Reminder • Midterm is two weeks from today (Oct

21st!)– Closed book, closed notes, no computers or

calculators or electronic devices– Will cover all material till then.

Overview

• Why qualitative reasoning?• Principles of qualitative representation and

reasoning• Using qualitative reasoning in cognitive modeling

What is qualitative physics?

• Formalizing the intuitive knowledge of the physical world– From person on the street to expert scientists and

engineers

• Developing reasoning methods that use such knowledge for interesting tasks.

• Developing computational models of human commonsense reasoning

Example

• What can happen when you leave a tea kettle on a stove unattended for an hour?

Example

• What can happen when you leave a tea kettle on a stove unattended for an hour?

T(s) T(w)

This conclusion can be reached without numerical parameters or differential

equations!

Knowing what might happen suggests when

more precise knowledge is needed

What will this system do?

Example

• Why are there seasons?

Example

• Suppose we have two identical ice cube trays.One tray is filled with cold tap water.The other tray is filled with warm tap water.We place both trays in a freezer at the same time.Q: Which will freeze first, the warmer water or the cooler water? And why?

Why do qualitative physics?

• Understanding the mind– What do people know? Physical, social, and mental

worlds.

– Universal, but with broad ranges of expertise• Unlike vision, which is automatic

• Unlike medical diagnosis

Why do qualitative physics?

• Can build useful software and systems– Intelligent tutoring systems and learning environments

– Engineering Problem Solving

• Diagnosis/Troubleshooting

• Monitoring

• Design

• Failure Modes and Effects Analysis (FMEA)

– Robots

– Models for understanding analogies and metaphors

• “Ricki blew up at Lucy”

Human-like understanding of complex systems requires qualitative models

Monitoring, diagnosis, failure modes and effects analysis,

creating control software,explanation generation,

tutoring…

Example: Understanding Engineering Analysis

• Important in understanding engineering, scientific reasoning

• Useful model: Solving textbook problems

Cycles

Uniform-StateUniform Flow

Initial State Final State

Single State Missing Information

First Thermodynamics Course

AirT= 25CP= ?

TurbineW=?Air

Air flow

Heater

Turbine

Cooler

Qualitative reasoning in engineering analysis: Example

• No mass flows in or out of the system

• Volume can increase until stop is reached

• Spring force will add to air pressure when it contacts the top

• The temperature will rise, or stay the same if saturated

Heat

Key Ideas of Qualitative Physics

• Quantize the continuous for symbolic reasoning– Example: Represent numbers via signs or ordinal

relationships– Example: Divide space up into meaningful regions

• Represent partial knowledge about the world– Example: Is the melting temperature of aluminum

higher than the temperature of an electric stove?– Example: “We’re on Rt 66” versus “We’re at Exit 42

on Rt 66”

• Reason with partial knowledge about the world– Example: Pulling the kettle off before all the water

boils away will prevent it from melting.– Example: “We just passed Exit 42, and before that was

41. We should see 43 soon.”

Comparing qualitative and traditional mathematics

• Traditional math provides detailed answers– Often more detailed than

needed– Imposes unrealistic input

requirements

• Qualitative math provides natural level of detail– Allows for partial

knowledge– Expresses intuition of

causality

F = MA

A Q+ F

A Q- M

Traditional quantitativeversion

Qualitative version

Example 1: How far will it roll?

• Infants sees baseline sequence of events – medium cylinder rolls

towards wheeled toy, collides, toy rolls some distance

• Infant sees new sequence of events– Like before, but with larger

or smaller cylinder

– Possible or impossible outcome

– Infants look longer event violates their expectations

Example 2: Understanding Science books

• Example: First field guide to weather, National Audubon Society

• “Water vapor is an invisible gas in the air. The amount of water vapor, which is called the relative humidity, can be anywhere between 0 and 100 percent. A relative humidity of 100 percent means that the air is saturated – as full of water vapor as it can be. Most water vapor comes from evaporation. When the sun heats the liquid water in the earth’s oceans, lakes, and rivers, some of it changes into water vapor and rises into the air. The atmosphere also gets small amounts of water vapor from plants and from moisture in soil.”

Qualitative Process Theory

• Key ideas (Forbus, 1981, 1984):– Quantity space: Ordinal relationships between

parameters provide a useful qualitative representation of numerical values

– Influences: A causal, qualitative mathematics that supports partial information provides a natural way to encode relationships involving continuous parameters

– Physical processes: Physical processes provide a notion of mechanism for natural changes.

Quantity Space

• Value defined in terms of ordinal relationships with other quantities

• Contents dynamically inferred based on distinctions imposed by rest of model

• Can be a partial order• Limit points are values

where processes change activation

Twater

Tboil

Tfreeze

Tstove

Examples of limit points in text

• “The temperature at which condensation occurs is called the dew point.”

• “The amount of water vapor, which is called the relative humidity, can be anywhere between 0 and 100 percent. A relative humidity of 100 percent means that the air is saturated – as full of water vapor as it can be.”

Qualitative proportionalities

• Examples– (qprop (T ?o) (heat ?o))– (qprop- (acceleration ?o) (mass ?o))

• Semantics of (qprop A B) f s.t. A = f(…,B,…) f is increasing monotonic

in B– For qprop-, decreasing monotonic– B is a causal antecedent of A

• Implications– Weakest causal connection that can propagate sign

information– Partial information about dependency requires closed

world assumption for reasoning

Qualitative proportionalities in text

• “The more air there is, the more it weighs and the greater its pressure”– (qprop (weight ?air-mass) (n-molecules ?air-mass))

– (qprop (pressure ?air-mass) (n-molecules ?air-mass))

• “As the air temperature goes up, the relative humidity goes down.”– (qprop- (relative-humidity ?air-mass) (temperature ?air-mass))

• Source: Weather: An Explore Your World ™ Handbook. Discovery Press

Correspondences

• Example:– (correspondence ((force spring) 0) ((position spring) 0)

– (qprop- (force spring) (position spring))

• Pins down a point in the implicit function for the qualitative proportionalities constraining a quantity.

• Enables propagation of ordinal information across qualitative proportionalities.

Correspondences as explanation• (correspondence

((distance-rolled bug) Initial) ((size cylinder) Medium))(qprop (distance-rolled bug) (size cylinder)))

• (< (size cylinder) Medium) predicts(< (distance-rolled bug) Initial)

Initial

Model Fragments

• Encode conditions under which domain knowledge is relevant– Participants are the individuals and relationships that

must hold before it makes sense to think about it

– Conditions must be true for it to hold (i.e., be active)

– Consequences are the direct implications of it being active.

• (defmodelFragment saturated :participants ((am :type air-mass)) :conditions ((= (relative-humidity am) 100-percent) :consequences ((saturated am)))

Physical Processes

• A kind of model fragment• But also has direct influences, which are

constraints on derivatives• Examples:

– “Most water [in the air] comes from evaporation. When the sun heats the liquid water in the earth’s oceans, lakes, and rivers, some of it changes into water vapor and rises into the air”

– (I+ (water-vapor am) (rate evap))(I- (amount-of water-body) (rate evap))

– N.B. accumulating bodies of water into an abstract entity, based on shared properties. This is a transfer pattern of influences.

Semantics of direct influences

• I+(A,b) D[A]=…+b+…• I-(A,b) D[A]=…-b+… • Direct influences combine via addition

– Information about relative rates can disambiguate

– Abstract nature of qprop no loss of generality in expressing qualitative ODE’s

• Direct influences only occur in physical processes (sole mechanism assumption)

• Closed-world assumption needed to determine change

Example of a physical process(defModelFragment heat-flow :subclass-of (physical-process) :participants ((the-src :type thermal-physob) (the-dst :type thermal-physob) (the-path :type heat-path :constraints ((heat-connection the-path the-src the-dst)))) :conditions ((heat-aligned the-path) (> (temperature the-src) (temperature the-dst))) :quantities ((heat-flow-rate :type heat-flow-rate)) :consequences ((Q= heat-flow-rate (- (temperature the-src) (temperature the-dst))) (I- (heat the-src) heat-flow-rate) (I+ (heat the-dst) heat-flow-rate)))

Causality in QP theory(Forbus, 1981; 1984)

• All causal changes stem from physical processes

• Changes propagate from quantities directly influenced by processes through causal laws to indirectly influenced quantities

• Naturally models human reasoning in many domains (i.e., fluids, heat, motion…)

F G

Liquid FlowF G

Amount-of(Wf)

Level(Wf)

Pressure(F)

Q+

Q+

I-

Amount-of(Wg)

Level(Wg)

Pressure(G)

Q+

Q+

I+

Time and change

• Time individuated by changes in qualitative state

• Qualitative states differentiated by– Set of active physical

processes– What dynamic

relationships hold– Quantity space values

Spring state

Block velocity

Event structure in QR and NL

• Hypothesis: QR decomposition of event structure is tightly coupled with event structure in NL semantics

• Similarities– Both carve continuous change into symbolic,

meaningful chunks

• Differences– QR suggests finer-grained decomposition on physical

grounds

– NL also decomposes based on non-physical aspects

– QR captures more possibilities

Partial knowledge Ambiguity

T(s) T(w)

Envisionments describe all

possible qualitative behaviors

Stopping,

dynamic friction

Stopping, staticfriction

Qualitative states and transitions

Many dynamical properties of systemscan be reasoned about based on

graph properties of envisionments

Loop in states oscillatio

n

Spring-block

oscillator envisionme

nt

Useful properties of first-principles qualitative simulation

• Handles incomplete/inexact data– Easier to extract qualitative data via perception

• 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

• Caveat: There are some complexities when viewed as a psychological model

Problems with standard QR as psychological model

• Exclusive use of 1st-principles domain theory – inconsistent with psychological evidence of

strong role for experience-based reasoning

• Exponential behavior of 1st-principles qualitative simulation – inconsistent with rapidity & flexibility of

human reasoning

• Generates more complex predictions than people report – logically possible, but physically

implausible

???

But, QR representations are psychologically plausible(once assumption of exclusive 1st-principle reasoning

is removed)

• Evidence: Protocol analyses– Kuipers, Bredeweg & deKonig, Forbus & Gentner, ...

• Examples– Signs, quantity space representations of number

– Symbolic descriptions of shape and space

– Influences, causal relationships

– Organizing abstractions: e.g., devices, processes

– Relevance conditions, modeling assumptions (for experts at least)

Analogy crucial incommon sense reasoning

Mr. Boffo, by Joe Martin, http://www.mrboffo.com, 3/16/98

RememberedSituation retrieved from

long-term memory

Qualitative simulation via analogical reasoningObserved

behavior

Analogical inference

provides prediction

Memory matched with

previous situation

Ruling out 1st principles predictions via analogical

reasoning

T(w) = T(fire)

T(w) constant

T(w) increasingT(w) = TBoil(w)

Never seen it happen

Building qualitative models yourself

• No better way to understand a formalism than to use it

• We have a user-friendly tool to help you do this.– VModel has been successfully used by middle-school

students in the Chicago Public Schools.

• Next time…