A Cognition Using Semantic Balance and Refinement of Internal and External Knowledge

topsalmonAI and Robotics

Feb 23, 2014 (3 years and 5 months ago)

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A Cognition Using Semantic Balance
and Refinement of Internal and
External Knowledge


The goal of this topic is to study knowledge refinement method
based on semantic balance of knowledge.


Reference:

Grebenyuk V., Kaikova H., Terziyan V., Puuronen S.,
The

Law of Semantic Balance and its Use in Modeling
Possible Worlds, In:
STeP
-
96

-

Genes, Nets and
Symbols
, Publ. of the Finnish AI Society, Vaasa,
Finland, 1996, pp. 97
-
103.


This topic presents a
knowledge refinement strategy

to
handle
incomplete knowledge

during a cognition process.


The goal of this research is to develop formal tools that
benefit the
law of semantic balance
. The assumption is
used that a situation inside the object’s boundary in some
world

should be in balance with a situation outside it.

It
means that continuous cognition of an object aspires to a
complete knowledge about it and knowledge about internal
structure of the object will be in balance with knowledge
about relationships of the object with other objects in its
environment.


It is

supposed that one way to discover incompleteness of
knowledge about some object is to measure and compare
knowledge about its

internal and external structures

in an
environment.

Basic Concepts


Let
A
i

and
A
j

be

atomic

objects
.


Let
L
k

be a
relation

between two objects or one object with
itself. If the relation is objects’ relation with itself then it
corresponds to the

properties

of the object.


The
semantic predicate

P

is
:

P
A
L
A
A
A
L
i
k
j
i
j
k
(
,
,
)
,
,
;
,






1
0
if there
is relatio
n between

and
that has
meaning
otherwise
.


Semantic network

S

is:
S
P
A
L
A
i
j
k
i
k
j


,
,
(
,
,
)
, where
A
i

is the
source

of the relation
L
k
,
A
j

is the
target
of the
relation
L
k
, and
L
k

is the
semantic meaning

of the relation.


Example:


Bill hates poor Mary
”.

A
1
:
<Bill>
;
A
2
:
<Mary>
;
L
1
:
<to hate>
;
L
2
:
<to be
poor>
.

S
P
A
L
A
P
A
L
A


(
,
,
)
(
,
,
)
1
1
2
2
2
2
.


Semantic Const
ants




semantic ZERO (notation
-

IGN
): (it means total ignorance
about relationship between the source object and the target object)




(
,
)
(
(
,
,
)
)
(
,
,
)
A
A
L
P
A
L
A
P
A
IGN
A
i
j
k
i
k
j
i
j



semantic UNIVERSE (notation
SAME
): (it means total
knowledge about relationship between the source obj
ect and the
target object)






A
A
World
P
A
SAME
A
i
i
i
i
(
)
(
,
,
)

There are two special relations
HAS_PART

and
PART_OF

which have their ordinary meanings. If it is true:

P
A
HAS
PART
A
i
j
(
,
_
,
)

or
P
A
PART
OF
A
j
i
(
,
_
,
)

then object
A
j

is included into th
e object
A
i
.

When an object is not part of any other object we call it as a
(possible)
World
:








A
A
P
A
PART
OF
A
A
World
i
j
i
j
i
(
(
,
_
,
)
)

When an object has no other object that is part of it, we call it as
Atom
:







A
A
P
A
HAS
PART
A
A
Atom
i
j
i
j
i
(
(
,
_
,
)
)

Semantic Operations


T
he ordinary
semantic operations

over semantic meanings are:



semantic inversion:

P
A
L
A
P
A
L
A
i
k
j
j
k
i
(
,
,
)
(
,
~
,
)

;

A
i
A
j
A
i
A
j

L
k
~
L
k




semantic addition:

P
A
L
A
P
A
L
A
P
A
L
L
A
i
k
j
i
n
j
i
k
n
j
(
,
,
)
(
,
,
)
(
,
,
)



;

A
j

L
k
A
i
L
n
A
j
A
i
L
L
k
n




semantic multiplication:

P
A
L
A
P
A
L
A
P
A
L
L
A
i
k
m
m
n
j
i
k
n
j
(
,
,
)
(
,
,
)
(
,
*
,
)


.

A
s
A
j

L
k
A
i
L
n
A
s
A
j
L
k
A
i
L
n
L
L
k
n
*


An Example of Possible World


W
A
1
A
2
A
3
A
L
1
L
2
L
3
L
4
L
5
L
7
A
4
A
5
A
6
A
8
A
7
L
6












The Internal Semantics of an Object


Internal semantics

E
A
in
i
(
)

of an object
A
i

is the
semantic sum over all possible paths between any
pairs of objects (
A
j

,
A
k

) included in the object
A
i

plus the paths from each incl
uded object to itself.

E
A
L
in
i
A
A
j
k
j
k
P
A
HAS
PART
A
P
A
HAS
PART
A
j
k
i
j
i
k
(
)
,
,
,
(
,
_
,
)
(
,
_
,
)







where
L
A
A
j
k


is a path from
A
j

to
A
k
.













The Internal Semantics of an Object:
An Example



W
A
1
A
2
A
3
A
L
1
L
2
L
3
L
4
L
5
L
7
A
4
A
5
A
6
A
8
A
7
L
6



E
A
L
L
L
L
L
in
(
)
~
*
~
~




1
2
2
1
7


(figure
a
)


W
A
1
A
2
A
3
L
1
L
2
A
W
A
L
3
L
4
L
5
L
6
a)
b)
A
4
A
5
A
6
A
7
A
8



The External Semantics of an Object


External semantics

E
A
ex
i
(
)

of an object
A
i

is the
semantic sum over all possible paths between any
pairs of objects (
A
j

,
A
k

) included in the World
outside the object
A
i

plus the paths from every of
such object to itself.

E
A
L
ex
i
A
A
j
k
j
k
j
k
i
A
W
A
A
A
A
W
A
A
A
j
k
j
i
j
i
k
i
k
i
(
)
,
,
,
,
(
/
)
(
)
,
(
/
)
(
)















On the other hand
E
A
ex
i
(
)

is the

internal
semantics

of the
World

when
A
i

is taken as
Atom

(without noticing its internal structure).
This gives another formula:

E
A
E
World
E
A
ex
i
in
in
i
(
)
(
/
(
)
)




The External Semantics of an Object:
An Example


W
A
1
A
2
A
3
A
L
1
L
2
L
3
L
4
L
5
L
7
A
4
A
5
A
6
A
8
A
7
L
6



E
A
L
L
L
L
L
L
L
L
L
L
L
L
L
ex
(
)
*
*
*
*
~
*
*
*
*
~







3
4
3
4
5
6
3
4
5
4
4
5
6






L
L
L
L
L
L
L
4
5
5
6
5
3
6
*
*
~
~

(
figure

b
)


W
A
1
A
2
A
3
L
1
L
2
A
W
A
L
3
L
4
L
5
L
6
a)
b)
A
4
A
5
A
6
A
7
A
8



The Law of Semantic Balance


Let us suppose that there exists a possible world
where the ideal situation for an object
A
i

is that
its internal semantics (i.e. its
internal struc
ture

=
objects and their relations) and its
external
semantics

(i.e. its properties when it interacts its
environment) are in
balance
. In this ideal
situation the
law of semantic balance

holds:


E
A
E
A
in
i
ex
i
(
)
=
(
)






The Law of Semantic Balance in
Know
ledge Bases


Usually, especially with knowledge bases, the
ideal situation has not been achieved. Our human
knowledge about objects is almost always
incomplete
. Sometimes we know more about the
structure of an object than its external properties
and someti
mes vice versa.


Let
ign
A
in
t
i
(
)


be our
ignorance

about the
internal semantics of the object
A
i

at the time
t
and let
ign
A
ex
t
i
(
)

be our ignorance about the
external semantics of the object
A
i

at
the time

t

then according the
law of semantic balance
:



E
A
ign
E
A
ign
in
t
i
in
t
ex
t
i
ex
t
(
)
(
)
(
)
(
)
(
)
+
=
(
)
+





The Strategy of Knowledge Refinement


Let us suppose that we have acquired some
knowledge
E
A
in
i
1
(
)

about the internal semantics
of the object
A
i

and that we have acquired some
knowledge
E
A
ex
i
1
(
)

about the external
semantics of it. Let us assume that these two
semantics are not in balance. We make them in
balance trying to remove some part of ignorance
from either or both sides of the

formula:

E
A
ign
E
A
ign
in
i
in
ex
i
ex
(
)
(
)
(
)
(
)
1
1
1
1
(
)
+
=
(
)
+

If this succeeds at least partially we receive
another amount of knowledge
E
A
in
i
2
(
)

about the
internal semantics of the object and another
amount of knowledge
E
A
ex
i
2
(
)

about the external
semantics of
it. If these two semantics are not in
balance or if some outer knowledge source gives
extra knowledge that makes them unbalance
again, then we try to make them in balance again:

E
A
ign
E
A
ign
in
i
in
ex
i
ex
(
)
(
)
(
)
(
)
2
2
2
2
(
)
+
=
(
)
+

and so on.



The Scheme of Knowledge Refinement


ign
ign
...
Bal ance
Step 1
Bal ance
Step 2
Bal ance
Bal ance
E
E
E
E
E
E
E
E
in
ex
in
in
in
ex
ex
ex
E
in
E
ex
a)
b)
c)
d)
e)
f)
IGN
IGN
i n
ign
i n
ign
i n
ign
i n
ex
ign
ex
ign
ex
ign
ex




Discussion


SEMANTIC BALANCE

-

BALANCE BETWEEN
REALITY AND FORMALITY

??!


1. Formal properties of an object


-

properties that are being conferred to object.

2.
Real structure of object


-

structure that object really has recently.

3.
Real Properti
es of object

-

properties that can be derived from
2
.

4. Formal structure of object


-

structure that can be derived from
1
.

Balance means conformity between
1

and
2
!

Doesn’t it ?




Discussion: An Example

Formal Properties of Object A:


P(A,<to be family
>,A)


Formal Structure of Object A:


P(A,HAS_PART,B);



P(A,HAS_PART,C);

P(B,<to be husband>,B);


P(C,<to be wife>,C);

P(B,<to bring money to>,C);

P(C,<to take care of>,B);

P(B,<to love>,C);



P(C,<to love>,B).



B
C
A
To be
husband
To be
wife
To bring money to;
To love
To take care of;
To love



Discussion: A
n Example


Real Structure of Object
:


P(B,<to be husband>,B);


P(C,<to be wife>,C);

P(B,<to bring money to>,D);

P(C,<to take care of>,E);

P(B,<to love>,D);



P(C,<to love>,E);

P(D,<to be friend to>,A);


P(E,<to be friend to>,A);

P(B,<to hate>,C);



P(C,<to

hate>,B).


B
C
A
To be
husband
To be
wife
To bring money to;
To love
To take care of;
To love
D
E
To hate
To hate
To be
friend of
To be
friend of


Real Properties of Object:


P(A,<to be crazy couple>,A)



Discussion


To be in balance it is necessary to
change
formalities

and
not to change real relations
!

Isn’t so ?

In the Example:


1) to divorce family


A =
(B & C);

2) to create new family

F = (B & D);

3) to create new family

G = (C & E).



B
C
F
To be
husband
To be
wife
To bring
money to;
To love
To take
care of;
To love
E
To be
friend of
To be
friend of
To be
husband
To be
wife
D
G