09 analogical-learning

© 2002, G.Tecuci, Learning Agents Laboratory
Learning Agents Laboratory
Computer Science Department
George Mason University
Prof. Gheorghe Tecuci
Learning by analogy

Overview
Learning by analogy: definition
Design issues
The structure mapping theory
Problem solving by analogy
Determinations
Recommended reading
Exercises

Learning by analogy: definition
Learning by analogy means acquiring new knowledge about
an input entity by transferring it from a known similar entity.
Which is the central intuition supporting the learning by
analogy paradigm?
Qa=3 Qb=9
Qc=?
Simple Hydraulics Problem
I1 I2
I3=I1+I2
Kirchoff's First Law
One may infer, by analogy, that hydraulics laws are similar to
Kirchoff's laws, and Ohm's law.

Discussion
Central intuition supporting learning by analogy:
If two entities are similar in some respects then they
could be similar in other respects as well.
Examples of analogies:
Pressure Drop is like Voltage Drop
A variable in a programming language is like a box.
Provide other examples of analogies.

Learning by analogy: illustration
sun
planet
yellow
mass
mass
temperature
greater
color
revolves-
around
attracts
Tsun
Tplanet
Msun
Mplanet
causes
temperature
greater
mass
mass
revolves-
around
attracts
Mnucleus
causes ?greater
nucleus
electron
Melectron
sun
planet
yellow
mass
mass
temperature
greater
color
revolves-
around
attracts
Tsun
Tplanet
Msun
Mplanet
causes
temperature
greater
mass
mass
revolves-
around
attracts
Mnucleus
causes ?greater
nucleus
electron
Melectron
Illustration: The hydrogen atom is like our solar system.
The Sun has a greater mass than the Earth and attracts it, causing the Earth to
revolve around the Sun. The nucleus also has a greater mass then the electron and
attracts it.Therefore it is plausible that the electron also revolves around the nucleus.

Learning by analogy: the learning problem
Given:
• A partially known target entity T and a goal concerning it.
• Background knowledge containing known entities.
Find:
• New knowledge about T obtained from a source entity S belonging
to the background knowledge.
Partially understood structure of the hydrogen atom under study.
Knowledge from different domains, including astronomy, geography, etc.
In a hydrogen atom the electron revolves around the nucleus, in a
similar way in which a planet revolves around the sun.

Learning by analogy: the learning method
• ACCESS: find a known entity that is analogous with the input entity.
• MATCHING: match the two entities and hypothesize knowledge.
• EVALUATION: test the hypotheses.
• LEARNING: store or generalize the new knowledge.
Store that, in a hydrogen atom, the electron revolves around the
nucleus. By generalization from the solar system and the hydrogen
atom, learn the abstract concept that a central force can cause
revolution.
In the Rutherford’s analogy the access is no longer necessary because
the source entity is already given (the solar system).
One may map the nucleus to the sun and the electron to the planet,
allowing one to infer that the electron revolves around the nucleus
because the nucleus attracts the electron and the mass of the nucleus is
greater than the mass of the electron.
A specially designed experiment shows that indeed the electron
revolves around the nucleus.

Discussion
How does analogy help?
Why not just study the structure of the hydrogen atom to
discover that new knowledge?
We anyway need to perform an experiment to test that
the electron revolves around the hydrogen atom.

Learning by analogy: Design issues
• ACCESS: find a known entity that is analogous with the input entity.
• MATCHING: match the two entities and hypothesize knowledge.
• EVALUATION: test the hypotheses.
• LEARNING: store or generalize the new knowledge.
How to learn?
Given a target, how to identify a few potential sources in a very large
storage?
Given a potential source, how to identify the knowledge to hypothesize?
Why and how to test the hypothesized knowledge?

Learning by analogy: Formalization
Given:
- a target entity T;
- a universe of potential sources U;
- an access function f1 with a threshold value φ1;
- a matching function f2 with a threshold value φ2.
Find:
- new knowledge about T (using analogical learning).

Learning by analogy: Access
Find potential sources for T in U :
f1(Sk, T) > φ1
This should result in S1, … , Sn

Learning by analogy: Matching
Find the best match between one of S1, …, Sn and T.
Let: Sk = A & B & C, T = A' & D
where f2(Sk, T) > φ2 gives the best match.
A and A' are the parts of Sk and T that make them analogous:
f2(Sk, T) = f2(A, A')
B, C and D are the other parts of Sk and T.
As a side effect of partially matching Sk with T (or totally matching A with A'),
one obtains a correspondence (substitution) list σ = ( o1 ← o1', ... , on ← on')
where oi is an element of A and oi' is the corresponding element from A'.
By applying the substitution σ to Sk one obtains:
σ(Sk) = σ(A) & σ(B) & σ(C) = A' & σ(B) & σ(C) = A' & B' & C'.
By analogy with Sk one concludes that T might also have the features B' & C'.

Learning by analogy: Evaluation and learning
By analogy with Sk one concludes that T might also have the features B' & C'.
However, the evaluation phase shows that T has the features B' but it does not
have the features C'.
Therefore:
- B represents the part of Sk that is transferred to T because of the similarity
between A and A‘;
- C is the part of Sk that is not transferred to T;
- D represents the features that are specific to T.

Case study discussion: Rutherford’s analogy
In this case, the fact that S and T are analogous is already known. Therefore,
the access part is solved and the only purpose of the matching function
remains that of identifying the correct correspondence between the elements
of the solar system and those of the hydrogen atom.
This is an example of a special (simpler form of analogy):
“A T is like an S.”
This is useful mostly in teaching based on analogy.
"The hydrogen atom is like our solar system".

Case study discussion: potential matchings
Which are the possible matchings between the elements of S
and the elements of T?
sun
planet
yellow
mass
mass
temperature
greater
color
revolves-
around
attracts
Tsun
Tplanet
Msun
Mplanet
causes
temperature
greater
mass
mass
attracts
Mnucleus
greater
nucleus
electron
Melectron
sun
planet
yellow
mass
mass
temperature
greater
color
revolves-
around
attracts
Tsun
Tplanet
Msun
Mplanet
causes
temperature
greater
mass
mass
attracts
Mnucleus
greater
nucleus
electron
Melectron

Case study discussion: potential matchings
There are several possible matchings between the elements of S and the elements
of T and one has to select the best one:
Matching1:
sun ↔ nucleus, planet ↔ electron, Msun ↔ Mnucleus, Mplanet ↔
Melectron,
which is supported by the following correspondences
mass(sun, Msun) ↔ mass(nucleus, Mnucleus)
mass(planet , Mplanet ) ↔ mass(electron, Melectron)
greater(Msun, Mplanet) ↔ greater(Mnucleus, Melectron),
attracts(sun, planet) ↔ attracts(nucleus, electron)
Matching2:
sun ↔ nucleus, planet ↔ electron, Tsun ↔ Mnucleus, Tplanet ↔ Melectron,
that is supported by the following correspondences
greater(Tsun, Tplanet) ↔ greater(Mnucleus, Melectron),
attracts(sun, planet) ↔ attracts(nucleus, electron)
Matching3:
sun ↔ electron, planet ↔ nucleus, Msun ↔ Melectron, Mplanet ↔ Mnucleus

Similarity estimation issues and sample solutions
4. How to define the similarity threshold ?
The similarity of two entities is the sum of the similarity of their elements.
Other solutions?
Exhaustive search.
Other solutions?
Two elements are similar if they represent the same concept or are
subconcepts of the same concepts. In such a case their similarity may be
considered 1 (on a 0-1 scale).
Other solutions?
Similarity threshold defined by the designer (a hard critical issue).
Other solutions?
1. How to search the space of all possible matchings ?
2. How to measure the similarity of two elements ?
3. How to combine the estimated similarities of the parts in
order to obtain the similarity between S and T ?

Case study discussion: Matching result
The best matching is Matching1 (because it leads to the highest number of common features
of the solar system and the hydrogen atom) that gives the following substitution:
σ = (sun ← nucleus, planet ← electron, Msun ← Mnucleus, Mplanet ← Melectron)
The features in light color are those that could
be transferred to the hydrogen atom as a result
of the analogy with the solar system:
• color(nucleus, yellow)
• temperature(nucleus, Tn)
• temperature(electron, Te)
• greater(Tn, Te)
• revolves-around(nucleus, electron)
• causes( (attracts(nucleus,electron),
greater(Mnucleus, Melectron)),
revolves-around(nucleus, electron))
yellow
mass
mass
temperature
greater
color
revolves-
around
attracts
Tsun
Tplanet
causes
temperature
greater
Mnucleus
nucleus
electron
Melectron
yellow
-
Tnucleus
Telectron
temperatureelectron
By applying the substitution to the solar system, one
obtains the following structure:

Case study discussion: Evaluation
The evaluating phase shows that
The hydrogen atom has the features:
• causes((attracts(nucleus,electron), greater(Mnucleus, Melectron)),
The hydrogen atom does not have the features:
• color(nucleus, yellow)
• temperature(nucleus, Tn)
• temperature(electron, En)
• greater(Tn, En)
Which is, in your opinion, the most critical issue in analogical
learning?

Discussion
What kind of features may be transferred from the
source to the target so as to make sound analogical
inferences ?
Which is the most critical issue in analogical learning?

attracts(sun,planet)
mass(sun,Msun)
mass(planet,Mplanet)
greater(Msun,Mplanet)
σ (sun <- planet,
planet <- electron,
Msun <- Mnucleus,
Mplanet <- Melectron)
=
attracts(nucleus,electron)
mass(nucleus,Mnucleus)
mass(electron,Melectron)
greater(Mnucleus,Melectron)
revolves-arround(planet,sun) revolves-arround(electron,nucleus)
σ
CAUSE CAUSE ?
Case study discussion: transfer of causal relation

Case study discussion: Learning
Store the new acquired knowledge about the hydrogen atom:
• causes(attracts(nucleus,electron), greater(Mnucleus, Melectron)),
By generalization from the solar system and the hydrogen atom one may learn
the abstract concept that a central force can cause revolution:
• causes(attracts(x, y), greater(Mx, My)), revolves-around(x, y))
Question:
When to store the acquired knowledge and when to generalize it?

Analogy in Disciple
similar example
explains?
similar
Identify and test a strategic COG
candidate for a force
The force is Germany_1943
I need to
Therefore I need to
candidate corresponding to a
member of a force
The force is European_Axis_1943
initial example
explanation
explains
candidate for a force
The force is US_1943
I need to
Therefore I need to
candidate corresponding to a
member of a force
The force is Allied_Forces_1943
US_1943
has_as_
memberAllied_Forces_1943
similar explanation
less general than
Analogy
criterion
less general than
?O2
has_as_
member?O1
forcemulti_member_force
instance_ofinstance_of
Germany_1943
has_as_
memberEuropean_Axis_1943
similar

A A'
B B'
similar
similar
causes causes ?
The basic scheme of analogy
Causal networks of relations
An important result of the learning by analogy research is that the analogy
involves mapping some underlying causal network of relations between
analogous situations.
By causal network of relations it is generally meant a set of relations related by
special higher order relations such as 'physical-cause(ri, rj)', 'logically-implies(ri,
rj)', 'enables(ri, rj)', 'justifies(ri, rj)', determines(ri, rj) etc.
The idea is that similar causes are expected to have similar effects:

Gentner’s structure mapping theory
The main claim of this theory is that relations between
objects, rather than attributes of objects, are mapped from
source to target. Moreover, a relation that belongs to a
mappable system of mutually interconnecting relationships
is more likely to be imported into the target than is an
isolated relation (the systematicity principle).
See:
Gentner D., The mechanisms of analogical reasoning, in J.W.Shavlik,
T.G.Dietterich (eds), Readings in Machine Learning, Morgan Kaufmann,
1990.

Gentner’s structure mapping theory (cont.)
Analogy maps the objects of the source onto the objects of the target:
s1 ↔ t1, ... , sn ↔ tn
These object correspondences are used to generate the candidate set of inferences
in the target domain.
Predicates from the source are carried across to the target, using the node
substitutions dictated by the object correspondences, according to the following
rules:
1. Discard attributes of objects A(si) -/-> A(ti)
For instance, the yellow color of the sun is not transferred to the hydrogen
nucleus.
2. Try to preserve relations between objects R(si, sj) -?-> R(ti, tj)
That is, some relations are transferred to the target, while others are not.
3. The systematicity principle: the relations that are most likely to be transferred
are those belonging to systems of interconnected relations
R'(R1(si,sj), R2(sk,sl)) → R'(R1(ti,tj), R2(tk,tl))

Literal similarity, analogy, and abstraction
Gentner's theory distinguishes between literal similarity,
analogy, and abstraction.
One says that a target T is literally similar with a source S if and only if a
large number of predicates is mapped from source to target, relative to the
number of nonmapped predicates and, also, the mapped predicates include
both attributes of objects and relations between objects.
For instance, 'kool-aid' is literally similar with 'water' since it has most of the
features of 'water' (both attributes of objects and relations between objects).
Give other examples of literally similar entities.

Literal similarity, analogy, and abstraction
One says that a target T is analogous with a source S if and only if relations
between objects, but few or no attributes of objects, can be mapped from
source to target.
For instance, 'heat' is analogous to 'water'.
Give other examples of abstractions.
One says that a source S is an abstraction of a target T if and only if the
source is an abstract relational structure and each predicate (a relation
between objects or an attribute of an object) from the abstract source is
mapped into a less abstract predicate of the target; there are no nonmapped
predicates.
For instance, 'through-variable' is an abstraction of 'heat', where by 'through-
variable' we mean something that flows across a difference in potential.

Similarity, analogy, and abstraction: discussion
Given that two entities overlap in relations, they are more literally
similar to the extent that their object attributes also overlap.
Therefore, literal similarity might be seen as a particular case of
analogy.
Abstraction may also be seen as a special case of analogy in which
all the predicates of the source entity are mapped into the target
entity.
What could we conclude from these observations?

Similarity, analogy, and abstraction: discussion
The contrast between literal similarity, analogy, and
abstraction is a continuum.
What could we conclude from these observations?
Overlap in relations is necessary for any perception of
similarity, analogy or abstraction.

Gentner’s theory: implementation and discussion
An implementation of the Structure-Mapping theory is the Structure-
Mapping Engine (Falkenhainer, Forbus & Gentner, 1989: The
Structure-mapping Engine. Algorithms and Examples, Artificial
Intelligence, 41:1-63. Also in Readings in Knowledge Acquisition and
Learning).
Given the descriptions of a source and a target, the Structure-Mapping
Engine constructs all syntactically consistent analogical mappings
between them. Each mapping consists of pairwise matches between
predicates and objects in the source and target, plus a list of
predicates which exist in the source but not the target. This list of
predicates is the set of candidate inferences sanctioned by the
analogy. The Structure-Mapping Engine evaluates syntactically each
possible analogy to find the best one.

Gentner’s theory: implementation and discussion
The Structure-Mapping Engine needs to be given the descriptions of a
source and a target. This requires the ACCESS problem to be solved
first:
How do we find potential sources for a target?
MAC/FAC (Forbus, Gentner, Law, 1995: “MAC/FAC: A model of
similarity-based retrieval,” Cognitive Science, 19(2):141-205) is a
system that addresses the access problem.
The MAC stage uses a simple, nonstructural matcher to filter our a few
promising candidates from a large memory of structured descriptions.
The FAC stage evaluates each candidate using SME to provide a
structural match.
MAC/FAC was scaled-up in the DARPA’s HPKB and RKF programs.
What is, however, a problem with Gentner’s theory?

Gentner’s theory: discussion
Gentner’s interpretation rules depend only on the syntactic properties of
the knowledge representation, and not on the specific content of the
domain.
What is a problem with Gentner’s theory?
Why is this a problem?
Consider these equivalent representations:
Book1-on-Table
On(Book1, Table)
causes((attracts(nucleus,electron), greater(Mnucleus, Melectron)),
Could you think of a different representation where the following
expression is no longer a second order relation?

Determinations: Definition
Instead of giving a general criterion for the validity of analogical knowledge
transfer (high order relations or causal network of relations), Russel and
Davis propose to specify explicitly what knowledge can be transferred. The
rules for specifying this are called "determination rules".
P(x, y) >- Q(x, z) (P plausibly determines Q) meaning
∀S, ∀T { If ∃y [P(S, y) & P(T, y)]
then it is probably true that ∃z [Q(S, z) & Q(T, z)] }
where P and Q are first order logical expressions.

Determinations: Definition (cont.)
A determination rule is an expression of the following form:
U(x1,...,xn,y1,...,ym) >- V(x1,...,xn,z1,...,zp)
One says that U determines V. That is, whenever the arguments of U have
certain values, the arguments of V are very likely to have corresponding
values.
Example: Rainfall(x, y) >- Water-in-soil(x, z)
Rainfall(Philippine, heavy), Water-in-soil(Philippine, high)

Given: Rainfall(x, y) >- Water-in-soil(x, z)
Rainfall(Philippine, heavy), Water-in-soil(Philippine, high)
Rainfall(Vietnam, heavy)
Conclude: Water-in-soil(Vietnam, high)
Rainfall(Philippine, heavy)
Water-in-soil(Philippine, high)
(Philippine -> Vietnam)
determines determines ?
Water-in-soil(Vietnam, high)
(Philippine -> Vietnam)
Analogical reasoning based on determinations
What is the difference between a determination rule
and a deductive rule?

Determinations: Discussion
A determination rule is different from a deductive rule.
The form of a deductive rule is:
U(x1,...,xn,y1,...,ym) --> V(x1,...,xn,y1,...,ym)
That is, the variables which appear in the left hand side of a rule also appear in
the right hand side. Therefore, if we know that 'U(a1,...,an,b1,...,bm)' is true, we
could apply modus ponens to infer that 'V(a1,...,an,b1,...,bm)' is also true.
This type of reasoning is not possible in the case of a determination
U(x1,...,xn,y1,...,ym) >- V(x1,...,xn,z1,...,zp)
because we do not know the values of the variables z1,...,zp.
In order to apply a determination rule, one would need a source entity, as will
be illustrated in the following.

The basic procedure for answering the query V(T, ?z) by analogy:
1. Find a determination such that U(?x, ?y) >- V(?x, ?z)
(i.e. decide which determinations could be relevant for T: U(T, ?y) >- V(T, ?z))
2. Find 'a' such that U(T, a)
(i.e. find how the facts are instantiated in the target)
3. Find a source S such that U(S, a)
(i.e. find a suitable source)
4. Find 'b' such that V(S, b)
(i.e. find the answer to the query from the source: U(S, a) >- V(S, b))
5. Return 'b' as the solution to the query
(U(T, a) >- V(T, b))
U(S,a) U(T,a)
V(S,b) V(T,?z)
b
Analogy based on determinations: Method

Let us consider the following target
Nationality (Jack, UK), Male(Jack), Height(Jack, 6'), ...
and the problem of answering the following question by analogy
What is the native language of Jack ? (i.e. Native-language(Jack, ?z))
1. Find a determination such that U(x, y) >- Native-language(x, z)
Such a determination is: Nationality (x, y) >- Native-language(x, z)
2. Find 'a' such that Nationality (Jack, a)
Nationality (Jack, UK) a = UK
3. Find a source S such that Nationality (S, UK)
Nationality (Jill, UK), Female(Jill) , Height(Jill, 5'10"),
Native-Language(Jill, English)
S = Jill
4. Find 'b' in S such that NativeLanguage(Jill, b)
Native-Language(Jill, English) b = English
5. Return 'English' as the solution to the query
Native-language(Jack, English)
Analogy based on determinations: Illustration

Consider the determination rule:
U(x1,...,xn,y1,...,ym) >- V(x1,...,xn,z1,...,zp)
Should U and V be terms or could they be arbitrary logical expressions?
Why?
What if we cannot find a source S for applying the determination?

U and V may be an logical expressions.
Example:
The rainfall of a flat area determines the quantity of water in the soil of the area
Rainfall(x, y) & Terrain(x, flat) --> Water-in-soil(x, z)
Rainfall(Philippines, heavy), Terrain(Philippines, flat), Water-supply(Philippines, high)
Rainfall(Vietnam, heavy), Terrain(Vietnam, flat)
Water-in-soil(Vietnam, ?t)
Rainfall(Philippines, heavy)
Terrain(Philippines, flat)
Water-in-soil(Philippines, high)
(Philippines <- Vietnam)
Terrain(Vietnam, flat)
Water-in-soil(Vietnam, high)
(Philippines <- Vietnam)

What if we cannot find a source S for applying the determination?
Sometimes there is no source S such that U(S, a) is true, but one may find S'
such that U(S', a') is true. In such a situation one needs a way to decide whether
a' and a are similar enough to infer V(T, b). Therefore, even in the case of
determinations one may need a matching function.
Example: Latitude of an area determines the climate of the area
Latitude(x, y) --> Climate(x, z)
Latitude(Romania, 45°), Climate(Romania, temperate)
Latitude(France, 47°)
Latitude(Romania, 45°)
Climate(Romania, temperate)
(Romania <- France)
(Romania <- France)
Climate(France, temperate)
Latitude(France, 47°)

Problem solving by analogy
Analogy means deriving new knowledge about an input
entity by transferring it from a known similar entity.
How could we define problem solving by analogy?

Problem solving by analogy: definition
Problem solving by analogy is the process of
transferring knowledge from past problem-solving
episodes to new problems that share significant
aspects with corresponding past experience and using
the transferred knowledge to construct solutions to the
new problems.
What could be the overall structure of a problem
solving by analogy method?

The problem solving by analogy method
Let P be a problem to solve.
First, look into the knowledge base for a previous
problem solving episode which shares significant
aspects with the problem to solve.
Next transform the past episode to obtain a solution to
the current problem.
What it means for problems to share significant aspects?
How is the past problem solving episode transformed so
as to obtain the solution to the current problem?
What questions need to be answered to develop such a
method?

The derivational analogy method (Carbonell)
•Two problems share significant aspects if they match within a
certain threshold, according to a given similarity metric.
•The solution to the retrieved problem is perturbed incrementally
until it satisfies the requirements of the new problem.
Previously
Solved
Problem
New
Problem
Solution
to Old
Problem
Solution
to New
Problem
Partial
Mapping
Transformation
Process

The derivational analogy method: illustration
GIVEN:
PROVE: AC = BD
A
B
C
D
AB = CD
AB + BC = BC + CD
AC = BD
AB = CD GIVEN:
PROVE: <BAD = <CAE
<BAC = <DAE
B
A
C
D
E
BC = BC
<BAC = <DAE
<BAC + <CAD= <CAD + <DAE
<BAD = <CAE
<CAD = <CAD
AB <- <BAC
CD <- <DAE
AC <- <BAD
BD <- <CAE )
σ = (

The derivational analogy method: discussion
How does analogy facilitate the problem solving process?
How does the derivational analogy method relates to the
generally accepted idea that the relations which are
usually imported by analogy from a source concept S to
the target concept T are those belonging to causal
networks?

The derivational analogy method: discussion
How does this method relates to the generally accepted idea that the
relations which are usually imported by analogy from a source concept
S to the target concept T are those belonging to causal networks?
Intuition: The relation between a problem and its solution is a kind of
cause-effect relationship.
Fermat’s last theorem: There is no integer solutions of xn
+ yn
= zn
for n>2
Previously solved problem: Find integer solutions of the problem x2
+ y2
= z2
Problem: Find integer solutions of the problem x3
+ y3
= z3
Consider the following problem solving situation:
What does this example suggests?

Discussion
Except for the trivial problems, a solution does not emerge
immediately from the problem formulation, as would be the case
in a cause-effect relation.
What other relation from the problem solving process might be
closer to a cause-effect relation?

What other relation from the problem solving process might be
closer to a cause-effect relation?
The relation between a problem and its derivation trace (i.e.
solution process).
What is transferred from a past problem solving episode is not a
problem solution but the problem solving process itself, what
questions have been asked, what factors have been
considered, etc. One would try to repeat the same process in
the context of the new problem.
With this interpretation we retrieve the derivational analogy
method:
Discussion

The transformational analogy method (Carbonell)
Two problems are considered to share significant aspects if
their initial analysis yields the same reasoning steps, that is, if
the initial segments of their respective derivations start by
considering the same issues and making the same decisions;
The derivation of the solved problem may therefore be
transferred to the new problem by reconsidering the old
decisions in the light of the new problem situation, preserving
those that apply, and replacing or modifying those whose
supports are no longer valid in the new situation.
Derivational analogy gives better results than transformational
analogy. However, it has the disadvantage to manipulate
complex structures representing derivational traces.

1. Compare explanation-based learning, empirical inductive learning, and learning by analogy from the
point of view of input information, background knowledge needed, and outcome of learning.
2. Define learning by analogy and give an example of analogy.
3. Describe the four stages of learning by analogy.
4. Illustrate learning by analogy with the help of the following example:
Exercises
sun
planet
yellow
mass
mass
temperature
greater
color
revolves-
around
attracts
Tsun
Tplanet
Msun
Mplanet
causes
temperature
greater
mass
mass
attracts
Mnucleus
greater
nucleus
electron
Melectron

Let us consider a learning by analogy system having the following background
knowledge:
Facts:
Economy-type (Germany, highly-industrial), Location(Germany, Europe)
Population(Germany, 70), …
Economy-type (Vietnam, agricultural), Location(Vietnam, Asia)
Population(Vietnam, 70), Economic-state(Vietnam, poor), …
Economy-type (Japan, highly-industrial), Location(Japan, Asia),
Population(Japan, 100), Economic-state(Japan, excellent), …
Determination:
Economy-type (x, y) >- Economic-state (x, z)
(the economy-type of a country determines the economic state of the country)
Write a detailed trace of the reasoning of the system for answering the following
question:
What is the economic state of Germany ? (i.e. Economic-state (Germany, ?z))
Exercise

Provide an example of a successful application of the transformational analysis
method.
Provide an example where the transformational analysis method does not apply,
but the derivational analogy method does apply.
What is the difference between a determination rule and a deductive rule?
Illustrate the difference with an example.
Exercises

Recommended reading
Gentner D., Holyoak K.J., Kokinov B.N. (eds.), The Analogical Mind: Perspectives from
Cognitive Science, The MIT Press, 2001.
Carbonell J.G., Learning by analogy: formulating and generalizing plans from past experience,
Machine learning I, 1983.
Carbonell J.G., Derivational analogy: a theory of reconstructive problem solving and expertise
acquisition, in Shavlik J. and Dietterich T. (eds), Readings in Machine Learning, Morgan
Kaufmann, 1990. Also in Readings in Machine Learning and Knowledge Acquisition.
Davies T.R., Russell S.J., A logical approach to reasoning by analogy, in Shavlik J. and
Dietterich T. (eds), Readings in Machine Learning, Morgan Kaufmann, 1990.
Gentner D., The mechanisms of analogical reasoning, in J.W.Shavlik, T.G.Dietterich (eds),
Readings in Machine Learning, Morgan Kaufmann, 1990.
Winston P.H., Learning and reasoning by analogy, Communications of the ACM, 23, pp.689-
703, 1980.
Forbus K.D., Exploring Analogy in the Large, in Gentner D., Holyoak K.J., Kokinov B.N. (eds.),
The Analogical Mind, 2001
Tecuci, Building Intelligent Agents: An Apprenticeship Multistrategy Learning
Theory, Methodology, Tool and Case Studies, Academic Press, 1998, pp: 101-108.

09 analogical-learning

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