Transcript MAP-ENTR 459-559 Lectures 4 Introduction to Information

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
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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
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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)
Past
V1
V1
V1
V2
V2
V2
V3
V3
V4
V4
Time
V3
V4
Present
OBJECT CLASS
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Time
AN OBJECT CLASS IS ALSO AN
INSTANCE OF AN OBJECT
•What properties would the class
normalize?
DISCRETE CHANGE
Past
V1
V1
V1
V2
V2
V2
V3
V3
V3
V4
V4
V4
Present
OBJECT CLASS
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Effect of
hammer
Effect of
strike 1
hammer
Effect ofstrike 2
hammer
strike 3
STATE OF AN OBJECT INSTANCE
P
R
O
P
E
R
T
I
E
S
O
F
O
B
J
E
C
T
C
L
A
S
S
Object Instances
(Individual glass panes)
Thickness
Color
Status:
Shattered (S)
or Whole (W)
Effect of
Hammer Strike:
Change status of
“Whole” glass to
“Shattered”
Instance
Instance
Instance
1/8”
1/2”
1/4”
red
blue
W
W
Effect of
hammer
strike 1
green
S
Effect of
hammer
strike 2
Effect of
hammer
strike 3
OBJECT CLASS
(Glass Pane)
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State Chart
PANE
Material
Wholeness
Color
Glass
Whole
Red
Hammer
Strike
(Whole)
Thickness
Blue
Shattered
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State Chart
PANE
Material
Wholeness
Color
Glass
Whole
Red
Thickness
X
Hammer
Strike
X
Blue
Broken
Shattered
Cracked
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State of a System
STATE OF INVENTORY SYSTEM
ST A T E O F V E N D O R
ST A T E O F
IN V E N T O R Y IT E M
ST A T E O F V E N D O R IT E M
ST A T E O F V E N D O R A PPR O V A L
Price
R eorder Q uantity
U nder Scrutiny
Q uantity on O rder
Passed
QA
Failed
QA
N ot recom m ended
Q uantity on H and
L ead tim e
O n R ecom m ended
V endor L ist
Poor
Perform ance
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State Space
Location of
1/4 inch., 11/2 lb
pane in this state
space
THICKNESS
1/2 inch
1/4 inch
1/8 inch
1 lb
11/2lb
2 lb
WEIGHT
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State Space with Ordinal axis
CAR SIZE
Maximum Car Size
Minimum Car Size
Most
Liked
Second
Most
Liked
Least
Liked
CAR TYPE
(Sequence does not matter. Cars can be
arranged in any order along this axis)
STATE SPACE IS COLORED BLUE
Infiniti
Honda Civic
Ford Explorer
Most
Liked
Second
Most
Liked
Least
Liked
JANE’S PREFERENCE
JANE’S PREFERENCE
(Sequence matters, but not the distance between the broken lines on this axis)
A. Example of State Space when one axis maps to a quantitative
B. Example of State Space when both axes map
domain and the other to a qualitative domain (Disjoint Lines)
to qualitative domains (Disjoint Points)
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THREE DIMENSIONAL STATE SPACE
Height
Location in state
space of an
individual of a
particular age,
height and weight
Weight
Age
•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?
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TRAJECTORY IN STATE SPACE
The cross section of the river
(instance of an object) moves
along this trajectory at a certain
speed
Depth
Width
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TRAJECTORY IN STATE SPACE
Depth
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
Time
Depth
Width
Width
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]
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TRAJECTORY IN STATE SPACE
Income
Location of the firm in
state space at a
particular time
The firm (instance of an object)
moves along this trajectory at a
certain speed
Time
Income
Borrowing
Borrowing
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]
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OBJECT
Instance
Instance
V1
V2
Instance
V1
Time
V2
V1
Time
Time
V2
V3
V3
V3
E1
E1
E1
OBJECT CLASS
•
•
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
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SUBTYPING
PERSON
Age
Height
Weight
GAS
A
AB
Subtype of
MALE PERSON
(Inherited)
Age
Height
Weight
POISON
A-B
set
intersection
B-A
set
difference
B
C
C A
subset
of A
Subtype of
POISON GAS
C A implies all members of C are also members of A, but not vice-versa.
Inheritance (Data, behavior & constraints)
AB is the set of objects that are members of both A and B.
Multiple inheritance
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OBJECT GENERALIZATION & ROLE PLAYING
e.g., Organization
e.g., Organizations
we own fully
partitioned by
OBJECT
partition of
partitioned by
(eg: organization)
e.g., Organizations
in which we own the
majority of shares
e.g., Organization
we do not own.
.......PARTITION
partition of
....PARTITION
SUBTYPE
*
SUBTYPE
SUBTYPE
SUBTYPE
SUBTYPE
e.g., Temporary organization
(e.g.: Task force,
Project team etc.)
e.g., Permanent. Organization
(e.g.: Corporation, human
resources department etc.)
Non-exhaustive Partition
Exhaustive Partition
PROPERTIES OF PARTITIONS
PARTITIONING CRITERIA
Irreducible fact:
Partitioning Criterion:
Our ownership of organizations
Irreducible fact:
Partitioning Criterion:
Permanence of organizations
EXHAUSTIVITY
Irreducible fact:
Subtypes are not exhaustively
defined in this partition:
Organizations in which we
have minority shares are not
shown
(Non-exhaustive Partition)
Irreducible fact:
Subtypes are exhaustively
defined in partition
(Exhaustive Partition)
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CONSTRAINTS BETWEEN SUBTYPES
OBJECT
OBJECT
PARTITION
SUBTYPE
A
PARTITION
PARTITION
Every instance of subtype A must
also be an instance of subtype B
(not necessarily vice-versa)
Another
subtype
SUBTYPE
B
Every instance of subtype A must
also be an instance of subtype B
(not necessarily vice-versa)
PARTITION
SUBTYPE
A
SUBTYPE
B
Another
subtype
Another
subtype
Every instance in one subtype
must be in the other subtype but
not necessarily vice-versa
Every instance of subtype B must
also be an instance of subtype A
(not necessarily vice-versa)
Another
subtype
Every instance in one subtype
must be in the other subtype and
vice-versa, I.e., the two sets are
equal
OBJECT
PARTITION
SUBTYPE
A
Another
subtype
An instance of subtype A must
not be an instance of subtype B
(mutually exclusive sets)
X
PARTITION
SUBTYPE
B
Another
subtype
Subtypes A and B are mutually exclusive
even though they are in different partitions
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Subtyping Criteria
SUBTYPING
CRITERIA
Attributes
Relationships
Constraints
Initial
Conditions
(Default State)
Constraints
on Attribute
Values
Constraints
on
Relationships
Constraints
on History
Constraints
on Initial
Conditions
Effects
Guard
Conditions
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THE PRINCIPLE OF SUBTYPING BY ADDING INFORMATION
INCLUSION
INHERITANCE
F eatures
•N am e
•A g e
•G end er
•H eigh t
•W eig h t
In h erited
from
P erson
F eatures
•N am e
•A g e
•G end er
•H eigh t
•W eig h t
© Amit Mitra & Amar Gupta
p a ren t of 1 o r m o re
(add ed to su b ty p e)
P A R E N T H O O D P A R T IT IO N
NONPARENT
VARIATION
INHERITANCE
EXCLUDE
FEATURE
FROM SUBTYPE
PER SO N
In h erited
from
P erson
F eatures
•P aren th ood
•N am e
•A g e
•G end er
•H eigh t
•W eig h t
PARENT
S u b typ es of P erso n
F eatures
•P aren th ood
•N am e
•A g e
•G end er
•H eigh t
•W eig h t
In h erited
from
P erson
F eatures
•N am e
•A g e
•G end er
•H eigh t
•W eig h t
+
P a ren th o od
(a d d featu re to
su b typ e)
ADD FEATURE
TO SUBTYPE
m ay b e p a ren t of 0 o r m o re
PER SO N
p a ren t of 1 o r m o re
(in h erited from P erso n )
P A R E N T H O O D P A R T IT IO N
NONPARENT
PARENT
S u b typ es of P erso n
In h erited
from
P erson
F eatures
•P aren th ood
•N am e
•A g e
•G end er
•H eigh t
•W eig h t
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POLYMORPHISM
●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.
E.G. PERSON
E.G. EVENT
TASK
MEETING
BIRTHDAY
E.G. INFORMATION
GUIDELINE
RULE
DESCRIPTION
PARENT
ETC..
ETC.
Polymorphism is
the quality of
appearing in
several apparently
different forms.
LIGHT
KINETIC
ETC.
E.G. COUNT
BY ONES
BY TWOS
BY THREES
ETC.
E.G. MOVE
E.G. ENERGY
HEAT
EMPLOYEE CUSTOMER
ETC..
HOP
RUN
ROLL
ETC.
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Adaptation through Inclusion Polymorphism
parameters
•Object=Frog; Move=Hop
OBJECT
•Object=Wheel; Move=Roll
•Object may be Frog or Wheel
•Move may be Hop or Roll
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Kinds of Polymorphism
O
UR
FO
CU
S
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KINDS OF INHERITANCE
(See endnote on kinds of inheritance in your text book)
M odel
I n h e r ita n c e
S u b ty p e
I n h e r ita n c e
E x te n s io n
I n h e r ita n c e
R e s tr ic tio n
I n h e r ita n c e
IN H E R IT A N C E
V a r ia tio n
I n h e r ita n c e
S o ftw a r e
I n h e r ita n c e
V ie w
I n h e r ita n c e
• 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
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The
Problem
of
Perspective
What you see or think depends on how you see or think
GOOD
BAD
WITHOUT THE
UNIVERSAL
DOES A
PERSPECTIVE
UNIVERSAL
THERE
PERSPECTIVE
WOULD
BE NO
EXIST
SHARED
UNDERSTANDING
?
BAD
© Amit Mitra & Amar Gupta
GOOD
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
P E R S P E C T IV E
P E R S P E C T IV E
P E R S P E C T IV E
P E R S P E C T IV E
SH A R ED
P E R S P E C T IV E
P E R S P E C T IV E
P E R S P E C T IV E
P E R S P E C T IV E
P E R S P E C T IV E
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• TRUTH DEPENDS ON CONTEXT
• CONTEXT ADDS INFORMATION
– PERSPECTIVE PROVIDES INFORMATION
– IS A KIND OF OBJECT
CONTEXT 1
GOOD
BAD
CONTEXT 2
© Amit Mitra & Amar Gupta
BAD
GOOD
THE TYRANNY OF WORDS
Synonyms and Homonyms
OBJECT 1
(meaning)
OBJECT 2
(meaning)
NAME
(homonym)
(synonym)
NAME
(homonym)
(synonym)
NAME
(synonym)
NAME
(synonym
&
homonym)
OBJECT 1
(meaning)
NAME
(synonym)
NAME
(synonym)
NAME
(synonym)
OBJECT 2
(meaning)
NAME
(synonym)
NAME
(synonym)
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Primary Name vs Alias
ALIAS
(synonym)
ALIAS
(synonym)
ALIAS
(synonym)
ALIAS
(synonym
&
homonym)
OBJECT 1
PRIMARY
NAME
ALIAS
(synonym)
ALIAS
(synonym)
ALIAS
(synonym)
OBJECT 2
PRIMARY
NAME
ALIAS
(synonym)
ALIAS
(synonym)
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Aliases and Perspectives
Each concept must
have a name, and may
have many
Each name must be in a
a context and may
be the same in many contexts
NAME
(synonyms, i.e.,
Aliases)
CONCEPT
(object)
Each name must
be the name of at
least one object,
perhaps many
Each perspective must be held
by at least one person or organization
and may be held by many
PERSPECTIVE
or CONTEXT
(Model)
Each perspective must have
at least one named concept,
probably more
PERSON/ or
ORGANIZATION
(Key stake holders:
Persons and Groups)
Each person or organization
must hold at least one
perspective, perhaps more
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The Metamodel of Object
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METAOBJECT
As a juggler plays many a part, wears many a guise
And doffs his mask when the show is done
So is our creator one; the only one
- Guru Arjan Singh of Sikhism in the holy
book, Adi Granth
Irreducible
Criteriafor differentiating
Irreduciblefacts
fact about a
su
bs
ets
of
o
bje
ct
O
B
JE
C
T
O
B
JE
CT
DOMAIN
FORMAT
CONSTRAINT
NAME
(Temporal
RELATIONSHIP
about Collections AGGREGATE
OBJECT
limitation
instancesinan object PARTITION INSTANCE
OBJECT
P
R
O
P
ER
TY
Occurrence)
and structures
Irreduciblefacts
class
Irreducible
ab
out formatsfor
Set of object
Ass
e
rtio
n
s
a
bo
ut
factabout
Isolated
S
Y
N
O
N
Y
M
H
O
M
O
N
Y
M
n
i
sta
nc
es
pr
e
senting object
S
ET
OF
m
e
a
su
re
m
en
t
a
nd
Irreducible fact
the existence
Collectionof
TRAJECTORY
irreducible
with some
POSSIBLE
propertiesto
clas
sifi
c
ation
of
o
bje
ct
IN
S
TA
T
E
o
f
a
co
nce
pt
involving twoor Different The same
Irreducible
TRAJECTORIE
fa
ct
ab
o
ut
s
h
ared
observers
S
PA
C
E
behaviorcommonto
Model:
oritemfor a
moreobjects, Names for Name for ALIAS CONCEPT
factsabout
SINSTATE
a
sin
g
le
(h
umanor
be
h
av
ior
m
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ltip
le
p
ro
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erties
of
Set of
finiteinterval
or thesame the same different
thecondition
SPACE
ID
o
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ct
m
e
cha
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T
he
se
t
of
A
lt
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object
structured ofan object
of time
object at
objectclass
Set of allpossible
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C
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a
m
es
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ss
es
in
tercon
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te
different times
instance at a
QUALITATIVE
QUANTITATIVE
MEASURE
changesin stateof an
Identifier OBJECT d concepts
c
ha
ng
e
s
in
DOMAIN
DOMAIN
moment in
(UOM)
ATTRIBUTE
(StatesofNam
e)
EFFECT
DYNAMIC
stateof an object instance
CLASS
tim
e
Irre
d
uc
ible
facts
STATIC
RELATIONSHIP
Irreduciblefact about the
STATE object
RELATIONSHIP
PERSPECTIVE STATE
Irre
du
cib
le
fa
ct
ab
ou
t
U
n
itsof
(Process)
SPACE instance
existence of asinglepropertyof
a
bo
ut
the
po
ssib
le
m
ea
s
ur
e
m
ent
rreducible fact Time
an object instance at amoment
Theset of all
Irreducible
ch
an
g
e
in
the
in
tim
e
D
IF
F
ER
EN
C
E
R
A
T
IO
about timingor independent factsabout
NOMINAL
ORDINAL
possible
stateofan object DOMAIN
SCALED
SCALED
DOMAIN
sequence
Irreducible fact existenceof a SUBTYPE SUPERTYPE
UNIVERSAL
OTHER
conditionsof
Irreducible fact the
DOMAIN
DOMAIN
fromonemoment
PERSPECTIVE PERSPECTIVE
a
n
o
bje
c
t
P
O
S
SIB
L
E
Irreduciblefacts
Irreducible subtype
Irreducible Irreduciblefacts
p
ossib
ility
of
a
n
o
bje
ct
to
a
n
othe
r
in
R
ep
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sitory
of
R
ep
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sitory
of
PA
R
T
IC
IP
AT
O
I
N
about
fact about
instance'sinvolvement ina
responsetoan fact about about orderor Irreduciblefactsabout
INA
Universally
Specialized
shared
SUBTYPING unshared
timingof/
specificrelationship RELATIONSHIP event
classification rankingof
magnitudesof differencesmagnitudesof
RELATIONSHIP irreducible irreducible shared concepts concepts and
ratiosbetween
triggersfor
only
objects
between objects
and meanings meanings
facts
facts
objects
behavior
EVENT
© Amit Mitra & Amar Gupta
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
© Amit Mitra & Amar Gupta
37