Reasoning and Decision Making
• Five general strategies
• Reasoning and Logic
• Two hypotheses
– inherently logical
– logic must be learned
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Reasoning and Decision Making
• Evidence
– categorical syllogisms
• sources of error
– conditional reasoning
• sources of error
• Bounded rationality
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Five General Strategies
• Prototype matching
– is an instance a member of a category
• Representativeness heuristic
– intuitive predictions
– stereotypes
– e.g. Is the man, with the glasses and tweed jacket who is reading a book at
the lunch table, a truck driver or a college professor?
– base rate probabilities
• Simulation heuristic
– imagine a mental model
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Five General Strategies
• Reasoning by analogy
– similarity to past experiences or problems
– problem of distinguishing valid from invalid analogies
• Availability heuristic
– frequency versus vividness of examples
– examplar search
• look for counter examples
– how easily does an example come to mind
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Reasoning and Logic
• Reasoning
– the thinking involved in determining whether one proposition logically follows
from another
– attempts to determine the validity of an argument or idea
• Formal Logic
– specify rules of inference that yield valid arguments
– validity is independent of content (truth value)
– how we “ought” to reason
• How do we “actually” reason?
– Do the rules of formal logic describe actual behavior or do they require
careful training?
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Two Hypotheses
• Information processing stages of reasoning
– Stage one - encode a representation in working memory
– Stage two - retrieve set of rules to check logic
• Humans are inherently logical
– LTM contains a set of rules of inference equal to formal logic
– when people make errors it is because:
• encode problem incorrectly
• fail to use inference rules and respond on some other basis
• Humans are not inherently logical
– LTM has no logic rules unless formally trained
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Two Hypotheses
• Evaluate the hypotheses based on evidence from two
types of reasoning
– categorical syllogisms
– e.g. All M are P
• All S are M
• therefore All S are P
– conditional reasoning
– e.g. If P, then Q
• P
• therefore Q
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Categorical Syllogisms
• Consist of a major and minor proposition (premise)
followed by a conclusion
• A valid syllogism is one in which the conclusion
necessarily follows logically from the premises
• There are four possible figures
M-P
P-M
M-P
P-M
S-M
S-M
M-S
M-S
S-P
S-P
S-P
S-P
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Categorical Syllogisms
• There are four possible moods
–
–
–
–
affirmative-universal
negative-universal
affirmative-particular
negative-particular
e.g. All S are P
e.g. No S are P
e.g. Some S are P
e.g. Some S are not P
• There are a total of 256 possible configurations
– only 24 of these are valid !
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Sources of Error in Categorical Syllogisms
• Atmosphere effect
– respond to the mood of the premises
– whenever at least one premise is negative (particular) then the conclusion
chosen tends to be negative (particular)
– irrational - not use logic rules just maintain mood (heuristic)
– generally true for the valid but can lead to invalid results
• Content
– especially with emotionally laden premises and conclusions
– based on believability of conclusion
– use biases and prior belief
All scientists are honest
All women are scientists
therefore: All women are honest
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Sources of Error in Categorical Syllogisms
• Failure to accept the logical task
– logic is theoretical NOT empirical
– must ignore the truth value of each premise
– error in encoding the nature of the problem
• subjects evaluate the truth not the logic
– e.g. Kpelle rice farmers
– e.g. children
– evidence that education may teach us “when” to reason
• Failure to discriminate information given in the premise
from information retrieved from LTM
– unintentionally supplement
– e.g. when premise is “Some men are honest”; add “but not all”
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Sources of Error in Categorical Syllogisms
• Incorrect conversion of premises
–
–
–
–
–
assumptions of symmetry
e.g. All A are B does not mean All B are A
real world examples help block incorrect conversions
e.g. All dogs are animals is not converted to All animals are dogs
real world examples may be biased by beliefs e.g. All republicans are rich
may convert to All rich people are republicans if you believe this
• Forgetting premises
– three types of common recall errors
• omit a premise
• displace terms from one premise to next
• change quantifiers (some to all)
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Conditional Reasoning
• Two parts
– statement of the condition rule
• if the first proposition is true then the second is true
– statement of the truth value of one of the propositions
– e.g.
If the world was flat, then you could fall off the edge
You fell of the edge
Therefore ?
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Conditional Reasoning
Form
If p, then q
p
therefore q
Name
Example
modus ponens
(valid)
If the objects is square, then it is blue
The object is square
The object is blue
If p, then q
modus tollendo
Not q
tollens (valid)
Therefore not p
If the objects is square, then it is blue
The object is not blue
The object is not square
If p, then q
denying the
Not p
antecedent
Therefore not q (invalid)
If the objects is square, then it is blue
The object is not blue
The object is not blue
If p, then q
Q
Therefore p
If the objects is square, then it is blue
The object is blue
The object is square
affirming the
consequent
(invalid)
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Sources of Errors in Conditional Reasoning
• Negatives
– people have trouble tracing the implications of negation
– make more errors when a “not” is present
• modus tollens and denying the antecedent
• Confirmation bias
–
–
–
–
bias to seek answers (evidence ) that confirms supports rather than denies
problem in scientific hypothesis testing
stereotypes and prejudice
e.g. given 2, 4, 6, 8
• generate sequences and guess the rule
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Sources of Errors in Conditional Reasoning
• Confirmation bias continued
– whenever we have an hypothesis (belief, prejudice) we seek confirmations
not disconfirmations
– one piece of disconfirmatory evidence is much more informative than several
confirmatory pieces of evidence
– problem: scientists have a confirmatory bias which interferes with progress
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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Bounded Rationality
• Human may be inherently capable of logic
• However
–
–
–
–
–
use heuristics
not always accept logical task
processing and memory errors
problems with negatives
“cruising” or “mindlessness” not use our capacity
Cognitive - reasoning.ppt © 2001 Laura Snodgrass, Ph.D.
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