Analogical thinking

Analogical Thinking

5

A Wise Man Once Said

Shore, Bradd. Culture in mind:
Cognition, culture, and the problem of
meaning. Oxford University Press,
USA, 1996.

Do you see something funny here?

“That’s a really small slice you have there.”

“Oh boy! That dinosaur exhibit was huge !”
“Yeah I guess you are right.”
“The referee made a terribly wrong decision.”
Why does green signal mean let’s go ahead with something? And why
does someone give you a red flag to warn about a potential danger?
“Lakoff, George, and Mark Johnson. Metaphors we live by. Vol. 111.
London: Chicago, 1980.”

What is an Analogy?
• It is not a mere numerical count of the number of features/attributes
which map from a source concept to a target concept.
• It is not a general account of relatedness.

“An analogy is an assertion that a relational
structure that normally applies in one
domain can be applied in another domain”

Preliminary Assumptions
• Domains and situations are a
system of objects, object Street Domain
MOTION(Vehicle
attributes and relations between , Stop)
objects
• Knowledge = Propositional
Network of nodes+predicates CAUSES[COLOR(Signal, Red),
Start
MOTION(Vehicle, Stop)]
• Attributes vs. Relations; First-
Order vs. Second-Order
Predicates MOTION(Vehicle
, Start)
• Representations mirror cognitive
constructs
Causal Relations

The next time your advisor Red Flags you…
Academic Domain
PROGRESS(Research, Halted)

RESULTS[PROGRESS(Research, Halted),
Stop RED_FLAG(Professor, Student)]

PROGRESS(Research, Smooth)

Diagnostic Relations

Structure Mapping: Interpretation Rules for Analogy
Class Hierarchy Analogy

A T(Target) is (like) a B(Base)

Vehicle
Target

Is-a Is like-a

Car Truck Base

Is this a meta-analogy?!

Let’s take an example
“…What light from yonder window breaks?/It is the east, and Juliet is the
sun!...”

I bet you would know this:

“Twinkle, twinkle little star,
How I wonder what you are
Up above the world so high,
Like a diamond in the sky.”

Rule 1: Discard Attributes of Objects
Star Diamond
• BRIGHTNESS: An absolute measure in • BRIGHTNESS
lumens. BRIGHTNESS(Star) = x lm
• DISTANCE: Distance from Earth (or some • RADIUS (?)
other referential celestial object).
DISTANCE(Star, Earth) = y x 10z km • CHEMICAL COMPOSITION: Cannot
obviously have a 1:1 match with a star
• LUMINOSITY. This is the amount of
energy generated in the star and released
as electromagnetic radiation. • TEMPERATURE
• RADIUS • Moh’s Scale of HARDNESS
• CHEMICAL COMPOSITION • COST
CARBON_CONTENT(Star) = k
NITROGEN_CONTENT(Star) = l
• VALUE AS GIFT
• TEMPERATURE

Rule 2: Preserve Relations Between Objects
Star Diamond
• Covered by several layers of thick, highly • Covered by several layers of thick, highly
carbon-dense gaseous layers. carbon-dense layers. SURROUNDS(Diamond,
SURROUNDS(Star, Carbon Layers) Carbon Layers)
• Appears to twinkle when viewed from a • Appears to twinkle when viewed from a
distance. APPEARANCE(Twinkles, Distance) distance. APPEARANCE(Twinkles, Distance)
• Twinkling is caused by multiple refractions of • Twinkling is caused by multiple refractions of
light in differently dense layers of the light in differently dense (solid) layers of the
atmosphere, eventually leading to total internal diamond, eventually leading to total internal
reflection. reflection.
1. CAUSES[SURROUNDS(Star, Carbon Layers), 1. CAUSES[SURROUNDS(Diamond, Carbon
MULTIPLE_REFRACTIONS(Light)] Layers), MULTIPLE_REFRACTIONS(Light)]
2. CAUSES[MULTIPLE_REFRACTIONS(Light), 2. CAUSES[MULTIPLE_REFRACTIONS(Light),
APPEARANCE(Twinkles, Distance)] APPEARANCE(Twinkles, Distance)]

Rule 3: The Systematicity Principle (aka more interesting = more appropriate)
[Isomorphism Constraint]

Noteworthy Points
• Rules are purely based on the structural representations of knowledge.
• Content plays a limited role.
• Need to express representations consistently across domains.
• Establishing “seemingly correct” relationships does NOT ensure an
instantiation of the concept mapping in the target.
• Technique can be used to generate hypotheses in a semi-automated
manner. No scope for verification of the hypothesis.
• Experiments/observations/methods exist for generating such
candidate relations for analogy mapping (e.g.., mass spectrometry in
the case of an atom to estimate weight of the nucleus and electrons)

Domain Comparisons – A Continuum of Categories
• Literal Similarity: A large subset
of attributes as well as relations
match between the source and
Analogy the target. “The sun is a star like
Attribute Matches the Alpha Centauri”.

few many • Analogy: There is a low attribute
match, but it is possible to
Abstraction establish a high relation match.
“The structure of the atom is
Relation Matches similar to the solar system”.

few many • Abstraction: Source and Target
concepts are not instantiated.
“The main driving force in an
atom is the centrifugal force of
rotation along a fixed orbit”.
Literal Similarity

Anomaly
Attribute Matches
“Twinkle, twinkle little star,
few many
How I wonder what you are
Up above the world so high, Relation Matches
Like an iPod Touch in the sky.” few many

• Hardly any (or no) attribute as
well as relational matches.
• “Totally unrelatable” Anomaly
• A conceptual fallacy if
assumed to be true. Its ABSURD!

Empirical Support of the Structure Mapping Theory

• Interpretation of rules = Meaning(Parti)
• Rules clearly demarcate the boundaries between
different categories of domain comparisons.
• Semantic relationships during the mapping process
are established syntactically (i.e., according to a well-
defined set of rules and a consistent notation)

Related Research
• Merlin System: Mechanism for viewing a target as a similar object to a
source. Involves explicitly comparing their shared and non-shared
predicates.
• Winston’s propositional representation: Perform an algorithm similar
to forward chaining to derive certain general (hidden) rules from
established analogies.
• Similar work by Gick & Holyoak: Constructing general schemas
representing the transformation in problem-solving techniques in
parallel to analogical matching.
• Theory of Analogical Shift Conjecture: Adapting the solution of a
problem in a different domain, to solve a “similar” problem in one’s
domain.

Analogical Shift Conjecture
Domain A Domain X
Problem
Statement

Select problem from X where
problem_type “LIKE” A.problem_type “Similar”
Abstraction
Problem

Abstracted Existing
Abstraction
Solution Solution

Solution to 1. Understand causal relations between domains
Adapt/Modify
Problem 2. A new relational model/data store required to
store sematic relations between objects

Analogical Mapping by Constrain Satisfaction

The Mapping Question
Components of Analogy
1. Selecting a “feasible” source
2. Mapping
3. Analogical Inference/Knowledge Transfer
4. Learning

• Correct conceptual mapping is central to the establishment of “meaningful”
analogies.
• Is there a common set of principles that govern mapping across different
domains?
• This cannot be established without taking into account goals and purposes of
the cognitive system.

Knowledge required depends on the type of analogy

Qualitative traits

1. Ruling Style
2. Control of the “parliament”
3. Popularity among people
Fidel Castro Daniel Ortega

Quantitative Results/Observations
Sugarcane production Sugarcane production
1. Temperature
2. Rainfall
3. Other relevant weather patterns

Cuba Nicaragua

A Constraint-Satisfaction Theory
•

ACME: A Cooperative Algorithm for Mapping
1. Governed by two principles of information
processing:
(a) Graceful degradation: As input degrades, output
should at least be partial (not non-existent).
(b) Least Commitment: Perform lazy updates. Do not
perform a mapping/update which may have to be
undone. (“If it ain’t broken don’t fix it).
2. It is co-operative in the sense that the algorithm can
be executed parallel in scenarios where the final
analogy can simply be represented as a composition of
the analogies of individual sub-units of the source and
target.
3. Supports two distinct types of queries:
(a) Cross-structure queries: Apply the inference from ACME Mapping Network. Combinatorial
one model to answer a question in the other. explosion of the states is prevented by
(b) Internal queries: Form a hypothesis of the source implementing correspondence
model from the target’s attributes. constraints.

Applications of ACME
AKA Functions served by Analogical Reasoning

1. Problem solving: Also in coming up with solutions to design problems in association
with a TRIZ-like approach (recall the laser surgery of cancer and the army attacking a
fort exercise).

2. Argumentation: Argue that the likelihood of two “similar” events is pretty close.
States/resources/objects true in one event are most probably true in the other.

3. Understand less familiar topics by drawing a parallel with more familiar ones (teaching
a KG kid laws of refraction from the nursery rhyme!)

4. Explain formal analogies and proofs in mathematics. (Mathematical Induction)

5. Use of metaphors to improve the aesthetic quality of language.

Scope for Improvement
1. Richer semantic information can be built automatically into the
constraint graph.

2. Allow for re-representations: Different propositions can be
established on the same set of predicates at different times or based
on the context of knowledge transfer.

3. Allow for m-to-n mapping. i.e., Allow relations from the source/target
to map to more than one relation of the other.

4. Flexible/dynamically modifiable set of constraints.

Objectives of the Presentation

Presenter should have fun presenting the content of the papers.

Content should be useful to the listeners.

Stimulating discussions emerge from the ideas of the paper.

? Listeners should have fun during the presentation.

Analogical thinking

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