1 © Amit Mitra & Amar Gupta Topics Introduction to information Space The concept of meta-object and meta-model Introduction to Perspective, Classification.

1© Amit Mitra & Amar Gupta

Topics

• Introduction to information Space• The concept of meta-object and meta-model• Introduction to Perspective, Classification and “The

Tyranny of Words”• Basic meta-object inventory

– Containers of normalized Knowledge– Also the basic components from which more

complex knowledge is configured

04/18/23 13:47 page 2#

© 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


DISCRETE CHANGE

• ATTRIBUTE VALUES & RELATIONSHIPS CHANGE IN RESPONSE TO DISCRETE EVENTS• CONSTRAINTS ON ENTITIES CHANGE IN RESPONSE TO DISCRETE EVENTS

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

AN OBJECT CLASS IS ALSO AN INSTANCE OF AN OBJECT•What properties would the class normalize?


DISCRETE CHANGE

OBJECT CLASS

Present

Past

V1

V2

V3

V4

V1

V2

V3

V4

Inst

ance

Tim

e

V1

V2

V3

V4

Effect of hammer strike 1Effect of

hammer strike 2Effect of

hammer strike 3


STATE OF AN OBJECT INSTANCE

1/8”

red

W

Instance

OBJECT CLASS(Glass Pane)

Status:Shattered (S) or Whole (W)

Color

Thickness

1/2”

blue

W

Instance

1/4”

green

S

Instance

Effect of Hammer Strike:Change status of “Whole” glass to

“Shattered”

Object Instances(Individual glass panes)

PROPERTIES OF OBJECT CLASS

Effect of hammer strike 3




State Chart

Material Wholeness Color Thickness

Glass

Shattered

Whole

Hammer Strike (Whole)

PANE

Red

Blue


State Chart

Material Wholeness Color Thickness

Glass Whole

Hammer Strike

PANE

Red

Blue

X

Cracked

Broken

Shattered

X


State of a System

STATE OF INVENTORY SYSTEM

Lead time

STATE OF INVENTORY ITEM

Reorder Quantity

Quantity on Hand

Price

Quantity on Order

Under Scrutiny

STATE OF VENDOR

On Recommended Vendor List

Not recommended

FailedQA

Poor Performance

STATE OF VENDOR ITEM STATE OF VENDOR APPROVAL

PassedQA


State Space

WEIGHT

TH

ICK

NE

SS

1/2 inch

1/8 inch

1 lb 2 lb

1/4 inch

11/2lb

Location of1/4 inch., 11/2 lbpane in this state space


State Space with Ordinal axis

JANE’S PREFERENCE

CA

R S

IZE

Maximum Car Size

Minimum Car Size

MostLiked

LeastLiked

Second MostLiked

JANE’S PREFERENCE

CA

R T

YP

E(S

eque

nce

does

not

mat

ter.

Car

s ca

n be

ar

rang

ed in

any

ord

er a

long

this

axi

s)

Infiniti

Ford Explorer

MostLiked

LeastLiked

Second MostLiked

Honda Civic

A. Example of State Space when one axis maps to a quantitative domain and the other to a qualitative domain (Disjoint Lines)

B. Example of State Space when both axes map to qualitative domains (Disjoint Points)

STATE SPACE IS COLORED BLUE

(Sequence matters, but not the distance between the broken lines on this axis)


THREE DIMENSIONAL STATE SPACE

Height

Age

Weight

Location in state space of an individual of a particular age, height and weight

•APPEARANCE OF STATE SPACE LOOK IF WE DID NOT CARE ABOUT THE AGE OF A PERSON?

•APPEARANCE OF STATE SPACE LOOK IF WE RESTRICTED THE AGE OF “PERSON” TO A SINGLE VALUE?


TRAJECTORY IN STATE SPACE

Depth

Width

The cross section of the river (instance of an object) moves along this trajectory at a certain speed



An object will move along a trajectory in State Space as its state changes with the passage of time

The object’s trajectory can be reinterpreted as a region in State Space (a static line in this case) when the time axis is added to its State Space

[When only discrete changes are considered, the region consists of a sequence of discrete points ( ) on the trajectory]

Depth

Width

The cross section of the river (instance of an object) moves along this trajectory at a certain speed

Location of a cross section of a river in state space at a particular time

Depth

Width

Time



An object will move along a trajectory in State Space as its state changes with the passage of time

The object’s trajectory can be reinterpreted as a region in State Space (a line in this case) when the time axis is added to its State Space

[When only discrete changes are considered, the region consists of a sequence of discrete points ( ) on the trajectory]

Income

Borrowing

The firm (instance of an object)moves along this trajectory at acertain speed

Income

Borrowing

Time

Location of the firm instate space at aparticular time


OBJECT

V1

V2

V3

E1

V1

V2

V3

E1

V1

V2

V3

E1

Instance Instance Instance

OBJECT CLASS

Time TimeTime

• OBJECT INSTANCE = SET OF VARIABLES– A single occurrence– Based on business meaning

• Person, place, category, concept or event relevant to the business • PROPERTY OF AN OBJECT (EXPANDED DEFINITION OF DATA ATTRIBUTES)

– A single meaning • Data Attribute/value• State/Relationship• Effect of event

• OBJECT CLASS = SET OF LIKE INSTANCES• TIME DIMENSION INTRINSIC TO BEHAVIOR OF THE OBJECT/CHANGES TO SPECIFIC PROPERTIES


SUBTYPING

A

B ABsetintersection

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

A-B

B-A

CCA

setdifference

subsetof A

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

PERSON

MALE PERSON

Subtype of

AgeHeightWeight

(Inherited)AgeHeightWeight

GAS POISON

POISON GAS

Subtype of


OBJECT GENERALIZATION & ROLE PLAYING

OBJECT

SUB-TYPE

.......PARTITION ....PARTITION

partitioned by partitioned by

partition of partition of

SUB-TYPE

SUB-TYPE

SUB-TYPE

(eg: organization)

e.g., Temporary organization(e.g.: Task force, Project team etc.)

e.g., Organization we do not own.

e.g., Organizations we own fully

e.g., Organizations in which we own the majority of shares

SUB-TYPE

e.g., Permanent. Organization(e.g.: Corporation, human resources department etc.)

PROPERTIES OF PARTITIONS

Irreducible fact: Subtypes are exhaustivelydefined in partition(Exhaustive Partition)

Irreducible fact: Subtypes are not exhaustivelydefined in this partition:Organizations in which we have minority shares are not shown(Non-exhaustive Partition)

Irreducible fact: Partitioning Criterion:Our ownership of organizations

Irreducible fact: Partitioning Criterion:Permanence of organizations

PARTITIONING CRITERIA

EXHAUSTIVITY

Non-exhaustive Partition Exhaustive Partition

*

e.g., Organization


CONSTRAINTS BETWEEN SUBTYPES

Every instance in one subtype must be in the other subtype and vice-versa, I.e., the two sets are equal

Every instance in one subtype must be in the other subtype but not necessarily vice-versa

SUB-TYPE

A

Anothersubtype

OBJECT

PARTITION PARTITIONEvery instance of subtype A must also be an instance of subtype B

(not necessarily vice-versa) SUB-TYPE

B

Anothersubtype

Subtypes A and B are mutually exclusive even though they are in different partitions

SUB-TYPE

A

Anothersubtype

OBJECT

PARTITION PARTITIONAn instance of subtype A must not be an instance of subtype B

(mutually exclusive sets)SUB-TYPE

B

Anothersubtype

X

SUB-TYPE

A

Anothersubtype

OBJECT

PARTITION PARTITIONEvery instance of subtype A must also be an instance of subtype B

(not necessarily vice-versa)

SUB-TYPE

BEvery instance of subtype B must also be an instance of subtype A

(not necessarily vice-versa)Anothersubtype


Subtyping Criteria

SUBTYPINGCRITERIA

Attributes EffectsRelationships Constraints

Constraintson Attribute

Values

Constraintson

Relationships

Guard Conditions

Constraintson Initial

Conditions

Initial Conditions

(Default State)

Constraintson History


VARIATION INHERITANCE

PERSON

NON-PARENT

PARENT

PARENTHOOD PARTITION

Subtypes of Person

may be parent of 0 or more

parent of 1 or more(inherited from Person)

Features•Parenthood•Name•Age•Gender•Height•Weight



Inherited from

Person

Inherited from Person

EXCLUDEFEATUREFROM SUBTYPE

ADD FEATURETO SUBTYPEADD FEATURETO SUBTYPE

PERSON

NON-PARENT

PARENT

PARENTHOOD PARTITION

Subtypes of Person

parent of 1 or more(added to subtype) Inherited

from Person

Features•Name•Age•Gender•Height•Weight



Inherited from

Person

Parenthood(add feature to

subtype)

+

THE PRINCIPLE OF SUBTYPING BY ADDING INFORMATIONINCLUSION INHERITANCE


Polymorphism is the quality of appearing in

several apparently different forms.

PARENT EMPLOYEE CUSTOMER ETC.

E.G. PERSON

HOP RUN ROLL ETC.

E.G. MOVE

MEETING TASK BIRTHDAY ETC..

E.G. EVENT

HEAT LIGHT KINETIC ETC..

E.G. ENERGY

BY ONES BY TWOS BY THREES ETC.

E.G. COUNT

GUIDELINE RULE DESCRIPTION ETC.

E.G. INFORMATION

●First identified by Christopher Strachey in 1967. ●Context specific behavior normalized by generalizing or subtyping objects.

– For example, the exact meaning of length depends on whether the object in question is a word or a room. “Word” and “Room” are parameters of length that fixes its meaning and properties more precisely than the generic concept of length:

•The length of a word is the number of letters in it, which can only be an integer•The length of a room may be any real number.

POLYMORPHISM


OBJECTparameters

Adaptation through Inclusion Polymorphism

•Object=Frog; Move=Hop

•Object=Wheel; Move=Roll

•Object may be Frog or Wheel•Move may be Hop or Roll


Kinds of Polymorphism

POLYMORPHISM

UniversalPolymorphism

AdhocPolymorphism

ParametricPolymorphism

InclusionPolymorphism

OverloadingPolymorphism

CoercivePolymorphism

Universal polymorphism is “true” polymorphism

Parametric polymorphism: Common behavior flows from domains and their mutual relationships. For example, the age of different kinds of objects such as people, documents or ideas may be computed by the following formula:

Age= Current Time - Time of creation

Current time and time of creation are two parameters needed to calculate “Age”, hence the term Parametric Polymorphism.

Inclusion polymorphism is the kind of polymorphism where subtypes inherit behavior. For example, Persons may speak, which means both male and female persons may speak.

Ad-hoc polymorphism is an artificial construct based on a somewhat unnatural and ad-hoc assignment of behavior or names to objects:

Overloading is the ability to use the same syntax for objects of different types, e.g. "+" for addition of complex numbers and integers or “length to compute the length of a room or a character string. Overloading reuses the name for a function) but requires different code for different types of objects. The function name is really a homonym (two different meanings with the same label) in overloaded polymorphism.

Coercive polymorphism occurs when an object instance is arbitrarily (and perhaps unnaturally) declared to belong to some subtype for a function. For example, special characters are assigned a sort sequence, just as numbers are, even though they do not have any natural sequence in which they must be arranged. Coercion also occurs when values in a nominal domain are arbitrarily assigned an order or magnitude; when differences or ratios between values in an ordinal domain are arbitrarily assigned a magnitude, or ratios of values in any but ratio scaled domains are compared.

OU

R FO

CU

S

OU

R FO

CU

S


KINDS OF INHERITANCE

•Subtype Inheritance: Mutually exclusive subtypes inherit behavior of the parent class

•Extension Inheritance: State space of the subtype extends the state space of the parent into additional dimensions (has additional properties)

•Restriction Inheritance: Constraint is added to parent to restrict its state space in the subtype

– Lawful vs. Conceivable state space

•View Inheritance: Object is an instance of two or more different subtypes simultaneously and inherits properties and restrictions of all. Eg:

– Parent and Employee are two roles (subtypes/polymorphisms) of Person

– An individual may simultaneously have a pay rate and children if he or she is an employee and a parent at the same time

INHERITANCE

ModelInheritance

VariationInheritance

SubtypeInheritance

ViewInheritance

SoftwareInheritance

RestrictionInheritance

ExtensionInheritance

(See endnote on kinds of inheritance in your text book)


The Problem of Perspective

What you see or think depends on how you see or think

GOOD BAD

GOODBAD

DOES A UNIVERSAL

PERSPECTIVE EXIST

?

WITHOUT THE UNIVERSAL

PERSPECTIVE THERE WOULD BE NO SHARED

UNDERSTANDING


Universal Perspective●Information and business services hub for semantic interoperability●Remember the Principle of Parsimony

–Generalized Classes and Interactions; Information Sparse●Remember the principle of subtyping by adding information

PERSPECTIVE

PERSPECTIVE

PERSPECTIVE

PERSPECTIVE

PERSPECTIVE

PERSPECTIVE

SHAREDPERSPECTIVE PERSPECTIVEPERSPECTIVE


GOOD BAD

GOODBAD

• TRUTH DEPENDS ON CONTEXT• CONTEXT ADDS INFORMATION

– PERSPECTIVE PROVIDES INFORMATION– IS A KIND OF OBJECT

CONTEXT 1

CONTEXT 2


Synonyms and Homonyms

NAME(synonym

&homonym)

NAME(synonym)

NAME(synonym)

NAME(synonym)

NAME(synonym)

NAME(synonym)

NAME(synonym)

OBJECT 1(meaning)

OBJECT 2(meaning)

NAME(synonym)

NAME(synonym)

THE TYRANNY OF WORDS

NAME(homonym)

NAME(homonym)

OBJECT 1(meaning)

OBJECT 2(meaning)


Primary Name vs Alias

ALIAS(synonym

&homonym)

ALIAS(synonym)

ALIAS(synonym)

ALIAS(synonym)

ALIAS(synonym)

ALIAS(synonym)

ALIAS(synonym)

OBJECT 1PRIMARY

NAME

OBJECT 2PRIMARY

NAME

ALIAS(synonym)

ALIAS(synonym)


Aliases and Perspectives

PERSPECTIVE or CONTEXT

(Model)

PERSON/ or ORGANIZATION(Key stake holders:

Persons and Groups)

CONCEPT(object)

NAME(synonyms, i.e.,

Aliases)

Each concept must have a name, and may have many

Each name must be in a a context and maybe the same in many contexts

Each perspective must be heldby at least one person or organizationand may be held by many

Each name must be the name of at least one object, perhaps many

Each perspective must have at least one named concept, probably more

Each person or organization must hold at least one perspective, perhaps more


DOMAIN

OBJECTINSTANCE

Described by exactly 1[Describes 1 or more]

Des

crib

ed b

y 1

or m

ore

[Pro

pert

y of

1 o

r m

ore]

EVENT

Triggers 1 or more[triggered by 1]

ATTRIBUTEVALUE

ATTRIBUTE

VALUE

Property of 1 or more[described by 1 or more]

Tak

es e

xact

ly 1

[sta

te o

f 1]

Described by exactly 1[Describes 1 or more]

STATEChange 1

[changed by 0 or more]Set of 1 or more

[component of 1 or more]

Subtype of

point in 1 or more[set of 0 or more]

OBJECT CLASS

Set (dimension) of 1 or more[described by 1 or more]

(implied)State Space

Belongs to 1[set of 1 or more]

AGGREGATEOBJECT

EFFECT

(Multiple occurrencesof an object are distinctmembers of a list)

LIST(Multiple occurrencesof an object count as a

single member)

CLASS or SET Subtype of

Partition of[partitioned by]

PERSPECTIVE

exists in 1 or more[pattern of 0 or more]

SequencedPattern

(Sequenced vs.Unsequenced Partition)

SequencedPattern

Relate 1 or more (relationship)

Subtype of 1 or more Represent 1 or more

Subtype of

OBJECTINSTANCE OBJECT

INSTANCE

Subtypeof

Subtype of

The Metamodel of Object


As a juggler plays many a part, wears many a guiseAnd doffs his mask when the show is done

So is our creator one; the only one- Guru Arjan Singh of Sikhism in the holybook, Adi Granth

M ET A OB JE C T

D YN A MI CRE LA T ION S HI P

(Proc es s )

ST A T I CRE LA T ION S HI P

RE L AT ION S HI PDOM A I N

Q UA L IT A TIV EDOM A I N

QU A NT ITA T IV EDOM A I N

D I FFE RE NC ES CA LE DDO MA I N

R A TI OS CA LE DDOM A I N

N OM INA LDO MA I N

O RD INA LDOM A I N

OB J E C TP R OP E RT Y

I r red uc ib le fac tin v ol ving tw o o r

mo re o bje ct s ,or t h e s am e

o bje c t a td iff e ren t t ime s

I rred uc ib le fac ta bou t t im i n g o rse que nce

T i m ein dep end en tI r red uc ib le fac t

A s ser ti ons ab ou tm eas ur eme nt an d

c la ss if ic a ti o n o f ob jec tb eh avio r c om mo n t om ul tip le pr ope r ti e s o f

ob j ec t s

I rre duc ib lefac t a bou tcla s si fic a tio nonl y

Ir r edu ci b le f ac t sa bo ut o rde r o rra n kin g o fob jec ts

Ir re du cib l e fac ts ab ou tma gni t ud es of d iff e ren c e sbe t we en obj ec t s

Ir r edu cib l e fac tsa bou tm ag nit ude s o fr a tio s b etw ee nobjec ts

UNI T O FM E AS UR E

( U OM )

F OR MA T

Ir r edu cib le fac tsa bo ut U ni t s o fm e asu rem en t

Ir r edu cib le f ac t sa bo ut f orm ats f o rp res en t ing ob jec t

pr ope rt ie s toob s er ver s

(hu ma n o rm ec h an ica l )

Is o la te dirre duc ib lefac t a bou ta s ing leob jec t

E V EN T

(Te mp ora lO c cu rre nce )

Ir re duc ib lefac t a bou tt im in g o f /t rigg er s f o rb eha vi o r

AT T RIB UTE

P O S S IB L EP A R T IC IP A T IO N

IN ARE LA T ION S HI P

EF F EC T

S UB T YP E

S T AT E

C olle c tio n o fI rre duc ib lef ac t s a bou t

th e c o nd itio no f an ob jec t

ins tan ce at amom e nt in

t im eS T AT ESP A C E

Th e s et o f a llp os s ible

co ndi t ion s o fan ob ject

R e pos ito ry o fun sha re dirre duc ib lefac ts

Re pos ito ry o fsha re dirre duc ib lefac ts

S UP E RT YP E

Ir r edu cib le f ac t ab ou t th eex ist e nce of a s ing le pro per ty o fan ob jec t ins tan ce at a m om en t

in t im e

Ir redu c ib le fact th epo s s ibilit y o f an ob jec t

in s ta nc e 's inv olv eme nt i n as pe cif ic r e la t ion s hip

OB J E C TCL AS S

S e t o f ob jec tin s tan ce sw ith s om esha re db eha vio r

OB J EC TIN S TA NC E

I rre duc ib lefac t a bou tt he ex is te nc eof a c on c ep to r it e m for afin i te i nt e rv a lof t im e

OB J EC TP A RT I T IO N

C ONS TR AIN T

C ri te r ia for d if fere ntia t in gs ub se t s o f ob jec t

ins tan c e s in an ob jec tc las s

I rre duc ib lef a ct a bo ut alim ita t io n

TR AJE CT OR YIN S T A TE

SP A C E

S E T O FP O S S IB L E

TR A JE CT ORI ES IN S T AT E

SP AC E

S e t of a l l p os s ib lec h an ges in st a te o f a nob jec t in s ta nc e

I r red uc ib le fac tab ou t th e p os s ib lec ha nge in th es tate o f an ob jectf rom on e m om en tto ano th er inre sp ons e t o a ne v en t

Th e s et o fac tua l

ch an ges ins tat e o f a n

ob jec tin s ta nc e

A GG RE G A TEOB JEC T

Ir r edu ci b le f ac t sa bo ut Coll ec t ion s

a nd st r uct ure s

NA ME

A l ter na t iv enam e s

UNI V E R S A LPE RS P E C TIV E

P E RS P EC T IV E

OT HE RP E RS P EC T IV E

M ode l:Se t o f

s tru c tu re di nt e rc o nn ect e

d c o nc epts

U niv ers a llys har ed c o nc eptsa nd me an ing s

S pec ia l iz e dc on cep ts an dme an i ng s

SY N ON YM H OM ON YM

D i f fe ren tN am es fo rthe sa m eob j ec t c las s

The sa m eNa me fo rd if fe ren tob jec tc l as se s

(Sta tes o f Name)

AL I AS C ON C EP TI D

Ob j ec t C l as sIde nt i fi e r

SU B TY P IN GRE L AT ION S HI P

I rre duc ib lef ac t s a bou texis ten c e of as ub t yp e


What We Have Covered• The concepts of object class and object instance

– The fundamental containers of reusable knowledge – Also the fundamental meta-component from which other components of

knowledge are forged

• The concept of meta-object and meta-model

• State and state space

• Subtyping Partitions and Polymorphism

• Shared Understanding, Perspective, Classification and “The Tyranny of Words”

• A basic meta-object inventory– Containers of normalized Knowledge– Also the basic components from which more complex knowledge is configured

1 © Amit Mitra & Amar Gupta Topics Introduction to information Space The concept of meta-object and meta-model Introduction to Perspective, Classification.

Documents

state space slide

example of state space

single state

axis slide

change change

information space

state space depth width

pane red blue slide