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
Ai
and
Let
Lk
be a relation between two objects or one object with
Aj
be atomic objects.
itself. If the relation is objects’ relation with itself then it
corresponds to the properties of the object.
The semantic predicate
P is:
1, if there is relation between

P( Ai , Lk , A j )  
Ai and A j , that has meaning Lk ;

0, otherwise.
Semantic network
S
is:
S   P( Ai , Lk , A j ) , where
i , j ,k
is the source of the relation
relation
Lk ,
and
Lk
Lk , Aj
Ai
is the target of the
is the semantic meaning of the relation.
Example: “Bill hates poor Mary”.
A1: <Bill>; A2 : <Mary>; L1: <to hate>; L2 : <to be
poor>.
S  P( A1 , L1 , A2 )  P( A2 , L2 , A2 ) .
Semantic Constants
 semantic ZERO (notation - IGN): (it means total ignorance
about relationship between the source object and the target object)
( Ai , Aj )Lk ( P( Ai , Lk , Aj ))  P( Ai , IGN , Aj )
 semantic UNIVERSE (notation SAME): (it means total
knowledge about relationship between the source object and the
target object)
Ai ( Ai  World  )  P( Ai , SAME , Ai )
There
are
two
special
relations
HAS_PART
and
PART_OF which have their ordinary meanings. If it is true:
P( Ai , HAS _ PART , Aj )
then object
Aj
or
P( Aj , PART _ OF, Ai )
is included into the object
Ai .
When an object is not part of any other object we call it as a
(possible) World:
Ai Aj ( P( Ai , PART _ OF, Aj ))  Ai  World 
When an object has no other object that is part of it, we call it as
Atom:
Ai Aj ( P( Ai , HAS _ PART , Aj ))  Ai  Atom 
Semantic Operations
The ordinary semantic operations over semantic meanings are:

semantic inversion:
Ai

~
P( Ai , Lk , A j )  P( A j , Lk , Ai ) ;
~
L
Lk
k
Aj

Aj
Ai
semantic addition:
P( Ai , Lk , Aj )  P( Ai , Ln , Aj )  P( Ai , Lk  Ln , Aj );
Lk
Ai
Aj
Ln


Lk  Ln
Ai
Aj
semantic multiplication:
P( Ai , Lk , Am )  P( Am , Ln , Aj )  P( Ai , Lk * Ln , Aj ) .
Lk
Ai
As
Ln
Aj

Lk
As
Ln
Aj
Ai
Lk * Ln
An Example of Possible World
A8
W
A4
L6
A
A1
L1
L3
L7
L 2 A2
L5
A3
L4
A5
A6
A7
The Internal Semantics of an Object
Internal semantics
Ein ( Ai ) of an object Ai
is the
semantic sum over all possible paths between any
pairs of objects (
Aj , Ak
) included in the object
plus the paths from each included object to itself.
Ein ( Ai ) 
where
LAj  Ak
 LA  A
j
k
j , k , j  k ,
P( Ai , HAS _ PART , A j )
P( Ai , HAS _ PART , Ak )
is a path from
Aj
to
Ak .
Ai
The Internal Semantics of an Object:
An Example
A8
W
A4
L6
A
A1
L1
L7
L 2 A2
L5
A3
L3
L4
A7
A6
A5
~ ~
~
Ein ( A)  L1 * L2  L2  L1  L7 (figure a)
a)
W
b)
A8
A
W
A
L6
A4
A1
L1
A3
L 2 A2
L5
L3
L4
A5
A6
A7
The External Semantics of an Object
External semantics Eex ( Ai ) of an object Ai is the
semantic sum over all possible paths between any
pairs of objects (
Aj
,
Ak
) included in the World
outside the object Ai plus the paths from every of
such object to itself.
Eex ( Ai ) 
 LA  A
j
k
j , k , j  k , j  k  i ,
( A j W / Ai ) ( A j  Ai ),
( Ak W / Ai ) ( Ak  Ai )
On the other hand
Eex ( Ai ) is the internal
semantics of the World when Ai is taken as
Atom (without noticing its internal structure).
This gives another formula:
Eex ( Ai )  Ein (World / Ein ( Ai ))
The External Semantics of an Object:
An Example
A8
W
A4
L6
A
A1
L1
L7
L 2 A2
L5
A3
L3
L4
A7
A6
A5
~
Eex ( A)  L3 * L4  L3 * L4 * L5 * L6 
~
 L3 * L4 * L5  L4  L4 * L5 * L6 
~
~
 L4 * L5  L5 * L6  L5  L3  L6 (figure b)
a)
W
b)
A8
A
W
A
L6
A4
A1
L1
A3
L 2 A2
L5
L3
L4
A5
A6
A7
The Law of Semantic Balance
Let us suppose that there exists a possible world
where the ideal situation for an object
Ai
is that
its internal semantics (i.e. its internal structure =
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:
Ein ( Ai ) = Eex ( Ai )
The Law of Semantic Balance in
Knowledge 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 sometimes vice versa.
t
ign
Let
in ( Ai ) be our ignorance about the
internal semantics of the object
and let
t
ex
ign ( Ai )
Ai
at the time t
be our ignorance about the
external semantics of the object Ai at the time t
then according the law of semantic balance:
(t )
in
(t )
in
E ( Ai ) + ign
(t )
ex
(t )
ex
= E ( Ai ) + ign
The Strategy of Knowledge Refinement
Let us suppose that we have acquired some
1
E
knowledge in ( Ai ) about the internal semantics
of the object Ai and that we have acquired some
1
Eex
( Ai )
knowledge
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:
(1)
in
(1)
in
E ( Ai ) + ign
(1)
ex
(1)
ex
= E ( Ai ) + ign
If this succeeds at least partially we receive
2
in
another amount of knowledge E ( Ai ) about the
internal semantics of the object and another
2
E
amount of knowledge ex ( Ai ) 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:
( 2)
( 2)
Ein ( Ai ) + ignin
and so on.
( 2)
( 2)
= Eex
( Ai ) + ignex
The Scheme of Knowledge Refinement
a)
b)
c)
d)
e)
IG N
IG N
i g n in
E in
i g n in
i g n in
E in
E in
i g n in
E ex
i g n ex
Step 1
E ex
i g n ex
Balance
E ex
E in
Balance
i g n ex
E ex
i g n ex
Step 2
Balance
...
f)
E in
E ex
Balance
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 Properties 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(B,<to be husband>,B);
P(B,<to bring money to>,C);
P(B,<to love>,C);
P(A,HAS_PART,C);
P(C,<to be wife>,C);
P(C,<to take care of>,B);
P(C,<to love>,B).
A
To be
husband
To be
wife
To bring money to;
To love
B
C
To take care of;
To love
Discussion: An Example
Real Structure of Object:
P(B,<to be husband>,B);
P(B,<to bring money to>,D);
P(B,<to love>,D);
P(D,<to be friend to>,A);
P(B,<to hate>,C);
P(C,<to be wife>,C);
P(C,<to take care of>,E);
P(C,<to love>,E);
P(E,<to be friend to>,A);
P(C,<to hate>,B).
A
To be
wife
To be
husband
To hate
B
To hate
C
To bring money to;
To love
To be
friend of
D
To take care of;
To love
To be
friend of
E
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
2) to create new family
3) to create new family
A = (B & C);
F = (B & D);
G = (C & E).
To be
wife
To be
husband
F
B
To bring
money to;
To love
To be
wife
C
To be
friend of
G
To take
care of;
To love
To be
friend of
To be
husband
D
E