Progress on the Structure-Mapping Architecture

forLearning

Dedre Gentner

Kenneth D. Forbus

Northwestern University

Symbolic modeling crucial for understanding cognition

• 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

Overview

• 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

• 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

Inferenceis selective. Not all base knowledge is imported

Candidate

Inferencecomplete

s common structure

SEQL

MAC/FAC

SME

Similarity-based

retrieval of relevant examples

and knowledge

Analyzing similarities and

differences, reasoning from

experience, applying relational

knowledge

Incrementally constructs

generalizations, producing human-

like relational abstractions within similar number of

examples.

Potentially relevant precedent

s

US Israel

Iraq Iran

WMD Nuclear Reactor

Invasion Bombing

Functional Overview

Long-term memory

Psychological Studies

1. Case-comparison method Previous work: Transfer New work: Learning of principles

2. Unaware analogical inferencePrevious work: Unaware inferenceNew work: Attitude congeniality & unaware

inferencesNew work: Unaware alignment-based

decision making

Analogy

• 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):

SimilaritySpecies-general

AnalogySpecies-restricted

AA

BB CD

Relational match

A

A B

Object match

Analogical Encoding in Learning

• Analogy can promote learning– Induces structural alignment

– Generates candidate inferences FamiliarSituation

NewSituation

Inferences

Standard analogical learning:

• 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

RelationalSchema

NewSituation

NewSituation

Analogical encoding:

NewSituationCompare

Separate Cases ConditionRead each case, write principle and give advice.

Comparison ConditionCompare the two cases and write the commonalities

case 1

case 2

SimulatedNegotiation

Case Comparison Method in Learning to Negotiate 

Studies of MBAs learning negotiation strategiesStudents study two analogous cases prior to negotiating

Loewenstein, Thompson & Gentner, 1999Thompson, Gentner & Loewenstein, 2000Gentner, Loewenstein & Thompson, 2003

On a new analogous case

Negotiation transfer performance across three studies: Proportion using strategy exemplified in the cases

Separate Cases

N=83

CompareN=81

0

.1

.2

.3

.4

.5

.6

.7

Pro

p.

Form

ing

Con

tin

gen

t C

on

tracts

.8

No CasesN=42

.24

.58*

.19

Better schemas Better transfer

0

.1

.2

.3

.4

.5

.6

.7

.8P

rop

. Form

ing

C

on

tin

gen

t C

on

tracts

Separate Cases

Compare

Dyadic Schema Rating0 0.5 1.0 1.5 2.0

So, what happens if we just give them the principle?

Aligning case and principle improves ability to use principle in transfer

Separate Cases

N=26 dyads

CompareN=27 dyads

.19

.44*

0

.1

.2

.3

.4

.5

.6

.7

Pro

p.

Form

ing

Con

tin

gen

t C

on

tracts

Error bars assume binomial with prop=.19 (baseline)

Case 1________________

Case 2______________________

Case 1Case 2___________________________________________

Test: Face-to-face negotiation

Separate ComparePrinciple PrinciplePlus case and Case

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 soloCase 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: caseppl and pplcase

• 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

Principle: Contingent ContractA 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.

Training CaseTwo 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.

Recall Scores (Max. = 8)

t(50) = 2.10, p = 0.041

Mean R

eca

ll Sco

re

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Separate Compare

Condition (26) (26)

2.5

3.4

Two blind ratersAgreement: 94%

Gentner & Colhoun

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 MerchantN=14; 7 sep, 7 comp

(4 days)

Long term Recall

New test caseN=14; 7 sep, 7 comp

Delayed Recall

Immediate Recall Scores Both Orders

0

1

2

3

4

5

6

Separate Compare

T(23) = -2.44, p = 0.023

Mean R

eca

ll Sco

re

(11) (12)

3.1

4.4

Delayed Recall Scores Both Order

Combines two groups with slightly different procedures

0

1

2

3

4

5

6

Separate Compare

Mean R

eca

ll Sco

re

(11) (12)

3.1

4.3

T(21) = -1.91, p = 0.07

Comparing case and principle greatly benefits comprehension of principle

The case provides firm relational structureand a clear (though overly specific)

interpretation of the relational terms

Comparing case with principle prompts re-representation and abstraction of the relational structure

Conclusions

Comparison group > Separate group

Case-first groups > Principle-first groups

Practical Implications

• 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 comparison-based instruction

– Harvard Business School• Exploring comparison-based method

– CMU – discussions with Marsha Lovett

Analogy as generally conceived:

• Conscious

• Discerning

• Deliberate

• Effortful

Unaware Analogical Inference

Current Studies:

• Non-aware

• Oblivious

• Non-deliberate

• Accidental

Suggestive evidence: Blanchette & Dunbar, 2002; Moreau, Markman & Lehman, 2001

New thrust: Study of “unwitting analogy”

• Can analogical inferences occur without awareness ofmaking the inferences?

• Can analogical inferences occur without awareness ofthe analogy itself?

• Can the highlighting effect of analogical alignmentInfluence future decision-making?

Analogical insertion effect:believing that the analogical inference from BT actually occurred in T

• Evidence for analogical insertionBlanchette & Dunbar 1999Analogy: 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?

Read paragraph “Is it OK to be gay”

Old-New recognition test

15-min filled delay

Analogy groupSecond paragraph analogizing

gayness to left-handedness

Control groupNo further text

Attitudes towards gayness assessed (Mass testing)

Rate soundness of analogy

3-4 weeks (unrelated context)

Perrott, Gentner & Bodenhausen, 2005

Proportion “old” responses

0

0.2

0.4

0.6

0.8

1

Text Item AnalogicalInference

PlausibleFalse Item

Blatantly FalseItem

Prop

orti

on o

f "o

ld"

resp

onse

s

Analogy

No-Analogy

*

Condition(2) X Item type(4)

F(3, 228) = 4.97, p= .002, MSE = .048

Perrott, Gentner & Bodenhausen, 2005

Results within analogy group

Attitudes towards gays within predicted the rated soundness of the analogy

ButLikelihood 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

Can analogical insertion occur without awareness of the analogy

• 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

Current Studies

• 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?

Day & Gentner; 2003, in prep

TEST:

• Participants answer TF questions about passages

• Dependent measure: Answering True to questions that are inferences from earlier analogous passages.

• If participants use analogical inference from the earlier similar base passage,

they will understand the target differently, depending on which base version they got.

Experiment 1

Two versions of each base passage

Target has some ambiguous portions

Example Source Passages

Base 1:Wealthy elderly woman dies mysteriouslyHer 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 mysteriouslyHer 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

Expt. 1 Results: More false recognitions for base-consistent statements

0

100

50

Base-consistent Base-inconsistent

73%

25%

Per

cen

tage

‘ye

s’ r

esp

onse

s

t (19) = 4.79, p < .001

Using base consistency as a within-subjects factor

Day & Gentner, 2003

Results: Analogical insertion

• 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 passagesBut, 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

E1

Experiment 3

Is the analogical insertion effect occurring during online comprehension of target, or is it a later memory error?

Experiment 3: Self-paced Reading Task

“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.”

• 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:

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

“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.”

• 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:

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

Results10

7

Base-consistent

Base-inconsistent

Rea

din

g ti

me

(sec

)

9

8

6

5

4

6.40

8.88

F (1,19) = 6.81, p < .05

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 ?

Day & Gentner; 2003, in prep

•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?

Current studies

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 inperceived 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 useRepeated alignment & use renders the dimension more salient in future encodings

Day & Bartels (2005)

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:

Yes4 hrNo

7 GbYes12 ftNo

2.5 in10 oz

Yes4 hrNo

4 GbYes12 ftNo

2.5 in10 oz

Model A Model B

Strongly prefer Model A

Strongly prefer Model B

Method

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:

Yes4 hrNo

7 GbYes12 ftNo

2.5 in10 oz

Yes4 hrNo

4 GbYes12 ftNo

2.5 in10 oz

Model A Model B

Strongly prefer Model A

Strongly prefer Model B

Method

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:

Yes4 hrNo

10 GbYes12 ftNo

1.5 in10 oz

Yes4 hrNo

7 GbYes12 ftNo

2.5 in10 oz

Model A Model B

Strongly prefer Model A

Strongly prefer Model B

Experiments

• 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 1

• 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?

Experiment 2

Diagnostic dimensionA--

B-

-

C

---

D----

E----

1 v. 2 back:

Diagnostic dimensionA-

B--

C --

D---

E---

1 back:

Diagnostic dimensionA---

B- --

C

----

D--

--

E-----

1 v. 3 back:Diagnostic dimension

A-- -

B- --

C

----

D--- -

E-----

2 v. 3 back:

Types of item series

Results

• 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

Experiment 1

Day & Bartels (2005)

Results

• 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

Experiment 2

Day & Bartels (2005)

ConclusionsDay & 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

Resistance is futile

•

• 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 retrieval• Challenges & Future work:

• How recent?• How similar and in what ways?• Effects of intervening items?

How do people do common sense reasoning?

• 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

The standard Qualitative Reasoning community answer

1st principlesDomain Theory

Model BuilderQualitativeSimulator

F G H F G H

F G H F G H

F G H

F G H

F G H

F G HF G H

i

ii

Situation description inputScenario model

Qualitativesimulation

First-principles qualitative simulation

• 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 1st-principles 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

Useful properties Problematic properties

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.

• 1st principles reasoning relatively rare– 1st principles domain theories fragmentary, partial

• Some 1st principles knowledge created by generalization over examples

• Much of it taught via language

• We built a similarity-based qualitative simulator to explore this approach

A Prototype SQS System

MAC/FAC

ExperienceLibrary

Situation

SEQL

PredictionsRerepEngine

Candidate Behaviors Projector

Experience Library Contents

• 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 1st-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

↓(AmountOf Water Liquid F)↑(AmountOf Water Liquid G)↓(Pressure Wf)↑(Pressure Wg)(> (Pressure Wf) (pressure Wg))(activeMF LiquidFlow)

↑(AmountOf Water Liquid F)↓(AmountOf Water Liquid G)↑(Pressure Wf)↓(Pressure Wg)(< (Pressure Wf) (pressure Wg))(activeMF LiquidFlow)

→(AmountOf Water Liquid F)→(AmountOf Water Liquid G)→(Pressure Wf)→(Pressure Wg)(= (Pressure Wf) (pressure Wg))(not (activeMF LiquidFlow))

State0 State1

State2

↓(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))

Input Scenario

Behavior Prediction

Example: Heat Flow

InputScenario

Retrievedanalogue

↓(Temperature Coffee)↑(Temperature IceCube)(> (Temperature Coffee) (Temperature IceCube))(activeMF HeatFlow)

State0

→(Temperature Coffee)→(Temperature IceCube)(= (Temperature Coffee) (Temperature IceCube))(not (activeMF HeatFlow))

State1

↓(Temperature Brick)↑(Temperature Water)(> (Temperature Brick) (Temperature Water))(activeMF HeatFlow)

Input Scenario

→(Temperature Brick)→(Temperature Water)(= (Temperature Brick) (Temperature Water))(not (activeMF HeatFlow))

Predicted Behavior

Example: Discrete action feedback system

Mappings for Feedback Example

Feedback Control System Water Level Regulation System

Sensor Floating ball

Comparator Ball Stick

Controller String + Pulleys

Actuator Valve

Temperature set point Proper water level

Room air Tank water

Room Water tank

Oven Water supply

Heat flow process Liquid flow process

Furnace on process Valve open process

Stored Feedback System Behavior

S1

S2

S3

S4

S5

S6

Quantities S1 S2 S3 S4 S5 S6

(Temperature Room)vs.SetPoint

< = > > = <

(Ds (temperature Room))

1 -1

(activeMF FurnaceOn) Yes No

(activeMF HeatFlow) Yes YesRetrieved Behavior

Mapped Feedback System Behavior

Quantities S1 S2 S3 S4 S5 S6

(Temperature Room)vs.SetPoint

< = > > = <

(Ds (temperature Room))

1 -1

(activeMF FurnaceOn) Yes No

(activeMF HeatFlow) Yes Yes

Retrieved Behavior

Quantities S1 S2 S3 S4 S5 S6

(Level TankWater) vs. ProperWaterLevel

< = > > = <

(Ds (Level TankWater)) 1 -1

(activeMF ValveOpen) Yes No

(activeMF LiquidFlow) Yes Yes

Predicted Behavior

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

F G H

Current Issue: Combining Behaviors

FR(FG)

Aof(Wf)

Level(Wf)

P(Wf)

Aof(Wg)

Level(Wg)

P(Wg)

Q+

I-

A B

Q+

Q+

Q+

I+

F

A

G

B

H

Two mappings, how to combine

?

Pastiche Mappings

• Retrieve behaviors for unexplained parts of system• Combine by re-evaluating closed-world

assumptions

F G H

Perform influence resolution to

combine influences across cases

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

Geometric Analogy Problems

• 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

54321

CB

Finding the Answer: Evans

A is to B as C is to 1, 2, 3, 4 or 5?

• Compute all transformations AB, C1, C2, …• Search for best match between transformation for

AB with all of the transformations for C1, C2, …

Finding the Answer: Our simulation

A is to B as C is to 1, 2, 3, 4 or 5?

SMEA

B

C

5

1 SME

SME

AB

C1

C5

...

...

SME

SME

Answer 1

Answer 5

...

...

Two-stage structure mapping

Differences compared at second level

Results(Based on Evans’ answer key)

MAT Problems ANALOGY sKEA/SME

1-9,11, 13-18, 20 Correct Correct

10 Incorrect Correct

12 Correct (prefers reflection)

Incorrect (prefers rotation)

19 Correct (prefers rotation)

Correct (prefers rotation)

Problem case 12

Summary: Geometric Analogies Simulation

• 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?

Future Directions

THE END