COGS 100
Mental Model
Farhana Zulkernine
Key Points in Johnson-Laird & Byrne
• People are rational in principle but fallible in practice.
• There are three main classes of theory about the process of
deduction:
– formal rules,
– content-specific rules, and
– mental models.
• The formal rule account is psychologically implausible
because people are affected by the content of deductions.
• But the content-specific rules view ignores the fact that
people are able to make valid deductions based solely on
logical propositions and rules of reasoning.
• Mental models form the basis for various kinds of
reasoning.
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Language and Mental Models
• Language can be interpreted very differently
based on individual perception
– You generate a message that will create your
thoughts in the listener’s mind………
I have
something to
tell you…
What can it
be?...
Construct
your thought
Construct your
thought
Say it…
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Mental Models
• A mental model is a structure that stands for something
in the world which is used in mental processes.
• Humans form mental models from the semantic
interpretation of statements – what we hear and
understand.
– Therefore, mental models vary based on the
communication and the language.
– We pay more attention to whether the model ‘makes sense’
than whether ‘it is logical’ – good for language but bad for
logical inferences.
– Examples:
Visual: maps, images
 Abstract: from statements based on perception, e.g. Wason cards
 General: features, knowledge (all sumo players are strong)

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Mental Model Theory
• Philip Johnson-Laird (1992, 1999, 2007)
proposes that humans solve logic problems
using subjective models of the situation, rather
than a set of rules.
– Johnson-Laird and Byrne (1991) argue that
deductive reasoning is carried out neither by
formal logic nor by content-specific rules or
schemas but by mental models, which are mental
representations that correspond in structure to
the situations that they represent.
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Mental Model and Deductive Reasoning
• Why do we have problems with logic?
– The simple answer: because we have language….
– But why would language create problems with logic
problems?
– Because language allows us to create Mental models
of perceived information in our mind which are easier
to follow.
• Johnson-Laird’s claim about how mental models
work for deductive reasoning is that people
1. First generate an example to conform with argument
(reject as invalid if cannot be done)
2. Generate an alternative example and continue until
all possibilities are explored.
3. Hold all the examples in memory.
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Rule vs Model
• Rules always work and are easier for large tasks
but rules are difficult to learn and remember, and
get complex with ‘and-or’ and chaining of if-then.
• So we intuitively prefer models. But wrong
models can lead to error.
• Rule-based or proof theoretic inference uses
rules of reasoning to draw valid conclusions.
• Model-based or model theoretic inference draws
conclusion by generating examples to explore all
logical possibilities.
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Example: Rule vs Model
• What is the probability of a family with two
boys?
• Rule: p(B-B) = p(B) x p(B)
p(B-B) = 0.5 x 0.5 = 0.25
• Model: B – B; B – G; G – B; G – G
4 possibilities of which one is B-B
• p(B-B) = ¼ = 0.25
• Both representations give the same result. We
often use models to explain why rules work so
well.
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Example: Logic Problem
• Is this a valid conclusion? (logic problem)
1. If there is a King in your hand then there is an
Ace in your hand or else if there is a Queen in
your hand then there is an Ace in your hand.
2. There is a King in your hand.
3. Therefore, there is an Ace in your hand.
• What is your answer and why?
– Take a minute to think about the answer.
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Inference
Or
else
• Obviously there are two possibilities and both
have Aces .
Yes
• Valid conclusion?
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Inference
Or
else
• Obviously there are two possibilities and both
have Aces .
Yes
• Valid conclusion?
• The correct answer is ‘No’. Can you think
why?
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Example: Logic Problem
• Is this a valid conclusion? (logic problem)
1. If there is a King in your hand then there is an
Ace in your hand or else if there is a Queen in
your hand then there is an Ace in your hand.
2. There is a King in your hand.
3. Therefore, there is an Ace in your hand.
• What is your answer and why?
– Take a minute to think about the answer.
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Reasoning for the Correct Answer
• 99.9% fail to answer correctly because they
generate the mental models.
• But … this isn’t ordinary language; it’s the
language of logic and a simple “or else”
implies that one of the two propositions is
true. It does not say which one is true.
• Therefore, the conclusion cannot be ‘yes’.
• … and this surprised Johnson-Laird who was
sure the answer had to be “yes” …but it isn’t!
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The Wason Selection Task
Hard Version
Peter Cathcart
Wason in 1966
• Problem: There are some errors in the coding of the above
documents, and you need to find the errors. Each document has a
letter rating on one side and a numerical code on the other.
• Rule: "If a document has an E rating, it must be marked with code
4."
• Question: Here are four documents. Which document(s) do you
need to turn over to check for errors?
• What are your answers?
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The Wason Card Problem
• According to mental model theory, the rule “if a
card has an A on one side, then it has a 4 on the
other”, is used to construct
Mental model: [E] 4.
• This explains why many people make mistakes by
choosing cards that show E and 4 because they
choose cards that are explicitly represented in
their mental models for the given rule.
• Also for the same reason they fail to choose the
card showing 8.
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Q/A
• Explain what is a mental model based on
Johnson-Laird?
• Who are Johnson-Laird and Byrne and what
did they propose?
• What are some of the arguments in support of
the use of mental model?
• Give examples of the use of mental model in
problem solving or decision making.
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Reading
• Mental Model
http://mentalmodels.princeton.edu/about/whatare-mental-models/
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