 2000.

(A)A tax cut will be passed by Congress between Jan. 1 and Mar. 31, 2000

with the support of most Democrats. (A&B)

“Scratch one off. An independent judge … will determine which bets will be paid off (50 cents per question) based only on the sentence left legible...”

Results: 65% committed conjunction fallacy at least once out of two possible occasions.

==> Not meaning of “probability” or “and” and not because stakes aren’t real.

Simultaneous contradictory belief

Logic of evidence: the Müller-Lyer illusion.

Association: Availability

• People assess the frequency of a class or the probability of an event by the ease with which instances or occurrences can be brought to mind.

– some examples of the conjunction fallacy– more salient objects judged more frequent– highly imaginable events judged more

probable

Conjunction Fallacy Attributable to Availability

In four pages of a novel, how many words would you expect to find that have the form

_ _ _ _ i n g ?3:1 favor first.

_ _ _ _ _ n _ ?

==> Cues aid memory but constrain outcome space.

Monty Hall Problem

• mental model theory account

==> extensional vs. non-extensional judgment

==> outside vs. inside view of events

==> 2 systems of judgment

Attribute Substitution

• Kahneman & Frederick’s general description of heuristics

– People substitute easy questions for hard ones • wealth for happiness

– E.g., evaluate extensional property via intensional property

• probability by similarity• time by intensity• monetary value by outrage

Descartes vs. SpinozaGilbert

Are acceptance and rejection symmetric?

The Cartesian (canonical view): First, comprehension, then decision to accept or not.

Spinozan view: comprehension = acceptance. Rejection requires further step.

==> acceptance is associative, rejection requires rules.

Judgment: Conclusions

1. Strong evidence for similarity and memory-based processing.

2. Strong evidence that these processes can be overridden by deliberative processing (often taking normative rules into account).

Decision Making

Paul Slovic

Choose between

a. 7/36 win $9

b. $2

Choose between

c. 7/36 win $9 and 29/36 lose 25 cents.

d. $2

U. of Oregon students:

33.3%: a > b.

60.8%: c > d.

Hsee (1998)

Option A: 7 oz. of ice cream overflowing out of 5 oz. cup.

Option B: 8 oz. of ice cream buried in 10 oz. cup.

Two preference tasks:

Willingness to pay: A > B

Choice: B > A

Decision making: Conclusions

1. Strong evidence for “affect-based” preference based on perceptual processing when normative rule is opaque.

2. Strong evidence that these processes can be overridden by choice, which makes normative rule transparent.

Reasoning

Inclusion fallacy

Robins have an ulnar artery.

Therefore, birds have an ulnar artery.

Robins have an ulnar artery.

Therefore, ostriches have an ulnar artery.

Inclusion-similarity

All birds have an ulnar artery.

Therefore, all robins have an ulnar artery.

All birds have an ulnar artery.

Therefore, all penguins have an ulnar artery.

Conditional Reasoning -- Wason 4-card selection task

Imagine that you are shown a display of four cards. Each card has a letter on one side and a number on the other side.

AC

4 3

Rule: "If a card has a vowel on one side, then it has an even number on the other side.”

Please identify those cards that must be turned over to decisively determine whether the rule holds.

Evans (1982) -- dual mechanisms• Constructed a stochastic model of subjects' reasoning:

– subjects respond either on the basis of "interpretation" (symbolic logic) or "response bias" which in this case amounts to matching cards with elements of the rule (associatively).

• Choice probability for a given card = linear function of these two tendencies.==> model fits choice data closely.

Also qualitative evidence: stochastic independence between choices of the various cards in the abstract version==> different mechanisms responsible for choices of different cards: associative mechanism based on matching for the incorrect "4" card a rule-based (symbolic) one for the correct "3" card.

Implications1. Two components in human processing

(associative/System 1 and rule-based/System 2).

2. Components are independent– functionally: they can provide different responses to a

single reasoning problem; and– computationally: they perform different types of

computation.• The associative system provides quicker but less reliable

solutions than the symbolic system

3. Processing is simultaneous.

4. The rule-based system has priority in the sense that it is able to inhibit associative responses.

Associative System Rule-based System

Principles of operation

Similarity and contiguity Symbol manipulation

Source of knowledge

Personal experience Language, culture, and formal systems

Nature of representation

Basic Units

Relations

Concrete and generic concepts, images, stereotypes, and feature sets

(a) Associations

(b) Soft constraints

Concrete concepts, generic, and abstract concepts, abstracted features, compositional symbols(a) Causal, logical, and hierarchical(b) Hard constraints

Nature of processing

(a) Reproductive but capable of similarity-based generalization(b) Overall feature computation and constraint satisfaction(c) Automatic

(a) Productive and systematic(b) Abstraction of relevant features(c) Strategic

Illustrative

cognitive

functions

Intuition

Fantasy

Creativity

Imagination

Visual recognition

Associative memory

Deliberation

Explanation

Formal analysis

Verification

Ascription of

purpose

Strategic memory

Final Conclusions1. Don’t have to decide on a single formalism to describe

processing. Evidence suggests there’s more than one.

• Main function of rules to construct appropriate representations.

2. Two kinds of rationality (Evans and Over; Stanovich and West): contextual/pragmatic vs. analytic.

3. Like other people, researchers’ reasoning is only locally coherent. Before jumping on a representational bandwagon, try to situate yourself in a larger task context.