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© 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
© Amit Mitra & Amar Gupta
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
© Amit Mitra & Amar Gupta
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
© Amit Mitra & Amar Gupta
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
© Amit Mitra & Amar Gupta
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
© Amit Mitra & Amar Gupta
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
© Amit Mitra & Amar Gupta
THE PROBLEM• TOO MUCH DETAIL NEEDED UP FRONT
• HOW CAN VARIABLES BE GROUPED?
GOOD BAD
GOODBAD
There are few absolute truths
© Amit Mitra & Amar Gupta
• 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
© Amit Mitra & Amar Gupta
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
© Amit Mitra & Amar Gupta
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
© Amit Mitra & Amar Gupta
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
© Amit Mitra & Amar Gupta
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
© Amit Mitra & Amar Gupta
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
15© Amit Mitra & Amar Gupta
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)
© Amit Mitra & Amar Gupta
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)
must contain only 1[contained in 0 or more]
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]
must contain only 1[contained in 0 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
© Amit Mitra & Amar Gupta
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”
© Amit Mitra & Amar Gupta
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
InstanceIdentifier 5(Attribute)
Attribute
Attribute
Attribute
Attribute Attribute
AttributeValue
Value
Value
Value
Value Value
ValueOBJECT 2
InstanceIdentifier 2(Attribute)
Attribute
Attribute
Attribute
Attribute Attribute
AttributeValue
Value
Value
Value
Value Value
Value OBJECT 3
InstanceIdentifier 2(Attribute)
Attribute
Attribute
Attribute
Attribute
AttributeValue
Value
Value
ValueValue
Value
Value
InstanceIdentifier 4(Attribute)
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)
© Amit Mitra & Amar Gupta
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”
© Amit Mitra & Amar Gupta
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
21© Amit Mitra & Amar Gupta
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]
22© Amit Mitra & Amar Gupta
Quantitative Attribute
FORMATUNIT
OFMEASURE
is expressed by 1 or many[express none or many]
convert to 0 or 1[convert from]
convert to 0 or 1[convert from]
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]
© Amit Mitra & Amar Gupta
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
is expressed by 1 or many[express]
is expressed by 1 or many[express]
is expressed by 1 or many[express]
convert to 0 or 1[convert from]
convert to 0 or 1[convert from]
© Amit Mitra & Amar Gupta
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 )
© Amit Mitra & Amar Gupta
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 )
© Amit Mitra & Amar Gupta
• 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]
© Amit Mitra & Amar Gupta
• 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
29© Amit Mitra & Amar Gupta
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.
© Amit Mitra & Amar Gupta
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
© Amit Mitra & Amar Gupta
Reading Assignments1. Supplementary materials in Modules 1 & 3 at
http://next.eller.arizona.edu/books/
2. Prologue and Chapter 1 of