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Analogical Reasoning
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Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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Page 1: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Analogical Reasoning

Page 2: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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

Page 3: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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

Page 4: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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?

Page 5: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Solution

INCORRECT CORRECT

Page 6: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Gick & Holyoak (1980)

Only 20% solved it

Participants were more likely to solve the problem if they were given an analogy.

Page 7: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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?

Page 8: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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.

Page 9: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Structural Similarities

Fortress Problem Radiation Problem

Fortress TumorMined Roads Surrounding tissueAttacking troops Rays varying in

intensity

Small groups of troopsConverging on fortress Weak rays focused

on tumor

Page 10: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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)

Page 11: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Transfer aspects of fortress problemto radiation problem

• Fortress problem was given with three different solutions: – Dispersion: the general’s 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

Page 12: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Problem Solutions

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;

Solutions to the Radiation problem fell into three main categories:

The OPEN-ROUTE solution, in which radiation is delivered to the tumor through the esophagus (tube leading from the throat to the stomach);

The TUNNEL solution, in which an incision is made which leaves the tumor in place but which allows direct delivery of radiation.

Page 13: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Distribution (%) of Solutions

What do the results show?

Page 14: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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

Page 15: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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.

Page 16: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:
Page 17: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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

Page 18: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

ALIGN RELATIONS

Page 19: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

BASED ON ALIGNED

RELATIONS,ALIGN OBJECTS

“the nucleus is like the

sun”

Page 20: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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?

| | 50 | | 60 | | 70 | | 80 | |

Current temp. Desired temp.

OR?Kempton, ‘86

Page 21: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

if you said “80”, what might your mental model be based on?

Page 22: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Children’s Mental Models

• Children were told facts:– Columbus

sailed around the earth

– Shown space photographs

• What is their Conception of earth given these facts?

Nussbaum ‘79

“there are two earths, one is flat, the other is a sphere out in space”

Page 23: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Intuitive Physics

• 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 ball’s path after it shoots out the tube?

Kaiser, McClosky & Profitt ‘86

OR?

Page 24: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

ResultsKaiser, McClosky & Profitt ‘86

(The C-curve problem is the same but shows just the C part of the spiral)

Page 25: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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

Page 26: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Intuitive Physics with a set of gears

Schwartz & Black, 1999

Suppose we swing this gear in this

direction

What is the direction of this gear?

Page 27: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Schwartz & Black, 1999

Suppose we swing this gear in this

direction

?

Page 28: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Schwartz & Black, 1999

Suppose we swing this gear in this

direction

?HINT:

Page 29: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

Time A Time B

Path XPath Y

Path Z

From McCloskey, 1983

Page 30: Analogical Reasoning. Types of reasoning Content free reasoning: –Deductive reasoning Reasoning by similarity –Inductive reasoning –Analogical reasoning:

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