Reasoning

1
Reasoning Problem Solving

• Models of Inductive Reasoning

2
Types of Arguments

• Socrates is a man.
• All men are mortal.
• Socrates is mortal.
• Mice have blood enzyme X.
• Rats have blood enzyme X.
• All rodents have blood enzyme X.

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Item 1

• 1a Cats have blood protein A.
• Foxes have blood protein A.
• 1b Dogs have blood protein A.
• Foxes have blood protein A.

4
Item 2

• 2a Robins have ileated bones.
• All birds have ileated bones.
• 2b Penguins have ileated bones.
• All birds have ilieated bones.

5
Item 3

• 3a Hawks have digestive enzyme Y.
• Robins have digestive enzyme Y.
• All birds have digestive enzyme Y.
• 3b Sparrows have digestive enzyme Y.
• Robins have digestive enzyme Y.
• All birds have digestive enzyme Y.

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Outline Inductive Reasoning

• Conclusion not necessarily true given premises.
• Premises provide stronger or weaker support for
  conclusion. Generalization.
• Inductive Phenomena
• Premise-Conclusion Similarity
• Premise Typicality
• Premise Diversity
• Models of Induction
• Similarity-Coverage Model
• Feature-Based Model
• Hypothesis-Assessment Model

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Similarity-Coverage Model

• Similarity-Coverage Model (Osherson et al.)
• Inductive strength derives from perceived
  similarities among relevant categories.
• Two mechanisms
• Similarity Principle How alike are the relevant
  categories?
• Coverage Principle To what degree are categories
  similar to other categories within the
  superordinate?
• Important based on comparison of categories.

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Inductive Phenomena Similarity

• 1a Cats have blood protein A.
• Foxes have blood protein A.
• 1b Dogs have blood protein A.
• Foxes have blood protein A.

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Cat
Fox
Dog
10
Cat
Fox
Dog
11
Cat
Fox
Dog
12
Inductive Phenomena Similarity

• 1a Cats have blood protein A.
• Foxes have blood protein A.
• 1b Dogs have blood protein A.
• Foxes have blood protein A.
• The more similar the premise category is to the
  conclusion category, the stronger the inference.
• Mechanism Similarity

13
Inductive Phenomena Typicality

• 2a Robins have ileated bones.
• All birds have ileated bones.
• 2b Penguins have ileated bones.
• All birds have ilieated bones.

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Owl
Hawk
Penguin
Eagle
Blue Jay
Cardinal
Robin
Chickadee
Sparrow
Duck
Goose
15
Owl
Hawk
Penguin
Eagle
Blue Jay
Cardinal
Robin
Chickadee
Sparrow
Duck
Goose
16
Owl
Hawk
Penguin
Eagle
Blue Jay
Cardinal
Robin
Chickadee
Sparrow
Duck
Goose
17
Inductive Phenomena Typicality

• 2a Robins have ileated bones.
• All birds have ileated bones.
• 2b Penguins have ileated bones.
• All birds have ilieated bones.
• The more typical the premise category, the
  stronger the inference to an inclusive category.
• Mechanism Coverage

18
Inductive Phenomena Diversity

• 3a Hawks have digestive enzyme Y.
• Robins have digestive enzyme Y.
• All birds have digestive enzyme Y.
• 3b Sparrows have digestive enzyme Y.
• Robins have digestive enzyme Y.
• All birds have digestive enzyme Y.

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Owl
Hawk
Penguin
Eagle
Blue Jay
Cardinal
Robin
Chickadee
Sparrow
Duck
Goose
20
Owl
Hawk
Penguin
Eagle
Blue Jay
Cardinal
Robin
Chickadee
Sparrow
Duck
Goose
21
Owl
Hawk
Penguin
Eagle
Blue Jay
Cardinal
Robin
Chickadee
Sparrow
Duck
Goose
22
Owl
Hawk
Penguin
Eagle
Blue Jay
Cardinal
Robin
Chickadee
Sparrow
Duck
Goose
23
Owl
Hawk
Penguin
Eagle
Blue Jay
Cardinal
Robin
Chickadee
Sparrow
Duck
Goose
24
Inductive Phenomena Diversity

• 3a Hawks have digestive enzyme Y.
• Robins have digestive enzyme Y.
• All birds have digestive enzyme Y.
• 3b Sparrows have digestive enzyme Y.
• Robins have digestive enzyme Y.
• All birds have digestive enzyme Y.
• The more premise categories differ from each
  other, the stronger the inference.
• Mechanism Coverage

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Summary SCM

• P-C Similarity - Similarity Principle
• P Typicality, P Diversity - Coverage Principle
• Comparison of categories

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Feature-Based Induction Model

• Sloman (1993)
• Inductive strength is a function of the
  similarity between relevant concepts.
• One Mechanism
• Similarity and coverage are calculated solely on
  the basis of shared features.
• Direct comparison of premises and conclusion.
• No need to calculate similarity to other members
  of immediate superordinate.

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Inductive Phenomena Similarity

• 1a Cats have blood protein A.
• Foxes have blood protein A.
• 1b Dogs have blood protein A.
• Foxes have blood protein A.
• The more similar the premise category is to the
  conclusion category, the stronger the inference.
• Mechanism Feature comparison

28
Inductive Phenomena Typicality

• 2a Robins have ileated bones.
• All birds have ileated bones.
• 2b Penguins have ileated bones.
• All birds have ilieated bones.
• The more typical the premise category, the
  stronger the inference to an inclusive category.
• Mechanism Feature comparison

29
Inductive Phenomena Diversity

• 3a Hawks have digestive enzyme Y.
• Robins have digestive enzyme Y.
• All birds have digestive enzyme Y.
• 3b Sparrows have digestive enzyme Y.
• Robins have digestive enzyme Y.
• All birds have digestive enzyme Y.
• The more premise categories differ from each
  other, the stronger the inference.
• Mechanism Feature comparison

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Summary FBIM

• P-C Similarity, P Typicality, P Diversity -
  direct feature comparison

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Hypothesis-Assessment Model

• Blank Properties Properties about which Ps have
  no specific prior expectations.
• Good Allow researchers to isolate effects of
  concepts on inductive reasoning.
• Bad Might miss much of the action.
• McDonald et al.
• Categories are embedded in coherent theories of
  the world
• Premises Evidence
• Conclusion Hypothesis

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Hypothesis-Assessment Model

• Argument strength is a function of
• Assessment of the confirming value of each piece
  of available evidence,
• The scope of the conclusion,
• The number of competing hypotheses that come to
  mind.
• Emphasizes that knowledge informs induction.

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Inductive Phenomena Typicality

• 2a Robins have ileated bones.
• All birds have ileated bones.
• 2b Penguins have ileated bones.
• All birds have ilieated bones.
• First argument
• Premise provides better evidence for conclusion.
• Generates fewer alternatives.

34
Inductive Phenomena Diversity

• 3a Hawks have digestive enzyme Y.
• Robins have digestive enzyme Y.
• All birds have digestive enzyme Y.
• 3b Sparrows have digestive enzyme Y.
• Robins have digestive enzyme Y.
• All birds have digestive enzyme Y.
• Second argument
• Premise provides better evidence for conclusion.
• Generates fewer alternatives.

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Differential Predictions

• 4a Grass contains vitamin Q.
• Cows contain vitamin Q.
• 4b Grass contains vitamin Q.
• Oaks contain vitamin Q.

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Differential Predictions

• 5 Birds have protein B.
• Robins have protein B.

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Summary

• Inductive reasoning generalization
• Similarity-Coverage Model
• Similarity, Coverage
• Comparison of categories
• Feature-based Induction Model
• Similarity
• Comparison of features
• Hypothesis-Assessment Model
• Value of evidence, competing hypotheses
• Real-world knowledge