Qualitative Reasoning: An Introduction · • Traditional (or quantitative) approach in physics and...

Qualitative Reasoning: An Introduction

Muhammad Fadlisyah

PMA Group, Informatics Department, University of Oslo

February 3, 2009

Overview

• Basic ideas of QR

• Basic representations of QR

• Application of QR

• A quiz!

2

An example: boiling water

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

3

An example: boiling water (cont)

• Traditional (or quantitative) approach in physics and engineering: using differential equations (ODEs) to describe the system and then drawing inferences about it.

• ODEs: analytical or numerical solution.

• Need: temperature of the water, temperature of the stove, the rate of change water temperature, water volume, boiling point, all initial conditions needed…

4

Quantitative approach

PhysicalSystem

DifferentialEquation

ActualBehavior

ContinuousFunctions

5

An example: boiling water (cont)

• Common sense approach:

6

What is Qualitative Reasoning?

• The area of Artificial Intelligence which creates representations for continuous aspects of the world (such as quantity, space, time) which support reasoning with very little information.

• Focused on scientific and engineering domain.

7

Why Qualitative Reasoning?

• Motivation 1: people draw useful and subtleconclusions about the physical world withoutdifferential equations.

• Motivation 2: Scientist and engineers appear to usequalitative reasoning when initially understanding a problem, setting up more formal methods to solveproblems, interpreting the results of quantitativecalculations and simulations.

• The fact: our knowledge is almost always incomplete, and we would like to be able to reason reliably with theknowledge we have.

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An Example: The Challenger Disaster

• What happened?

• 28 Jan.1986: The Space Shuttle Challenger broke apart 73 seconds into its flight.

• All seven crew members were dead.

• 32 months no‐activity of shuttle program.

9

An Example: The Challenger Disaster(cont)

• The space shuttle: an orbiter, an external tank, two Solid Rocket Boosters (SRBs).

• An O‐ring seal in its right SRB failed at liftoff.

• The failure caused a breachin the SRB joint it sealed, allowing a flare to reachthe outside.

• The SRBs were build by Morton Thiokol, Inc (MTI).

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• Before the launch:• Forecast for 28 Jan.: predictedunsual cold morning, temperature close to ‐1° C (the minimum temp. permitted for launch).

• The low temp. raised concernof MTI’s engineers: effect ofthe temp. on the resilience ofthe rubber O‐rings.

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• From observation since Jan. 1985 (plus analysis and discussions): the post flight inspection of hardware : hot combustion gases had blown, lowest temp. 12° C.

• Conclusion: low temperature indeed caused significantly more hot gas blow‐by occur in the joints.

13


• MTI’s engineers: Not recommended!

• NASA: Not happy.

• MTI’s management: Recommended…

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• The result…

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Qualitative approach

PhysicalSystem

DifferentialEquation

QualitativeModel

ActualBehavior

ContinuousFunctions

QualitativeBehavior

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Qualitative Representations

• No single, universal ”right” or ”best” qualitative representation.

• A spectrum of choices, each with their own advantages and disadvantages.

• A common thing: provide notations for describing and reasoning about continuous properties of physical world.

• Basic representations: quantity, equations, ontology, behavior.

• Two key issues: resolution and composionality.17


Resolution:

• Concerns the level of information detail in a representation (low vs high resolution).

• One QR goal: How little information suffices to draw useful conclusions.

18


Composionality:

• Concerns the ability to combine representations for different aspects of a phenomenon or system to create a representation as a whole.

• One QR goal: to formalize the modeling process itself.

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Representing Quantity

• Most of the research effort has gone into understanding the properties of low –resolution representations, since the properties of high‐resolution representations tend to already be well‐understood due to work in mathematics.

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Representing Quantity (cont)

Representations Description Examples

Status abstraction The lowest representation forcontinuous values.

”normal” & ”not normal””working” & ”not working”

Sign algebra Can be used for reasoning aboutdynamics (continues values and their derivatives).

•”+”, ”‐”, ”0”•”increasing”, ”decreasing”, ”constant”

Finite algebra • Motivation: observations are oftennaturally categorized into a finite setof labels.• Using fuzzy logic.

”very small”, ”small”, ”normal”, ”large”, ”verylarge”

…

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Representing Quantity (cont)

Representations Description Examples

Quantity space • The set of statements containing thevalue of a number.• Using inequalities.• Two kinds of comparison points: limit points and landmark values.

The temperature ofwater in a kettle on a stove: the temperatureof the stove, itsfreezing, boiling points

Interval • A well‐known variable‐resolutionrepresentation for numeical values.• A quantity space: as a partialinformation about set of intervals

[0, 1]

Orders ofmagnitude

•N1 is so large compared to N2 that N2 maybe ignored.•Useful in avoiding ambiguities and in simplifying models since they enablereasoning about phenomena thay maysafely be ignored.

The effort ofevaporation on the levelof a lake maybe ignoredif the dam holding it has burst.

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Representing MathematicalRelationship

• A variety of qualitative representations of mathematical relationships have been developed, often by adopting and adapting systems developed in mathematics.

• Abstraction of the analytic functions are commonly used, to provide lower resolution and compositionality desired.

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Representing MathematicalRelationship

Confluences • Equations constructed from basicarithmetic operations but using onlySign values.• Confluences are solved by propagation of constraints, usingusing generate and test whenunresolvable simultaneities occur.

f = m [*] a

Monotonicfunctions

One of the weakest statements thatcan be made about the relationshipbetween two equations is that whenone increase, the other tends to increase

M+(force, acceleration) : force depends only onthe acceleration, and the function relatingthem is increasingmonotonic.

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Ontology

• Ontology concerns how to carve up the world, i.e. what kinds of things there are and what sorts of relationships can hold between them.

• Ontology is central to qualitative physics because one of its main goals is formalizing the art of building models of physical systems.

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Ontology

Ontology Desc. Advantages/disadvantages

Deviceontology

• Inspired by network theoryand system dynamics (esp. electronic).• A system as a collection ofdevices which have ports for interaction between devices.• The behavior of a device: internal laws, decomposedinto distinct states or operating regions.

(+) Fixed topology: efficientcomputation.(+) Closely related with acceptedstandard used in traditionalengineering.(‐) No guidance for the constructionnetwork model.(‐) Many phenomena do not fit neatly.

…

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Ontology (cont)


Processontology

• People often describechanges in the physical world in terms of processes (motion, liuid flow, boiling).

(+) Intuitively appealing for manydomains.(+) Provide a simple notion of causalityby imposing a distinction betweenindependent variables and dependent ones.(+) Exlicit modeling assumptionrepresentation.(‐) Not compatible in some domains.(‐) Requires more inference and manipulation.(‐) Not has been formally explored.

...

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Ontology (cont)


Subtancesontology

• For reasoning about liquids.• Two ontologies: piece of stuffontology and contained stuffontology.

”No ontology”

• Use differential equations as basis to derive the structure ofthe system.

(+) Can be applied to all domains.(‐) Compositionality issue is not considered.

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Representing Behavior

• A qualitative state is a set of propositions that characterize a qualitatively distinct behavior of a system.

• A qulaitative state can abstractly represent an infinite number of quantitative states.

• Behavior is a sequence of qualitative states occuring over a particular span of time.

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Representing Behavior (cont)

Representation Desc.

Histories • A history: a piece of space‐time, containing properties.• Consists of a collection of episodes, which serve as thespatiotemporal scope for the validity of facts associatedwith them.• Describe a specific behavior of an object.• Each episode can be described as an occurence of oneof a finite set of abstract qualitative states.

Envisionments • An envisionment: a graph formed by the collection ofqualitative states of a system and transition betweenthem.• Envisioning: qualitative simulation.• Attainable envisionment: starts from a given initial state.• Total envisionment: starts from all possible states.

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Example

System: a simple mass‐spring

• x: position of the block

– x = 0: equilibrium position

– x > 0: to the right

– x < 0: to the left

• v: velocity of the block

• a: acceleration of the block

• f: force acting on the block

• m: mass of the block, positive constant

• k: spring constant, positive

0 x

f = m [*] a Newton’s second law

f = -k [*] x Hooke’s ideal spring law

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Example (cont)

Qualitative arithmetic:

• x [+] y

• x [*] y

+ 0 ‐

+ + + ?

0 + 0 ‐

‐ ? ‐ ‐

+ 0 ‐

+ + 0 ‐

0 0 0 0

‐ ‐ 0 +

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Example (cont)

• Qualitative states of the mass‐spring system.

• Transition graph of the mass‐spring system.

s1 s2 s3 s4 s5 s6 s7 s8 s9

x + + + 0 0 0 ‐ ‐ ‐

v + 0 ‐ + 0 ‐ + 0 ‐

a ‐ ‐ ‐ 0 0 0 + + +

f ‐ ‐ ‐ 0 0 0 + + +

s5

s4

s2

s1

s6s3

s8

s9

s7

v

x

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The following subjects are skipped:

• Representing Time

• Representing Space (Kinetics) and Shape

• Reasoning techniques

But research results and direction show more integration between Qualitative and Quantitative approaches (often called as Semi‐quantitative).

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Applications• Monitoring and dignosis

Application QR Approach

DEDALE, testing electroniccircuits coming off assemblylines.

To map numerical measurements into order ofmagnitude ranges for diagnosing tasks.

FaultFinder (NASA), to detectengine trouble in civiliancommercial aircraft, and thento provide easily understoodadvice to pilots.

Low‐resolution qualitative information is used by a causal model to construct failure hypotheses, to be communicated to the pilot in a combination ofnatural language and graphics.

Qualitative ProcessAutomation, process controltasks in curing compositeparts.

Incorporates a qualitative description of behaviorinto the controller, allowing it to detect thechange in qualitative regime and control thefurnace accordingly.

…

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Applications (cont)• Monitoring and dignosis (cont)


Intelligent alarm system for fault detection.

To replicate some expertise of experienced alarm operators by using a combination of causalmodels and statistical reasoning over historicaldata of the system.

MIMIC, to track system behavior.

To use a set of fault models to track the behaviorof a system with a qualitative and semi‐quantitative simulator.

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Applications (cont)• Design


MITA Corporation’s DC‐6090 photocopier, a self ‐maintenance machine.

An envisionment including fault models, createdat design time, is used as the basis for constructing the copier’s control software.

Chemical engineering. Design methods for distilation plants have beenformalized using Qualitative Process Theory, beingable to generate plant designs automatically.

Automatic analysis and synthesis of kinematicmechanisms.

Qualitative simulation for complex fixed‐axismechanisms and simplified dynamics to produceanimation.

Failure modes and effectsanalysis (FMEA), to reasonabout the effects of failuresand operating procedures.

To identify potential hazards in a chemical plant design by perturbing a qualitative model of thedesign with various faults, then using qualitativesimulation to ascertain the possible indirectconsequences of each fault.

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Applications (cont)• Intelligent tutoring systems and learning environments


Electronic learning Describe a sequence of qualitative models to helpstudents learn electronics. Qualitative terms areused to analyse student protocols to diagnose misconceptions.

Systems for teachingoperation of powergeneration plants, includingnuclear plants.

Qualitative representations can help to provideteaching software with the physical intuitionsrequired to help student’s problems.

Tutoring systems for ecology(Brazil) to support conservation effort.

Uses qualitative representations to explain howenvironmental conditions affect plant growth.

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Quiz

Qualitative arithmetic

• [x] = +, [y] = ‐, [x] + [y] = [z]

• What is [z]?

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References• Forbus, K.D., Qualitative Reasoning, 1996.

• Forbus, K.D., Qualitative Physics: Past, Present, and Future.

• Forbus, K.D., Commonsense Physics: A Review, 1988.

• Iwasaki, Y., Real world applications of qualitative reasoning: Introduction to the special issue.

• Struss, P., Qualitative modeling of physical systems in AI research.

• Bredeweg, B. and Struss, P., Current topics in qualitative reasoning, 2003.

• Trave‐Massuyes, et al, Mathematical foundations of qualitative reasoning, 2003.

• William B.C., and de Kleer, J., Qualitative reasoning about physical systems: a return to roots, 1991.

• Kuipers, B., Commonsense reasoning about causality: deriving behavior from structure, 1984.

• Kuipers, B., Qualitative reasoning: modeling and simulation with incomplete knowledge, The MIT Press, 1994.

• Bobrow, D.G. (ed), Qualitative reasoning about physical systems, Elsevier Science Pub., 1984.

• Space shuttle Challenger disaster, http://en.wikipedia.org/wiki/Space_Shuttle_Challenger_Disaster.

• Boisjoly, R.M., Ethical decisions – Morton Thiokol and the Space Shuttle Challenger Disaster.

• Days that shook the world ‐ series 2: Conquering the sky; Disaster in the sky, BBC Documentary, 2005.

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http://en.wikipedia.org/wiki/Space_Shuttle_Challenger_Disaster

Tusen takk!

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