Analogical Reasoning

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Analogical Reasoning
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Types of reasoning

• Content free reasoning
• Deductive reasoning
• Reasoning by similarity
• Inductive reasoning
• Analogical reasoning
• analogical transfer solving problem in one
  domain based on solution in another domain
• Analogical inference generalizing
  properties/relations from one domain to another

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Analogical transfer

• Reason from base problem (previously solved) to
  target problem
• Recognition identify a potential analog
• Abstraction abstract general principle from base
  problem
• Mapping apply principle to target

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Radiation Problem

• Problem
• Patient has an abdominal tumor (in center of
  body)
• Radiation will kill tumor
• But rays strong enough to kill tumor will also
  destroy healthy tissue that rays pass through on
  way to tumor
• Solution?

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Solution
INCORRECT
CORRECT
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Gick Holyoak (1980)
Only 20 solved it Participants were more likely
to solve the problem if they were given an
analogy.
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Fortress Problem

• Army general wants to attack a fortress in center
  of forest.
• Many roads lead to fortress like spokes of a
  wagon wheel.
• All the roads have land mines that are triggered
  by heavy traffic.
• If entire army travels down a road, land mines
  will go off.
• Solution?

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Solution

• The general sends small groups of soldiers down
  each of the roads, co-ordinating their movements
  so that they all arrive at the fortress at the
  same time.

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Structural Similarities
Fortress Problem Radiation Problem Fortress
?? Tumor Mined Roads ?? Surrounding
tissue Attacking troops ?? Rays varying in
intensity Small groups of troops Converging on
fortress ?? Weak rays focused on tumor
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Recognition Process

• Radiation problem hard problem
• Preceded by Fortress problem, 20 solved it
• If given hint that problems are related, 92
  solved it
• Subjects do not produce corresponding solutions
  with any great frequency unless given a hint
• These results demonstrate the difficulty of
  recognizing the relevance of one problem and its
  solution to another

Gick Holyoak (1980)
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Transfer aspects of fortress problemto radiation
problem

• Fortress problem was given with three different
  solutions
• Dispersion the generals army approaching the
  fort from several roads at once.
• Tunnel a general digging a tunnel to the fort
• Open-route a general attacking the fort via a
  supply route

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Problem Solutions
Solutions to the Radiation problem fell into
three main categories
The DISPERSION solution, in which small doses of
radiation are aimed at the tumor from different
directions so that the radiation accumulates and
destroys the tumorous tissue
The TUNNEL solution, in which an incision is made
which leaves the tumor in place but which allows
direct delivery of radiation.
The OPEN-ROUTE solution, in which radiation is
delivered to the tumor through the esophagus
(tube leading from the throat to the stomach)
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Distribution () of Solutions
What do the results show?
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Abstraction Process

• Does performance improve if principle of base
  problem is stated? No
• Showing diagrams helps? No
• Showing multiple problems with related solutions
  helps? Yes

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Analogical Inference

• An atom is like the solar system

TARGET BASE
Knowledge about the base domain can be used to
reason about the target domain. Structure mapping
theory is a theory for how this could work.
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Structure Mapping Theory(Dedre Gentner, 83, 89)

• Theory on how to interpret an analogy
• 1) set up correspondences
• 2) focus on matches of relations, not attributes
• 3) focus on higher-order relations
• 4) extend knowledge about target by mapping
  relations from source to target

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ALIGN RELATIONS
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BASED ON ALIGNED RELATIONS, ALIGN OBJECTS
the nucleus is like the sun
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Mental Models

• Knowledge structure used to understand how
  objects and physical processes work
• Sometimes, mental models are based on poor
  analogies and can lead to incorrect predictons
• Example thermostats. How to heat up a room
  quickly?

Current temp.
Desired temp.
50 60 70 80
OR?
Kempton, 86
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• if you said 80, what might your mental model
  be based on?

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Childrens Mental Models
there are two earths, one is flat, the other is
a sphere out in space

• Children were told facts
• Columbus sailed around the earth
• Shown space photographs
• What is their Conception of earth given these
  facts?

Nussbaum 79
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Intuitive Physics
Kaiser, McClosky Profitt 86

• Intuitive physics is based on naive mental models
  of physical processes
• The diagram shows a curved tube, lying flat on a
  table. A ball is shot into the opening and out
  the other end. What is the balls path after it
  shoots out the tube?

?
OR
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Results
Kaiser, McClosky Profitt 86
(The C-curve problem is the same but shows just
the C part of the spiral)
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Explanation by Kaiser et al.

• Grade school children start constructing theories
  of motion
• Theories of persistence of motion an object
  persists in the way it is moving, unless there is
  friction. E.g., bouncing ball continues to
  bounce
• Theory is wrongly applied to spiral problem
  overgeneralization

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Intuitive Physics with a set of gears
What is the direction of this gear?
Suppose we swing this gear in this direction
Schwartz Black, 1999
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?
Suppose we swing this gear in this direction
Schwartz Black, 1999
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HINT
?
Suppose we swing this gear in this direction
Schwartz Black, 1999
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Time A
Time B
Path Z
Path X
Path Y
From McCloskey, 1983
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• Mental models might be initially be based on
  perceptual simulations (e.g., turning the gears
  in your mind)
• After training, these models might shift to more
  abstract rules to solve problems