• Heavy use of conceptual knowledge is a signature phenomena of human cognition
– People understand, make, compare, and learn from complex arguments
– People learn conceptual knowledge from reading texts, and apply what they have learned to new situations
– People reason and learn by analogy, applying precedents and prior experience to solve complex problems
– People use symbolic systems (e.g., language, maps, diagrams)
• Symbolic models remain the best way to explore many conceptual knowledge issues

• Structure-Mapping Architecture
• Accelerating learning via analogical encoding
– Brief review
• Tacit analogical inference
– Analogy on the sly
• Similarity-based qualitative simulation
• Transfer and outreach activities

Structure-Mapping Theory (Gentner, 1983)
• Analogy and similarity involve
– correspondences between structured descriptions
– candidate inferences fill in missing structure in target
Inference is selective.
Not all base knowledge is imported
Candidate
Inference completes common structure
• Constraints
–
Identicality: Match identical relations, attributes, functions. Map non-identical functions when suggested by higher-order matches
–
1:1 mappings: Each item can be matched with at most one other
–
Systematicity: Prefer mappings involving systems of relations, esp. including higher-order relations

Analyzing similarities and differences, reasoning from experience, applying relational knowledge
SEQL
US
Iraq
WMD
Invasion
Functional Overview
Israel
Iran
Nuclear Reactor
Bombing
Similaritybased retrieval of relevant examples and knowledge
Potentially relevant precedents
SME
Incrementally constructs generalizations, producing human-like relational abstractions within similar number of examples.
Long-term memory
MAC/FAC

Psychological Studies
1. Case-comparison method
Previous work: Transfer
New work: Learning of principles
2. Unaware analogical inference
Previous work: Unaware inference
New work: Attitude congeniality & unaware inferences
New work: Unaware alignment-based decision making

•
Core process in higher-order cognition
•
A general learning mechanism by which complex knowledge can be acquired
• e.g., causal structures & explanatory principles
• Unique to humans (or nearly so):
Similarity
Species-general
Analogy
Species-restricted
A
A B
Object match
AA
BB CD
Relational match

• Analogy can promote learning
– Induces structural alignment
– Generates candidate inferences
Standard analogical learning:
Familiar
Situation
Inferences
New
Situation
• But, memory retrieval of potential analogs is unreliable
Inert knowledge : Learned material often fails to transfer to new situations
• Solution: Analogical encoding
Use comparison during learning to
highlight the common relational system
promote relational abstraction & transfer
Analogical encoding:
New
Situation
Compare
New
Situation
Relational
Schema
New
Situation

Case Comparison Method in Learning to Negotiate
Studies of MBAs learning negotiation strategies
Students study two analogous cases prior to negotiating case 1
Loewenstein, Thompson & Gentner, 1999
Thompson, Gentner & Loewenstein, 2000
Gentner, Loewenstein & Thompson, 2003 case 2
Separate Cases Condition
Read each case, write principle and give advice.
Comparison Condition
Compare the two cases and write the commonalities
Simulated
Negotiation
On a new analogous case

Negotiation transfer performance across three studies:
Proportion using strategy exemplified in the cases
.8
.7
.6
.5
.4
.3
.2
.1
0
.19
.24
.58*
No Cases
N=42
Separate Cases
N=83
Compare
N=81


.8
.7
.6
.5
.4
.3
.2
.1
0
Compare
Separate
Cases
0 0.5
1.0
1.5
2.0
Dyadic Schema Rating
So, what happens if we just give them the principle?

.7
.6
.5
.4
.3
.2
.1
0
.19
Separate Cases
N=26 dyads
.44*
Separate
Principle
Plus case
Case 1
________
________
Case 2
___________
___________
Compare
Principle and Case
Case 1
Case 2
__________
____________
____________
_________
Test: Face-to-face negotiation
Compare
N=27 dyads
Error bars assume binomial with prop=.19 (baseline)

Comparison promotes transfer even when the principle is given - Why?
Principles utilize abstract relational language
• Relational language—verbs, prepositions, relational nouns— is contextually mutable
 interpretation difficulties
– e.g., force in physics =/= force in commonsense language
• Assembling a complex relational structure is errorful
• So, beginning learners don’t understand principles when presented solo
Case provides a firm relational structure that is correct but overly specific
– learning is context-bound – strongly situated
– So unlikely to transfer
Comparing a principle and a case
– grounds the principle in a firm structure
– invites abstracting the specific relations in the case

Learning Negotiation Principles- Experiment 1
Training:
• participants read two passages
– a negotiation principle (Contingent Contract)
– an analogous case
•
Separate condition : Participants consider each passage separately.
•
Compare condition : Participants consider how the case and principle are alike.
• Two orders: case  ppl and ppl
 case
• All participants answer the question
"How could this be informative for negotiating?"
20-minute delay
Test: Recall task: subjects write out the principle they learned

A contingent contract is a contract to do or not to do something depending on whether or not some future event occurs. At least two kinds of situations exist in which contingent agreements add potential for joint gains – when disagreeing over probabilities and when both parties try to influence an uncertain outcome. When the uncertain event itself is of interest, there are familiar economic contingent contracts with “betting” based on the probability of differences.
Parties are dealing with uncertain quantities and actually or apparently differ in their assessment, and here contingent arrangements offer gains. When the parties feel capable of influencing an uncertain event, making the negotiated outcome dependent on its resolution may be a good idea. In both cases of course, contingent arrangements based on underlying differences are not a panacea. Crafting them effectively can be a high art. And once the outcome of the uncertain event is known, one party may have “won” and the other “lost.” Whether the outcome will then be considered fair, wise, or even sustainable is an important question to be planned for in advance.

Two fairly poor brothers, Ben and Jerry, had just inherited a working farm whose main crop has a volatile price. Ben wanted to sell rights to the farm’s output under a long-term contract for a fixed amount rather than depend upon shares of an uncertain revenue stream. In short, Ben was risk-averse. Jerry, on the other hand, was confident that the next season would be spectacular and revenues would be high. In short,
Jerry was risk-seeking. The two argued for days and nights. Ben wanted to sell immediately because he believed the price of the crop would fall; Jerry wanted to keep the farm because he believed the price of the crop would increase.
Finally, Jerry proposed a possible agreement to his brother: They would keep the farm for another year. If the price of the crop fell below a certain price (as Ben thought it would), then they would sell the farm and Ben would get 50% of the farm’s current value, adjusted for inflation; Jerry would get the rest. However, if the price of the crop were to rise (as Jerry thought it would), Jerry would buy Ben out for 50% of the farm’s current value, adjusted for inflation, and would get to keep all of the additional profits for himself. Jerry was delighted when his brother told him he could agree to this arrangement, thereby avoiding further conflict.

Two blind raters
Agreement: 94%
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
Recall Scores (Max. = 8)
Gentner & Colhoun
2.5
3.4
Separate Compare
(26)
Condition
(26)
t(50) = 2.10, p = 0.041

Quotes from the Compare Group
• P18: "Contingent contract Principle: if there is an uncertain event occurring in the future which two parties disagree on, the outcome of this event becomes the determining factor in the outcome of the negotiation."
• P30: "The contingency contract is created as an agreement to do/not do something in the future in the event of a situation. As the future is unknown, the CC is created on the probability that something will occur…"
Quotes from the Separate Group
•P50: "It is important to consider how much you will lose or win when betting on an uncertain event. Negotiating in this situation is more complicated than just predicting the outcome." (this was the entire answer)
•P51: "We read about the two poor brothers on the farm. One was risk-seeking and the other was risk-seeking, so they couldn't decide on whether or not to sell the farm…" (no mention of the principle)

Read Principle & Case
(20 mins)
Immediate Recall
Test case : Asian Merchant
N=14; 7 sep, 7 comp
(4 days)
Long term Recall
New test case
N=14; 7 sep, 7 comp

6
5
4
3
2
1
0
Both Orders
3.1
4.4
Separate
(11)
Compare
(12)
T(23) = -2.44, p = 0.023

Both Order
6
5
4
3
3.1
4.3
2
1
0
Separate Compare
(11) (12)
T(21) = -1.91, p = 0.07
Combines two groups with slightly different procedures

Comparison group > Separate group
Case-first groups > Principle-first groups
Comparing case and principle greatly benefits comprehension of principle
The case provides firm relational structure and a clear (though overly specific) interpretation of the relational terms
Comparing case with principle prompts rerepresentation and abstraction of the relational structure

• Case-based training is heavily used in professional schools (business, medicine, law) – intensive analyses of single cases
– Our results suggest that learning could be greatly increased by changing to a comparison-based instructional strategy
• Based on our findings, some institutions are revising their instructional methods
– Medical School of McMaster University
• Developing a new curriculum relying heavily on comparisonbased instruction
– Harvard Business School
• Exploring comparison-based method
– CMU – discussions with Marsha Lovett

Analogy as generally conceived:
•
Conscious
• Discerning
• Deliberate
• Effortful
Current Studies:
•
Non-aware
• Oblivious
• Non-deliberate
• Accidental
Suggestive evidence: Blanchette & Dunbar, 2002; Moreau, Markman & Lehman, 2001

•
Can analogical inferences occur without awareness of making the inferences?
•
Can analogical inferences occur without awareness of the analogy itself?
• Can the highlighting effect of analogical alignment
Influence future decision-making?

believing that the analogical inference from
B

T actually occurred in T
•
Evidence for analogical insertion
Blanchette & Dunbar 1999
Analogy: Anti-marijuana laws are like Prohibition
Participants misrecognized parallel inferences as having occurred in marijuana passage
• But, these pro-marijuana inferences were likely to be congenial to college students
•
Will analogical insertion occur if the inference is not so congenial?

Attitudes towards gayness assessed (Mass testing)
3-4 weeks (unrelated context)
Read paragraph “Is it OK to be gay”
Analogy group
Second paragraph analogizing gayness to left-handedness
15-min filled delay
Old-New recognition test
Control group
No further text
Rate soundness of analogy
Perrott, Gentner &
Bodenhausen, 2005

Proportion “old” responses
Perrott, Gentner &
Bodenhausen, 2005
1
0.8
0.6
0.4
0.2
0
*
Analogy
No-Analogy
Text Item Analogical
Inference
Plausible
False Item
Blatantly False
Item
Condition(2) X Item type(4)
F (3, 228) = 4.97, p = .002, MSE = .048

Attitudes towards gays within predicted the rated soundness of the analogy
But
Likelihood of analogical insertion was not predicted by rated soundness of the analogy
Even more surprisingly,
Likelihood of analogical insertion was not predicted by attitude towards gays – No “attitude congeniality effect”
Attitudes measured on 15-item questionnaire  composite scale from
1 (very negative) to 7 (very positive). Range: 1.8-6.8 (M = 4.7)
Cutoffs for lower and upper quartiles = 3.3 and 5.8

• Participants read a series of passages
• Told that they would be asked questions about content of passages
• We observed extent to which analogous passages early in the set influenced the interpretation of later passages
• No goal other than comprehension
• Inferences support understanding the input

Day & Gentner; 2003, in prep
•
Participants read a series of passages
• Some early passages are relationally similar to later passages
•
Will participants use structure-mapping in interpreting the later passages?
TEST:
• Participants answer TF questions about passages
•
Dependent measure: Answering True to questions that are inferences from earlier analogous passages.

Two versions of each base passage
• If participants use analogical inference from the earlier similar base passage, they will understand the target differently, depending on which base version they got.
Target has some ambiguous portions

Base 1:
Wealthy elderly woman dies mysteriously
Her niece respectfully flies into town for the funeral
People are surprised when the will leaves everything to the niece
Base 2:
Wealthy elderly woman dies mysteriously
Her niece suspiciously leaves town when the death is announced
People are surprised when the will leaves everything to the niece
Target Passage:
Wealthy elderly man dies mysteriously
As soon as the death is announced, the man’s nephew immediately buys a ticket and flies to
Rio de Janeiro
People are surprised when the will leaves everything to the nephew

100
73%
50
25%
0
Day & Gentner, 2003
Base-consistent Base-inconsistent
Using base consistency as a within-subjects factor
t (19) = 4.79, p < .001

E1
• P’s interpreted the ambiguous portion of the target in a manner consistent with structurally matching information in the base.
• The same target passage was interpreted differently, as a function of which base P’s had read
• Evidence suggests that analogical inference influences the interpretation of new material
•
Not due to deliberate strategies:
90% noticed similarities between passages
But, 80% said all passages were understandable on their own.
• Not due to simple priming: further study showed inferences are specific to the structural role of the inserted information

Experiment 3: Self-paced Reading Task
•
Base passage and target passage same as in Expts 1 and 2, except:
•
Target contains a later key sentence that is consistent with one base’s inference and inconsistent with the other’s:
“George's absence from the service was conspicuous, especially since he had been seen around his uncle's estate prior to his death, and the police soon found out about his flight to Rio.”
If P’s insert the seeded inference into the target story, they will take longer to read the key test sentence when it is inconsistent with that inference

Experiment 3: Self-paced Reading Task
•
Base passage and target passage same as in Expts 1 and 2, except:
•
Target contains a later key sentence that is consistent with one base’s inference and inconsistent with the other’s:
Results
“George's absence from the service was conspicuous, especially since he had been seen around his uncle's estate prior to his death, and the police soon found out about his flight to Rio.”
10
9
8
8.88
7 6.40
If P’s insert the seeded inference into the target story, they will take longer to read the key test sentence when it is inconsistent with that inference
6
5
4
BaseBaseconsistent inconsistent
F (1,19) = 6.81, p < .05

Day & Gentner; 2003, in prep
Tacit analogical inferences
•
People interpolated analogical inferences from a prior similar passage due to shared representational structure, not simply to general priming
• Implication: Structure-mapping can operate in nonaware, non-deliberative processing
• But –what about large number of analogy studies that show failure to transfer ?
Current studies
•
Vary delay: 20 minute vs. 4 days later
• Vary surface similarity between the passages
•
Future work: Progressive alignment effect? Does an obvious alignment potentiate more analogical creep?

Day & Bartels (2005)
Unaware effects of analogy: Decision-making
Structure mapping theory proposes that comparison involves the alignment of representational structures ( Gentner, 1983; Gentner & Markman, 1997)
This implies two kinds of differences: alignable differences : different values on same predicate or dimension; related to common structure non-alignable differences : none of the above
Alignable differences are weighted more heavily in perceived similarity ( Markman & Gentner, 1996 ) difference detection (Gentner & Markman, 1994) recall ( Markman & Gentner, 1997 ) preference ( e.g., Roehm & Sternthal, 2001 )
Hypotheses:
Alignment along a dimension renders that dimension more salient in immediate use
Repeated alignment & use renders the dimension more salient in future encodings

Method: P’s choose among portable digital video players
1. First, participants gave preference ratings for models that varied on only one alignable dimension:
Firewire and USB connectivity:
Battery life:
Voice recorder:
Hard drive capacity:
Built-in FM radio:
Wireless projection range :
Support for WMV and MP2 formats:
Screen size:
Weight:
Model A
Yes
4 hr
No
7 Gb
Yes
12 ft
No
2.5 in
10 oz
Model B
Yes
4 hr
No
4 Gb
Yes
12 ft
No
2.5 in
10 oz
Strongly prefer
Model A
Strongly prefer
Model B

1. First, participants gave preference ratings for models that varied on only one alignable dimension:
Firewire and USB connectivity:
Battery life:
Voice recorder:
Hard drive capacity:
Built-in FM radio:
Wireless projection range :
Support for WMV and MP2 formats:
Screen size:
Weight:
Model A
Yes
4 hr
No
7 Gb
Yes
12 ft
No
2.5 in
10 oz
Model B
Yes
4 hr
No
4 Gb
Yes
12 ft
No
2.5 in
10 oz
Strongly prefer
Model A
Strongly prefer
Model B

2. Eventually, they make judgments between models varying on two dimensions, each favoring a different alternative
Firewire and USB connectivity:
Battery life:
Voice recorder:
Hard drive capacity:
Built-in FM radio:
Wireless projection range :
Support for WMV and MP2 formats:
Screen size:
Weight:
Model A
Yes
4 hr
No
10 Gb
Yes
12 ft
No
1.5 in
10 oz
Model B
Yes
4 hr
No
7 Gb
Yes
12 ft
No
2.5 in
10 oz
Strongly prefer
Model A
Strongly prefer
Model B

Experiment 1
• Are more recently used dimensions weighted more in future decisions?
That is, does aligning a dimension make it more salient for some period of time?
Experiment 2
• Are dimension that have been used more frequently weighted more in future decisions?
That is, does repeated alignment along a dimension render that dimension more salient in future encodings?

1 back:
Diagnostic dimension
A
-
B
-
-
C
-
-
D
-
-
-
E
-
-
-
1 v. 2 back:
Diagnostic dimension
A
-
-
B
-
C
-
-
-
-
-
D
-
-
-
-
E
-
-
1 v. 3 back:
Diagnostic dimension
A
-
-
-
B
-
-
-
C
-
-
-
-
D
-
-
-
-
-
-
E
-
-
-
2 v. 3 back:
Diagnostic dimension
A
-
-
-
B
-
-
-
C
-
-
-
-
D
-
-
-
-
-
-
-
-
E
-

Day & Bartels (2005)
Experiment 1
• Each response was coded as a value between 0 and 1
• .5 would be chance; averages closer to 1 indicate a preference for the more recently diagnostic dimension
Average response was .62 (p < .001)
18 out of 20 participant had average ratings greater than .5
Participants weighted a dimension more if it had been used in a more recent decision

Day & Bartels (2005)
Experiment 2
• Found correlation between preference ratings and number of prior uses of a dimension for each participant
• Individual correlations transformed into Fisher’s Z for use in analysis
Average transformed correlation was .20 (p < .01)
Participants weight a dimension more if it had been used more frequently in prior decisions

Day & Bartels (2005)
• Finding an alignable difference along a dimension makes that dimension more salient for a period of time more recently aligned dimensions play a larger role in future decisions
• Repeated alignment of a dimension increases its salience in future encodings higher numbers of repetitions
 greater dimension weights in decisions
• These effects of comparison may go unnoticed, but may have pervasive effects on the mental landscape

• Analogical insertion—interpolation of inferences into the target situation—can occur
• when an analogy is given explicitly
• when an alignable analog has been presented recently
• Online comparisons increase the salience of aligned dimensions for future encodings
• Hypothesis: Continual subtle learning occurs via structural matching and inference
• Fits with MAC/FAC assumption of continual unbidden
•
• Challenges & Future work:
• How recent?
• How similar and in what ways?
• Effects of intervening items?

• Today’s methods of qualitative reasoning are very useful
– Many successful applications in engineering, education, supporting scientific reasoning
• Are they also good models of how people common sense reasoning?
– Yes, but similarity plays major role in reasoning
• Important question for cognitive science
– Central to understanding mental models

Situation description input
F
The standard Qualitative Reasoning community answer
G H

Scenario model

F

G

H
Model Builder
1st principles
Domain Theory
Qualitative
Simulator
Qualitative simulation
F G

H i
F

G

H
F G H i
F

G

H F

G H i
F

G

H
F G H

First-principles qualitative simulation
Useful properties Problematic properties
• Handles incomplete and inexact data
• Supports simple inferences
• Explicit representation of causal theories
– To prevent melting, remove kettle from stove
• Representation of ambiguity
– We easily imagine multiple alternatives in daily reasoning
• Exclusive use of 1stprinciples domain theory
– inconsistent with psychological evidence of strong role for experience-based reasoning
• Exponential behavior
– inconsistent with rapidity & flexibility of human reasoning
• Generates more complex predictions than people report
– logically possible, but physically implausible

Working hypotheses about human common sense reasoning and learning
(Forbus & Gentner, 1997)
• Common sense = Combination of analogical reasoning from experience and first-principles reasoning
• Within-domain analogies provide robustness, rapid predictions
– Human learning requires accumulating lots of concrete examples
– Structured, relational descriptions essential – feature vectors inadequate
• First-principles reasoning emerges slowly as generalizations from examples
– Human learning tends to be conservative
– But human learning also tends to be faster than pure statistical learning
• Qualitative representations are central
– Appropriate level of understanding for communication, action, and generalization

An alternative: Hybrid qualitative simulation
• Most predictions, explanations generated via within-domain analogies
– Provides rapidity and robustness in common cases
– Multiple retrieved behaviors leads to multiple predictions.
– Logically possible behaviors that are rarely observed aren’t predicted.
• 1 st principles reasoning relatively rare
– 1 st principles domain theories fragmentary, partial
• Some 1 st principles knowledge created by generalization over examples
• Much of it taught via language
• We built a similarity-based qualitative simulator to explore this approach

Situatio n
MAC/FAC
A Prototype SQS System
Rerep
Engine
Candidate
Behaviors
Projector
Predictions
Experience
Library SEQL

• Current sources
– Classic QR examples
• Generated envisonments using Gizmo Mk2
– Feedback systems
• Generated descriptions of behavior by hand
• Test of whether system can operate without a complete 1 st principles domain theory
• Each case consists of a qualitative state
– Individuals, ordinal relations, model fragments
– Concrete information about entities (stand-in for perceptual properties)
– Description of transitions to other states

Example: Two Containers Liquid Flow
State0
↓(AmountOf Water Liquid F)
↑(AmountOf Water Liquid G)
↓(Pressure Wf)
↑(Pressure Wg)
(> (Pressure Wf)
(pressure Wg))
(activeMF LiquidFlow)
State1
↑(AmountOf Water Liquid F)
↓(AmountOf Water Liquid G)
↑(Pressure Wf)
↓(Pressure Wg)
(< (Pressure Wf)
(pressure Wg))
(activeMF LiquidFlow)
State2 →(AmountOf Water Liquid F)
→(AmountOf Water Liquid G)
→(Pressure Wf)
→(Pressure Wg)
(= (Pressure Wf)
(pressure Wg))
(not (activeMF LiquidFlow))

Input Scenario
↓(AmountOf Water Liquid Beaker)
↑(AmountOf Water Liquid Vial)
↓(Pressure Wb)
↑(Pressure Wv)
(> (Pressure Wb)
(pressure Wv))
→(AmountOf Water Liquid Beaker)
→(AmountOf Water Liquid Vial)
→(Pressure Wb)
→(Pressure Wv)
(= (Pressure Wb)
(pressure Wv))
Behavior Prediction

Example: Heat Flow
State0
↓(Temperature Coffee)
↑(Temperature IceCube)
(> (Temperature Coffee)
(Temperature IceCube))
(activeMF HeatFlow)
State1
→(Temperature Coffee)
→(Temperature IceCube)
(= (Temperature Coffee)
(Temperature IceCube))
(not (activeMF HeatFlow))
Retrieved analogue
Input
Scenario
Input Scenario
↓(Temperature Brick)
↑(Temperature Water)
(> (Temperature Brick)
(Temperature Water))
(activeMF HeatFlow)
Predicted Behavior
→(Temperature Brick)
→(Temperature Water)
(= (Temperature Brick)
(Temperature Water))
(not (activeMF HeatFlow))

Example: Discrete action feedback system

Feedback Control System
Sensor
Comparator
Controller
Actuator
Temperature set point
Room air
Room
Oven
Heat flow process
Furnace on process
Water Level Regulation System
Floating ball
Ball Stick
String + Pulleys
Valve
Proper water level
Tank water
Water tank
Water supply
Liquid flow process
Valve open process

Quantities
(Temperature
Room)vs.SetPoint
(Ds (temperature Room))
(activeMF FurnaceOn)
(activeMF HeatFlow)
S1 S2 S3 S4 S5 S6
< = > > = <
1
Yes
Yes
-1
No
Yes
Retrieved Behavior
S1
S6 S2
S5
S3
S4

Retrieved Behavior
Quantities
(Temperature
Room)vs.SetPoint
S1 S2 S3 S4 S5 S6
< = > > = <
(Ds (temperature Room))
(activeMF FurnaceOn)
(activeMF HeatFlow)
1
Yes
Yes
-1
No
Yes
Quantities
(Level TankWater) vs.
ProperWaterLevel
(Ds (Level TankWater))
(activeMF ValveOpen)
(activeMF LiquidFlow)
S1 S2 S3 S4 S5 S6
< = > > = <
1
Yes
Yes
Predicted Behavior
-1
No
Yes

Example: Proportional action control system
• Amount of correction applied is proportional to the error signal
• SQS prototype with current library makes incorrect prediction
– Retrieves discrete-action controller behavior
– Currently has no means of detecting inconsistencies
• Possible solutions
– Include some first-principles reasoning for reality checks
– When failure detected, add new behavior to Experience
Library to improve future performance

Two mappings, how to combine?
A

P(Wf)
F

Q+
P(Wg)

Level(Wf)
FR(F

G)
Level(Wg)
G 
Q+


Q+
B 
Aof(Wf)
II+
Aof(Wg)


Q+

H
A B
F G H

• Retrieve behaviors for unexplained parts of system
• Combine by re-evaluating closed-world assumptions
Perform influence resolution to combine influences across cases
F G H

Next steps: Hybrid qualitative simulation
• Significantly expand Experience Library
– Plan: Use EA NLU system to describe qualitative states in
QRG Controlled English
• Test skolem resolution strategies
– Identify hypothesized entities with unmapped current situation entities when possible.
• Formulate criteria for using multiple remindings
– When to generate alternate predicted behaviors?
• Develop more selective rerepresentation strategies
– Currently performed exhaustively
• Explore learning strategies
– Store rerepresented results and new behaviors
– Use SEQL to construct generalizations

• Evans classic 1968 work ANALOGY
– Miller Analogies Test geometric problems
– Non-trivial human intelligence task
• Goal of our simulation:
– Show that general-purpose simulations can handle this task
– Another source of data for tuning visual representations in our sketching system

Sketching the Geometric Analogy Problems
A B C
1 2 3 4 5

Finding the Answer: Evans
A is to B as C is to 1 , 2 , 3 , 4 or 5 ?
• Compute all transformations A g
B , C g
1 , C g
2 , …
• Search for best match between transformation for
A g
B with all of the transformations for C g
1 , C g
2 ,
…

A
B
Finding the Answer: Our simulation
A is to B as C is to 1 , 2 , 3 , 4 or 5 ?
SME AB
Differences compared at second level
C
1
SME
SME
C1
...
...
C5
Answer 1
...
...
Answer 5
5
SME
SME

Results
(Based on Evans’ answer key)
MAT Problems ANALOGY sKEA/SME
1-9,11, 13-18, 20 Correct
10 Incorrect
12
19
Correct
Correct
Correct (prefers reflection)
Correct (prefers rotation)
Incorrect (prefers rotation)
Correct (prefers rotation)

• SME + qualitative spatial representations provide a basis for solving geometric analogy problems
• Two-stage structure mapping provides an elegant model for this task
– Explicit transformation rules unnecessary
– Applicable to other analogy tasks?