© Amit Mitra & Amar Gupta ANALYZING THE REAL WORLD WHAT IS A MODEL? –ONLY REPRESENTS, AND IS NOT REALITY »Repeatable, consistent & accurate within a limited

© Amit Mitra & Amar Gupta

ANALYZING THE REAL WORLD• WHAT IS A MODEL?

– ONLY REPRESENTS, AND IS NOT REALITY

» Repeatable, consistent & accurate within a limited scope

– PARTIAL VIEW OF REALITY =SCOPE OF MODEL

• REAL WORLD HAS– No Data, No process - only behavior

– SCOPE OF MODEL= BEHAVIOR OF INTEREST

» STIMULUS & RESPONSE: Repeatable, consistent & accurate

» ABSTRACTION OF RULES

• WHAT IS BEHAVIOR?

• TECHNIQUES FOR REPRESENTING BEHAVIOR

Make cookieDough

Arrange doughglob on cookiesheet

Bake dough RemoveCookie

BAKE COOKIE


BEHAVIOR

• RESPONSE TO A GIVEN STIMULUS– HIT METAL SHEET: it bends

– HIT GLASS SHEET: it breaks

• INVOLVES OBJECTS, EVENTS, CHANGE

• CHANGE INVOLVES TIME

• TECHNIQUES FOR REPRESENTING BEHAVIOR– BLACK BOX

» “INPUT-OUTPUT” VIEW

– NODE BRANCH

» “ERD TYPE” TECHNIQUES


PROCESS

BAKE COOKIE

DOUGH

OVEN

COOKIE

COOKIE SHEET(new)

COOKIE SHEET(used)

COOK

REAL

WORLD

OBJECTS

REAL

WORLD

OBJECTS

REAL WORLD RELATIONSHIP

BEFORE AFTER

TIME


BLACK BOX VIEW

RULES & FORMULAE

Operations on values of v1..v4to derive values of v5 thru v7

at various points in TIME

V1

V2

V5

V6

INPUTS OUTPUTS

V7

(BEFORE) (AFTER)

time

value v`1

v2

v3

v4

value

time

v6v7

v5

(INPUTS CHANGE) (OUTPUTS RESPOND)

Examples:•Oven Temperature

•Ingredient Quantities

Examples:•No. of cookies•Crispness of cookies

•Weight of each cookie

BLACK BOX(TRANSFORM)

V3

V4

Example: Transform for baking a cookie


THE PROBLEM• THE REAL WORLD CHANGES

• THE REAL WORLD CAN BE COMPLEX– CAN WE FILL IN DETAIL IN SUCCESSIVE STEPS?

– PROCESS DECOMPOSITION

V1

V2

V3

V4

V5

V6

INPUT VARIABLES OUTPUT VARIABLES

V7

RULE 1

RULE 2

BEFORE(CAUSE)

AFTER(EFFECT)

• PROCESS DECOMPOSITION = INFLEXIBLE SYSTEMS– WE DIVIDE EVEN BEFORE WE KNOW WHAT WE DIVIDE

– ALMOST LIMITLESS WAYS OF DIVIDING THE BOX

■ SOME WORK IN A LIMITED CONTEXT, OTHERS DO NOT

■ NO PRECISE RULES FOR WHAT WILL WORK AND WHAT WON’T

– THE PROBLEM OF CHAOS

• DATA FLOW INTERPRETATION

RULE 3

RULE 4

BLACK BOX


NODE BRANCH REPRESENTATION

RULE

V1

V2

V3

V4

V5

V6

V7

The future of v1depends on itspast values RULE

RULE

RULE

RULERULE

RULE

RULE

RULE

How can we represent cross effects between v2 & v3 ?

• MORE “HOLISTIC” VIEW– State vs Input-output

• CYCLE: a loop

• EQUILIBRIUM: May or may not exist

• LOGICAL UNIT OF WORK– assumes equilibrium– physical design concept

• ERD IS DERIVED FROM THIS: Static rules


THE PROBLEM• TOO MUCH DETAIL NEEDED UP FRONT

• HOW CAN VARIABLES BE GROUPED?

GOOD BAD

GOODBAD

There are few absolute truths


• FACT BASED BEHAVIOR MODELING– GROUPING: THEORY OF CATEGORIES APPLIED TO REAL WORLD OBJECTS

– FACT BASED ENTITY & PROCESS DESIGN

• PHASED INFO CAPTURE– BASED ON COMMON “IRREDUCIBLE” FACTS

– CROSS SCOPE COMMONALITY

THE ANSWER


FACTS • A FACT IS ...

– ASSERTION: SIMPLE, COMPLEX, CAVEATS

• AN IRREDUCIBLE FACT ...– CANNOT BE DIVIDED WITHOUT LOSING INFORMATION OR A PART OF

ITS ORIGINAL MEANING

» eg: product sold to customer at a place thru a distribution channel

• WHY DIFFERENT MODELS FOR THE SAME BUSINESS REQUIREMENTS?

– DIFFERENT GENERALIZATIONS AND SPECIALIZATIONS OF THE REAL WORLD

– NEED FOR STANDARD OBJECT TAXONOMY

– NEED TO START WITH IRREDUCIBLE FACTS


BUSINESS RULES• Business Rules are…

–Policies, practices, facts, assertions and rules about required business behavior

–Individually simple, complex in combination

• The Business Rule Approach focuses systems development on business constraints & opportunity

–Unified view of knowledge about products & customers

–Separated from technology constraints

–Business rule changes can be automatically reflected in applications

• Framing business rules in a real world object ontology helps avoid repetition & unmanageable “rule tangling” for the most frequently used rules of the enterprise

–Combined with Object Inheritance it can provide a powerful method of building systems that will facilitate, not control change


An example of how business rules are assembled from meanings…

ship PRODUCT

TRUCK

Sh

ip on

shipORGANIZATION PRODUCTWeight Domain+

TRUCK

= + =ship

Weight

(SHIPMENT)

Unit of MeasureConversion Rules

PoundsKgs

Tons

Units of Measure

Measurement Unit of

0

Cannot be less than

8 tons

ORGANIZATION

Weight

Unit of MeasureConversion Rules Pounds

KilogramsTons

Units of Measure

Cannotbe lessthan 0

Unit of MeasureConversion Rules Pounds

KilogramsTons

Units of Measure

Cannotbe lessthan 0

INHERITED FROMWEIGHT DOMAIN

INHERITED FROMWEIGHT DOMAIN

NEW CONSTRAINT

Must be less than

8 tons

Must be less than


MODEL COMPONENTS• OBJECT

– INSTANCES– INSTANCE MAY PLAY MULTIPLE ROLES AT THE SAME TIME– SET THEORY– FOUR SET OPERATIONS

» SUBSET, UNION, INTERSECTION, CARTESIAN PRODUCT» BOREL OBJECTS

• PROPERTIES– ATTRIBUTES: DATA, STATE– EFFECT OF EVENT

» FINITE NO. OF POSSIBLE OPERATIONS ON OBJECT

• DOMAIN (an abstraction)– COMMON TO MANY ATTRIBUTES AND OBJECTS– NORMALIZES REAL WORLD MEASURABILITY INFORMATION– NOMINAL, ORDINAL, DIFFERENCE & RATIO SCALED– DIFFERENCE & RATIO SCALED DOMAINS MUST HAVE ATLEAST ONE, AND MAY HAVE

MANY UNITS OF MEASURE (uom)– EACH UOM MAY HAVE MANY PHYSICAL REPRESENTATIONS: (FORMATs)

OFTEN CONFUSED WITH EACH OTHER


ASSUMPTIONS• PROPERTIES (ATTRIBUTE VALUES & RELATIONSHIPS) CHANGE IN RESPONSE TO DISCRETE EVENTS• CONSTRAINTS ON ENTITIES CHANGE IN RESPONSE TO DISCRETE EVENTS• DETERMINISTIC SYSTEM

Time slice(a single state of an

instance of an object)

OBJECT CLASS

Present

Past

V1

V2

V3

V4

V1

V2

V3

V4

Inst

ance

TimeTime

V1

V2

V3

V4

14© Amit Mitra & Amar Gupta

SETS & SET OPERATIONS

A

B ABsetintersection

AB is the set of objects that are members of both A and B.Multiple inheritance

A-B

B-A

A-B is the set of objects that are members of set A, but not B.

B-A is the set of objects that are members of set B, but not A.

CCA

setdifference

subsetof A

CA implies all members of C are also members of A, but not vice-versa.Inheritance (Data, behavior & constraints)

A

BAB

AB is the set of object that are members of either set A, or set B, or both.

set union


XSET C=A B

a1a2a3

SET A

b1b2

SET B

X

(a1, b1)(a1,b2)(a2, b1)(a2, b2)(a3, b1)(a3, b2)

=

CARTESIAN PRODUCTOF SETS A AND B

SET OPERATIONS (CONTINUED)


A Knowledge Artifact is abstract

FormattingRules

SequencingRulesDisplay

OBJECTCLASS

INFORMATIONSOURCING

CONNECTION(OPTIONAL)

INCLUSION/EXCLUSION SET(S)

Components of View

must contain only 1[contained in 0 or more]

FormattingRule

SequencingRule

(OPTIONAL) INCLUSION/EXCLUSION

SET GROUP(S)


May contain 0 or 1[contained in 0 or more]

VIEW

ACTOR

VIEW

Expressed by 0 or more[of 1 or more]

OBJECT

Display

Formats for 0 or more[formatted by 1 or more]


Intersection of 0 or more[Intersection of 0 or more ]

Union of 0 or more[Union of 0 or more ]

Intersection of 0 or more[Intersection of 0 or more ]

Union of 0 or more[Union of 0 or more ]

Selectioncriteria


Attributes of ObjectsDOMAIN

OBJECT AttributeE

ach

Att

rib

ute

is a

Sub

type

of a

sin

gle

Each Object is an aggregation of one or more

Each Attribute is a Property of a single

AttributeAttribute

Attribute

Attribute

Attribute

Attribute Attribute

AttributeValue

Value

Value

ValueValue

Value Value

Value

OBJECT

Ins tanceIdentifier

(Attribute)

[Each domainmay be thesupertype fornone, or severalattributes]

DOMAIN

OBJECT Attribute

Eac

h A

ttri

but

e is

a S

ubty

pe o

f a s

ingl

e

Each Object is an aggregation of one or more

Each Attribute is a Property of a single

AttributeAttribute

Attribute

Attribute

Attribute

Attribute Attribute

AttributeValue

Value

Value

ValueValue

Value Value

Value

OBJECT

Ins tanceIdentifier

(A ttribute)

[Each domainmay be thesupertype fornone, or severalattributes]

DOMAIN 3

DOMAIN 2

DOMAIN 1OBJ ECT 1

OBJECT 3

OB

JEC

T 4

attr ibute

attribute

attr ibute

attr

ibut

e

OBJECT 2

attr ibute

OBJECT 5

attr ibute

attr ibute

attr

ibut

e

attr

ibut

e

“Value” includes•“Any” (i.e., “All”)•“Don’t Know”•“Null”


Relationships are objects

Relationships are also features of objects

AttributeAttribute

Attribute Attribute

Attribute

Value

ValueValue

Value Value

InstanceIdentifier 1(Attribute)

Attribute

Attribute

Attribute

Attribute

AttributeValue

Value

Value

ValueValue

Value

Value


Attribute

Attribute

Attribute

Attribute Attribute

AttributeValue

Value

Value

Value

Value Value

ValueOBJECT 2


Attribute

Attribute

Attribute

Attribute Attribute

AttributeValue

Value

Value

Value

Value Value

Value OBJECT 3


Attribute

Attribute

Attribute

Attribute

AttributeValue

Value

Value

ValueValue

Value

Value


PARTICIP

ATION IN

RELATIO

NSHIP PARTICIPATION IN RELATIONSHIP

Attribute Attribute

Attribute Attribute

Value Value

Value Value

PARTICIPATIONIN

RELATIONSHIP

Attribute Attribute Attribute Attribute

AttributeAttribute

OBJECT 1

OBJECT 5 OBJECT 4

The instance identifier ofone object may be anattribute of another.Thetwo are merely differentroles of the same thing.

InstanceIdentifier 6

(relationship identifier)(Attribute)

OBJECT 6(Relationship)


What is a Metamodel?

• Information about information– A model of information that structures the

concept of “model”

• Consists of “Meta-Objects”– Eg. “Object Class”, “Object Instance”,

“Relationship”, “Process”


Metamodel of StateDOMAIN

(Exhaustive) Qualitative/Quantitative Par tition

OBJECT

QualitativeAttribute

Ea

ch O

bje

ct i

s a

na

ggre

gat

ion

of o

ne

or

mor

e Ea

ch A

ttribu

te is a P

rop

erty o

f a sin

gleA ttribute

Each Qualitative Attribute

is a Subtype of an AttributeEach Quantitative Attribute

is a Subtype of an Attribute

FORMATUNIT

OFMEASURE

is expressed by 1 or many[express]

conver t to 0 or 1[convert from]

conver t to 0 or 1[convert from]

Eac

h Q

ua

nti

tati

ve

Att

rib

ute

is a

Su

bty

pe

of

a

QUALITATIVE DOMAIN QUANTITATIVE DOMAINis expressed by

1 or many

is expressed in 1 or many

QuantitativeAttribute

InstanceIdentifier

Eac

h Q

uali

tati

ve

Att

rib

ute

is a

Su

bty

pe

of

a

(Exhaustive) Ordinal/Nominal Par tition

OrdinalDomain

NominalDomain

Eac

h O

rdin

al A

ttri

bu

teis

a S

ub

typ

e o

f a

Eac

h N

om

ina

l Att

rib

ute

is a

Su

bty

pe o

f a

OrdinalAttribute

NominalAttribute

is aSubtype

of

is aSubtypeof

is aSubtype

of

Each objec t musthave exactly 1

[Identif iesexactly 1]

is aSubtype

of

is aSubtype

of

is aSubtype

of

(Exhaustive) Difference/Ratio Scaled Par tition

OrdinalDomain

NominalDomain

DifferenceScaled

Attribute

RatioScaled

Attribute

is aSubtype

of

is aSubtypeof

Eac

h D

iffe

ren

ce S

cale

dA

ttri

bu

te is

a S

ub

typ

e o

f a

Eac

h R

ati

o S

cale

d A

ttri

bu

teis

a S

ub

typ

e o

f a

is aSubtype

of is aSubtype

of

is a Subtype of

is a Subtype ofVALUE

The two setsare equal

Is a

sub

typ

e of

Must take only 1

[may be value of

none , or many]

RelationshipIdentifier is a

Subtypeof

STATE OF OBJECT

THE STATE OF ANOBJEC T IS A

COLLECTION OFATTRIBUTE VALUES


Qualitative Attribute

FORMAT

convert to 0 or 1[convert from]

QualitativeAttribute

OrdinalAttribute

NominalAttribute

is a Subtype

of

is a Subtype of

Ordinal/Nominal Partition

is expressed by 1 or many[express none, or many]

(INHERITED FROM DOMAIN)

QUALITATIVE DOMAIN

QualitativeValue

The two sets are equal

is a Subtype of

Must take only 1

[may be value of

none, or many]


Quantitative Attribute

FORMATUNIT

OFMEASURE

is expressed by 1 or many[express none or many]



QuantitativeAttribute

DifferenceScaled

Attribute

RatioScaled

Attribute

is a Subtype

of

is a Subtype of

Difference/Ratio Scaled Partition

is expressed in 1 or many

[express none or many]

(INHERITED FROM DOMAIN)

QuantitativeValue

The two sets are equal

QUANTITATIVE DOMAIN

is a Subtype ofM

ust take only 1

[may be value of

none, or many]


DOMAIN

Q U A LIT A T IV ED O M A IN

N O M IN A LD O M A IN S

O R D IN A LD O M A IN S

Q U A N T IT A T IV ED O M A IN

D IFFE R E N C ES C A LE D

D O M A IN S

R A T IOS C A LE D

D O M A IN S

INCREASING INFORMATION CONTENT

QUALITATIVEDOMAIN

QUANTITATIVEDOMAIN

FORMATUNIT

OFMEASURE







Subtype ofNOMINALVALUE

ORDINALVALUE

DON’TCARE

ALL

Partition of[partitioned by]

MEANINGFULNESS

RATIOSCALEDVALUE

Subtypeof

DIFFERENCESCALEDVALUE

Metamodel of Value

Subtypeof

Subtypeof

Instance ofNIL

NULL(MEANINGLESS)

(absence of magnitude )


KINDS OF DOMAINS

MUST EVERY OBJECT HAVE ATTRIBUTES

?Subtype of

Subtype of

Subtype of

NOMINALDOMAIN

ORDINALDOMAINDOMAINS WITH

NIL VALUES

DOMAINS WITH LOWER BOUNDS

UNKNOWNDOMAIN

ORDINAL DOMAIN WITH NIL VALUES

RATIO SCALED DOMAIN

Su

btyp

e of

Subtype of

Subtype of

DIFFERENCE SCALED DOMAIN

Subtype of

Subtype of

(can be logically [automatically] inferred)

(impossibility can be logically [automatically] inferred )


• Names of object properties emerge naturally from the structure of information– Names reflect Meaning

– Meanings are patterns of information

• NAMING RULE: Object Class (optionally possessive form), Domain, IN Unit of Measure– Car (‘s) Color

• Multiple interactions between object and domain needs qualifier– E.g. Car body Color, Car Seat Color

– Person (‘s) Color-Preference• Person’s (Visual) Car-Color-Preference

– String (‘s) Length• String (‘s) Length IN Feet

• Person Length?; Room height Length? Room Width Length?!!

• NAMING RULE: All nominal domains are subtypes of the Type domain (aka Class, Category)– Classify cars into sedans, hatchbacks, SUVs etc

• Object = Car, Domain = Type, Attribute Name = Car Type

NAMING RULE: All ordinal domains are subtypes of the Rank domain

– Titles in an organization• The same title may imply different levels in different organizations

– VP in the insurance industry is 2 levels above a Director; Director in a bank is several levels above VP

• Object = Title, Domain = Rank, Attribute Name = Title Rank

ATTRIBUTE NAMES

(difference & Ratio Scaled domains only)

PERSON VISUAL CAR

COLORPREFERENCE

PREFERENCE

COLOR

COLORPREFERENCE

PERSON

CAR

VisualizeCarse

e

Analysis item Design item

DOMAINOBJECT AttributeAttribute is a Subtype of a singleAttribute is a Property of a single

[Domain is a class of none, or several attributes]

[state described by 1 or more]


• NAMING RULE: Object Class, Domain, IN Unit of Measure EXPRESSED IN Format– Object Class must be singular– Domain name must be singular– Unit of Measure must be Plural– String Length

• Object = String, Domain = Length, UOM= Feet, Format = Numeric Digits– Attribute Name = String Length IN Feet EXPRESSED IN Numeric Digits

• Format = English Speech– Attribute Name = String Length IN Feet EXPRESSED IN English Speech

• REALIZING ATTRIBUTES IN A COMPUTER SYSTEM– What is an attribute?

• Current technology does not recognize the meaning of an attribute or the pattern that creates attributes• Each tangible expression is considered a separate and independent attribute in most database systems and many CASE

tools• But times are a –changing!

– XML partly separates the meaning from its expressions– The Metamodel of Knowledge can be the blue print for tools better aligned with the real world

Tangible expression

ATTRIBUTE NAMES (continued)

DOMAINOBJECT Attributeis a Subtype of a singleis a Property of a single

[is a class of none, or several attributes]

[state described by 1 or more]FORMAT

expressed in none or more

UOM

expression of only 1


IDENTIFYING DOMAINS

Yes.Eg:Policy premiums

Is the attribute a basis, or potential basis, for creating mutually exclusive entity subtypes?

No

The attribute is at least Nominal Scaled, and may be Ordinal, Difference or Ratio Scaled.

Can the valuesof the attribute be arranged in a natural order from least to most?

#2

The attribute is at least Ordinally Scaled, and may be Difference or Ratio Scaled.

Can attribute values be meaningfully subtracted?

#3

The attribute is at least Difference Scaled, and may be Ratio Scaled.

A Nominally Scaled Attribute.

An Ordinally Scaled Attribute.NoEg: Color preference.

NoEg:Policy effective date

NoE.g: Color of car

Are attribute ratios meaningful?#4

#1

A Difference Scaled Attribute.

#2

Yes.

Yes.

A Ratio Scaled Attribute.

#3

#4

Yes.

#1

STOPMay be “fuzzy”

concept. Rethink.


OBJECT

D YN A M ICR E LA T IO N S H IP

(P ro cess)

S T A T ICR E LA T IO N S H IP

R E LA T IO N S H IP D O M A IN

Q U A LIT A T IV ED O M A IN

Q U A N T IT A T IV ED O M A IN

D IFFE R E N C ES C A LE DD O M A IN

R A T IOS C A LE DD O M A IN

N O M IN A LD O M A IN

O R D IN A LD O M A IN

O B JE C TP R O P E R T Y

Irreducib le fact invo lv ing twoo r m o re o bjects , o r the sam e

o bject a t d if ferent tim es

Irreducib le factabo ut tim ing o r

sequence

T im e independentIrreducib le fact

A ssertio ns abo ut m easurem entand c lass if icatio n o f o b ject

behavio r co m m o n to m ultip lepro perties o f o b jects

Irreducib le factabo ut

c lass if icatio no nly

Irreducib le factsabo ut o rder o r

ranking o fo b jects

Irreducib le factsabo ut m agnitudes

o f d if ferencesbetween o bjects

Irreducib le factsabo ut m agnitudeso f ra tio s between

o bjects

U N IT O FM E A S U R E

(U O M )FO R M A T

Irreducib le factsabo ut U nits o fm easurem ent

Irreducib le facts abo ut fo rm atsfo r presenting o bject

pro perties to o bservers(hum an o r m echanica l)

Iso lated irreducib le factabo ut a s ing le o b ject

E V E N T(O ccurrence in tim e)

Irreducib le factabo ut tim ing o r

triggers fo rbehavio r

“Although I am one, I shall become Many.”

- passage from Chandogya Upanishad, an ancient text from India, on manifestation of material

reality, translated by Swami Prabhupada


Reading Assignments1. Supplementary materials in Modules 1 & 3 at

http://next.eller.arizona.edu/books/

2. Prologue and Chapter 1 of




Documents

© Amit Mitra & Amar Gupta ANALYZING THE REAL WORLD WHAT IS A MODEL? –ONLY REPRESENTS, AND IS NOT REALITY »Repeatable, consistent & accurate within a limited