Analogy
Lecture notes
Phil/Psych 256
Feb. 4, 1997
Analogy preview:
1. Representation - proportional, geometric, predicate,
domains, levels
Constraints on mapping - similarity, structure, purpose
2. Computation - analogy formation
Problem-solving - decision, explanation, learning
Psychological plausibility - similarity, metaphor
Applications - Case Based Reasoning
Q: What is an analogy?
A1: "proportional," (Hofstadter) e.g.,
abc : ijk :: abd : ?
(ijl, ijd, ijj)
"abc" is to "ijk" as "abd" is to __?
"What education is to the individual human being,
that revelation is to the whole human race." (Lessing)
A2: "geometric" (Evans)
A3: recognition, e.g.,
"He looks just like Elvis!"
A4: categorization, e.g.,
"He's the Michael Jordan of bowling"
"Way to go, Einstein!"
A5: "me-too," e.g.,
"I'm going to pay for my beer now"
"Me too"
A6: remindings
A7: explanations, e.g.,
Bohr model of the atom
Q: What are the components of an analogy?
A1: a source (base) domain - a concept, usually well
understood, e.g.,
planets, sun, orbits (trajectory)
A2: a target domain - a concept, often not so well
understood, e.g.,
electrons, nucleus, orbits (quantum)
Q: How are the domains organized (multiconstraint theory -
Holyoak & Thagard)?
A1: attributes - basic objects and their properties, e.g.,
planet, sun, gravity
A2: relations - relations that hold among attributes, e.g.,
orbits(planet,sun)
A3: systems - systemic facts that hold among other predicates,
e.g.,
because(orbits,gravity)
So, the Bohr model analogy could be expressed by the mappings:
Source Target
planet electron
sun nucleus
gravity charge
orbits(planet,sun) *orbits(electron,nucleus)
because(orbits,gravity) because(orbits,charge)
The *orbits predicate is imported into the target domain,
to explain the structure of the atom.
Q: What constitutes a good analogy (MT)?
A1: similarity - corresponding predicates are similar in
meaning, e.g., near neighbors in a semantic network, visual
similarity
A2: structural isomorphism (systematicity) - each predicate
corresponds with one other predicate, and their slot-fillers
correspond similarly
A3: purpose - mappings contain predicates that address the
problem to be solved
Example:
Armor, n. The kind of clothing worn by a man whose taylor
is a blacksmith.
Source Target
clothing armor
taylor blacksmith
man man
needle, thread, cloth hammer, rivet, metal
makes(taylor,clothing) makes(blacksmith,armor)
uses(taylor,n-t-c) uses(blacksmith,h-r-m)
buys(man,clothing,taylor) buys(man,armor,blacksmith)
wears(man,clothing) wears(man,armor)
in-order-to(uses,makes) in-order-to(uses,makes)
because(makes,buys) because(makes,buys)
in-order-to(buys,wears) in-order-to(buys,wears)
Q: What about analogies in arguments?
A1: The truth of the source predicates needs to be examined,
e.g., guns are like cricket bats
Phil/Psych 256
Feb. 6, 1997
Q: What is the process of analogy formation?
1. Characterize the target
2. Pick out a source that matches target:
- given, or
- search memory and retrieve, or
- construct one
(fishing expedition)
3. Map source to target; find correspondences
4. Evaluate solution
5. Learn schema from target for next time
Q: What factors affect the different stages?
A1: retrieval (2) depends on similarity
- mere-appearance matches, e.g., "A
cloud is like a sponge" --> "both are
round and fluffy" (5-year old) or
"both hold water" (adult) (Gentner)
- tumor problem (Holyoak & Thagard)
A2: mapping (3) depends on structure and representation
(Gentner)
- competing mappings
- the "frame problem," e.g.,
hotter-than(a,b) vs. colder-than(b,a),
cause(a,b) vs. because(b,a)
A3: solving (4) depends on purpose (Holyoak & Thagard)
- are electrons like planets?
- are guns like cricket bats?
Example: Analogy and explanation
Darwin used several analogies to describe the concept
of natural selection:
1. Artificial selection, e.g., dogs, pigeons
2. Laissez-faire economics (Smith)
3. Exponential population growth vs. linear resource
growth (Malthus)
4. The "argument from design" (Paley)
Q: How does analogy lead to learning?
A1: a useful analogical source may be generalized to
form a schema
- irrelevant detail is ignored
- specifics are made defaults or stripped away
A2: multiple sources may suggest a schema (convergence),
e.g., armies & firemen --> tumors
Example: Analogy and decision
Operation Desert Storm was conceived in response to several
previous analogues:
1. WWII - Hussein as Hitler, massive invasion
2. Vietnam - Hussein as Ho Chi Min, incremental involvement
3. Vicksburg - Civil War battle in which Grant outflanked
the Confederate Army (Schwarzkopf as Grant)
Q: How are metaphor and analogy related?
A1: good metaphors share the properties of good analogies,
e.g., "my job is a jail"
- my job is like a place of confinement
(categorization), but also,
- my job is unpleasant
- my job is not easy to leave
- ignore some details of jail
A2: the source domain is re-conceived or extended
(unlike analogy); consider
- "That acrobat is a hippopotamus"
vs.
- "That hippopotamus is an acrobat"
A3: literal and metaphorical interpretations interfere,
e.g., (Glucksberg)
- some desks are junkyards [slow]
- some desks are roads [faster]
Example: Case Based Reasoning
- Case Based Reasoning systems solve problems by identifying
and adapting previous "cases" similar to the given (current)
one.
- previous cases are stored in a case library (often static)
- good systems can apply several library cases (perhaps
piecemeal) to a given problem
Review of analogy:
1. Database - semantic network of concepts, e.g., case library
2. Knowledgebase - characterization, retrieval, mapping,
evaluation, learning
3. Goals - categorization, decision, explanation, learning, ...
4. Learning strategies - generalization, convergence
5. Accords with basic psychological data, but still in early
stages of research
Next week:
- sample midterm
- essay 2
- visual imagery
- Kosslyn
Further materials
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