Common Sense on the Envelope

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Common Sense on the Envelope

• Praveen K. Paritosh Kenneth D. Forbus
• Qualitative Reasoning Group
• Department of Computer Science
• Northwestern University
• http//www.qrg.nwu.edu/

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Outline

• Back of the Envelope Reasoning
• Common Sense QR
• Relevant Research
• A Similarity-Based Model
• Open Issues
• Conclusions

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Real-world examples of BotE
How muchoxygen is left?
Is anyone still alive in there?
Kursk
Mir
How longto repair it?
USS Cole
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Examples of Back of the Envelope Reasoning
Q2.  Estimate the drag force on a bicycle and
rider traveling at 20 mph. Q3.  Estimate the
energy stored in a new 9-volt transistor battery.
Q5.  How long does it take to reach home from
your office, or to get ready in the morning? Q6. 
How much money would you be spending on that
vacation you have planned? Q7.  You know a
recipe that you made for yourself some time back
now you have to make it for eight people, and
you want it less spicy and you ran out of one of
the ingredients.
Claim Same processes underlie Q2, Q3 and Q5, Q6,
Q7.
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Back of the Envelope (BotE) Reasoning

• Accurate data/models unavailable
• Available data incomplete and/or inconsistent.
• Need answers fast
• Need a quantitative answer!

Qualitative ? Not Quantitative
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Where do we do BotE 1

• Real-world problems (nearly always incompletely
  specified)
• Engineering/Design/Experimental Science
• Evaluating Feasibility of an Idea
• Planning Experiments and sizing components
• Setting up and double-checking detailed analysis
• Domains where BotE is the best one can do
• Environmental Science (Consider a Spherical Cow,
  Harte, 1988)
• Biophysics (OConnor and Spotila, 1992)

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Where do we do BotE 2

• Everyday physical situations
• How long will it take to get there?
• Do I have enough money with me?
• How much of the load can I carry at once?
• A world of quantitative dimensions Need to make
  quick, quantitative estimates to
• Interact (How much salt do I add while cooking
  some recipe?)
• Understand (Is 7,000 too expensive for this
  laptop?)

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The Specificity/Economy Tradeoff
Specificity Resolution and certainty in the
answer Resources Time, information,
formalization and computation required to reach
the answer.
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What underlies BotE

• Qualitative Reasoning
• Provides analytic framework
• Facilitates comparison
• Similarity from similar scenarios
• Borrow modeling assumptions
• Supply default, pre-computed information,
  parameter values
• Reality check
• Generalization along quantitative dimensions
• Whats high, low or moderate?
• 1 Amp is too high a current for a walkman

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Constraints guiding Common Sense QR
1. Incompleteness Domain theories incomplete in
coverage.
2. Concreteness Knowledge of concrete, specific
situations (made use of by analogical reasoning)
in addition to first-principles reasoning.
3. Highly experiential Experience improves -
ability to reason through similar scenarios. -
intuitions for what is reasonable, high, low in a
domain.
4. Focused reasoning Tight reasoning, as opposed
to maintaining ambiguity for completeness
5. Pervasively quantitative Real-world actions
require that estimates manifest as exact values.
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Psychological Research

• Quantitative estimation
• Intuitive statistics (Peterson and Beach, 1967)
• Heuristics and biases (Tversky and Kahneman,
  1974)
• Metrics and mappings (Brown and Siegler, 1993)
• Estimation in mechanical engineering curricula
  (Linder, 1999)
• Models of similarity
• Multidimensional scaling (Shepard, 1962
  Torgerson, 1965)
• Set-theoretic feature based account (Tversky,
  1977)
• Structure-mapping engine (Gentner, 1983)
• Commonalities, alignable, and non-alignable
  differences (Markman and Gentner, 1993)
• An account of generalization SEQL

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SME Structure-Mapping Engine
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SEQL Category learning via progressive alignment

• Produces abstractions incrementally, based on
  commonalties resulting from comparisons between
  exemplars.
• Models conservative nature of concept learning
• Skorstad, Gentner, Medin (1988) showed SEQL
  could model sequence effects in learning

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Similarity-Based Model of BotE Reasoning

• Two distinct processes -
• Direct parameter estimation
• Domain knowledge
• Previous experience
• Adapt from one or more similar scenarios
• Building an estimation model
• Parameter to be estimated not directly available
• Estimation model relates it to parameters that
  can be directly estimated
• Possibly recursive

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A Simple Example

• How many pieces of popcorn would fit in this
  room?
• Possibly dont have num-popcorn in memory,
• num-popcorn volume-room/volume-popcorn (1)
• Approximating room to a cuboid, and popcorn to a
  cube (considering the voids left after packing in
  popcorn kernels this is a reasonable assumption),
  
• num-popcorn lbh / a3 (2)

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An Extended Example

• Estimate the energy stored in a 9v transistor
  battery. (Linder, 1999)

• Nobody used first-principles chemistry.
• People recalled walkmans, clocks, flashlights
  and other scenarios where they came across 9v
  battery.
• A lot of people adapted estimates from 1.5v
  battery, or car battery.

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An example solution
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Open Issue 1

• How do quantitative dimensions factor in our
  similarity judgments?
• Quantitative dimensions effect similarity
  judgments.
• Aligned versus non-aligned dimensions
• Quantitative similarities/differences ?
  Relational representations

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Open Issue 2

• What are the quantitative inferences that analogy
  sanctions?
• Dont need an overall match to make estimates
  along a certain dimension only
• A good match does not mean that all the aligned
  dimensions in the base and the target are equally
  close.

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Open Issue 3

• How do we generalize along quantitative
  dimensions?
• No formal/given qualitatively distinct regions
• e.g., price of a computer
• Experiential development of a sense of
  quantitativeness
• Abstract central tendency and distributions
• What does a mid-range server cost?
• Managing multiple distributions of different
  quantities of the same dimension
• A notion of expensiveness over prices of
  different things
• Cars, computers, houses are expensive, but houses
  are the most expensive.

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Conclusions

• Understanding BotE is an interesting problem
• Key component of commonsense qualitative
  reasoning.
• Important real-world problem-solving strategy
• Raises new questions about similarity.
• Current efforts
• Implementation in progress
• Using IPSA (Pisan, 1998) as starting point
• Exploring extensions to SME, SEQL
• Taking account of numerical similarity in SME
• Computing distribution information via
  alignable differences in SEQL

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Extra slides
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Q2 Estimate the drag force on a bicycle and rider
traveling at 20 mph (9 m/s).
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(No Transcript)
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Structure-Mapping Theory (Gentner, 1983)

• Analogy involves
• 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
• 11 mappings Each item can be matched with at
  most one other
• Systematicity Prefer mappings involving systems
  of relations, esp. including higher-order
  relations
• Growing body of evidence that same processes are
  used in perception, problem solving, conceptual
  change (Goldstone, Medin, Gentner, 1991
  Markman Gentner, 1993 Medin, Goldstone,
  Gentner, 1993 Goldstone 1994 Gentner Markman,
  1995, 1997)

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Correctness

• Generate multiple solutions
• Use the sense of quantity for a reality check
• Is that too small?

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Integrated Problem Solving Architecture (Pisan,
1998)