Optimization of Fuzzy Semantic Networks Based on Galois ... - arXiv

Eighth international Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems.

Optimization of Fuzzy Semantic Networks Based on Galois Lattice and Bayesian Formalism Mohamed Nazih Omri ERPAH-FST & DMI-IPEIM, Route de Kairouan, 5019 Monastir. Tel. 216 3 500 273, Fax. 216 3 500 512 E-mail: [email protected]

Abstract

always

optimal

because

some

relationships

This paper presents a method of optimization,

between couple of user objects can be generalized

based on both Bayesian Analysis technical and

and others suppressed according to values of forces

Galois Lattice of Fuzzy Semantic Network. The

that characterize them.

technical System we use learns by interpreting an

obtained Net, we propose to proceed to an

unknown word using the links created between this

Inductive Bayesian Analysis, on the Net obtained

new word and known words. The main link is

from Galois lattice. The objective of this analysis

provided by the context of the query. When

can be seen as an operation of filtering of the

novice’s query is confused with an unknown verb

obtained descriptive graph.

Indeed, to simplify the

(goal) applied to a known noun denoting either an object in the ideal user’s Network or an object in

Keywords: Fuzzy semantic Networks, Fuzzy

the user’s Network, the system infer that this new

semantic Networks, Optimization.

verb corresponds to one of the known goal. With the learning of new words in natural language as

1

Introduction

in

In order to respond to a query, an executive

agreement with the user, the system improves its

assistant might know very precisely the goal

representation scheme at each experiment with a

the user has in mind, which means an object

new user and, in addition, takes advantage of

in a given state (the properties of the object

the

interpretation,

which

was

produced

previous discussions with users. The semantic Net

being transformed). Moreover, even when

of user objects thus obtained by learning is not

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Eighth international Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems.

goals are fairly well defined, it is often

and he often would like to ask an expert

necessary to think about superordinate goals.

operator about how to execute an action such

Let’s take (example 1) the query of a subject

as "how to rub letters" [12], [13].

using a Macintosh Computer. 2

The Ideal Expert’s and Novice User’s

The Galois lattice [6] and the fuzzy set methods Fuzzy Semantic Net have been used to develop the "on-line instructions" We define the ideal Expert knowledge of a mechanisms of an Intelligent Assistance System. It system as the knowledge that is sufficient to can be seen as a supervisor of task execution that the system and that is described in a semantic has the "ideal user's knowledge" of (i) prerequisites network (figure1). Construction of the Ideal of procedures, (ii) subGoals structure. And (iii) the Expert Knowledge starts if given a set of semantic network of the elements of the device tasks that are executed using elements of one where applied procedures are used as properties, as technical device through procedures. The first well as (iv) the knowledge of perceptible and step is the task decomposition as a hierarchy imperceptible effects of user's actions. With an of Goal decomposition into subGoals from interactive dialogue with a user, the Assistance the level of the Goal of the task to primitive System tries to match items provided by users in actions. The second step consists in (i) natural language with the knowledge included in drawing up a list of possible Goals and the the ideal user's semantic network [7], [12]. procedures

to

reach

these

Goals

(ii)

The example of the technical system we constructing the Ideal Expert Net as a consider here is Word Processor software classical semantic network. But, instead of (figure1), with Objects such as "chain-ofusing

structural

properties

of

systems

characters", and procedures such as "cut" or interface Objects; Goals reachable with those "copy". For a novice user of the software, the Objects are used as properties. The ideal list of standard denominations is not obvious

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Eighth international Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems.

user's description uses valid procedures that

the Ideal Expert Net [12]. If the Assistance

have to be applied to the elements of the

System does not understand the meaning of

device in order to successfully complete the

an instruction, it discusses with the user until

task. Classes of Objects and relations between

it is able to interpret the query in its own

classes of Objects merge from routines for

language [14]. With the learning of new

classification

words

and

routines

for

classes

in

natural

language

as

the

organization [22].

interpretation produced in agreement with the

However given the polysemic aspects of

user, the system improves its representation

natural language (verbs and nouns which

scheme at

express goals and device objects), with the

each experiment with a new user. And, in

necessity of a man-machine interface that

addition,

involve queries of users, the problem that is

discussions with users. In a first time the

under investigation is how to match the

standard Objects and recognized by the

content of a query (the label of an Object and

software are described in a semantic network

the label of a Goal applied to this Object, as

where goals stand for properties of Objects.

expressed by a novice user) to their

And in a second time, as the queries of an

corresponding items (class of Objects and

user are expressed in natural language and as

Goals as properties) in the Ideal Expert Net.

they correspond more or less to these standard

By answering queries of the users while they

denominations, the system establishes fuzzy

try to perform a given goal, the Expert

connections between its primary knowledge

Assistant

and the new labels of Objects or procedures

delivers

not

only

planning

takes

advantage

of

previous

information, but also a goal structure and the

expressed by the user [12], [16].

knowledge of what justifies the procedure by

The obtained semantic Net of user objects is

providing the knowledge that is included in

not

always

optimal

because

some

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Eighth international Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems.

relationships between couple of user objects

construct the semantic user object system.

can be generalized and others suppressed

This construction consists; from a symbolic

according to values of forces that characterize

table of linguistic data (table 2), to construct,

them. Indeed, to simplify the obtained Net,

in a first time the binary table (crossed

we propose to proceed to an inductive

system’s objets with user objects are obtained

Bayesian analysis on the obtained Net from

by 0 and 1) (table 3), and in a second time,

Galois lattice [8],[25]. The objective of this

the different implications between each

analysis can be seen as an operation of

couple of user objects.

filtering of the obtained descriptive graph.

To illustrate this method, we propose to construct the semantic user objects Net

3

Optimization of the Fuzzy Semantic Nets by

corresponding to the following symbolic table

Bayesian Analysis

(table 2). This last allows us to construct the

The approach that we present in this paper

is

established

from

Procope‘s

user objects Net with all possible implications between each couple of objects according to

formalism [18], [19], based on the Galois

the next rule.

lattice

Bayesian

defined by a set of property ai with i ∈ [1, n],

formalism [1], [2], [5]. The underlying idea is

we have A implies B if and only if ∀ ai

to end to a hierarchical structure of object

verifying A then ai verifying also B. To

users

construct this graph, we have used the

method

allowing

categorization

[9]

and

having by

the

a

process

discrimination

of and

software

GLG

Let A and B two Objects

(Galois

lattice’s

Graph)

generalization. To end to a hierarchical

developed

structure of user objects in the form of a

Department of the Preparatory Institute to

symbolic data table, the method of the Galois

Studies of Engineer of Monastir and that is

lattice is the means that we have adopted to

going to be published later.

in

Mathematics

and

Physics

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Eighth international Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems.

The obtained semantic Net of user objects is

implicative structures corresponding to the

not

form of implicative graph (figure 2).

always

optimal

because

some

relationships between couple of user objects can be generalized and others suppressed

3.1

according to values of forces that characterize

From observations realized on each couple of

them. Indeed, to simplify the obtained Net,

user objects, we have built the following table

we propose to proceed to an inductive

(table 4) that presents sorting crossed in

Bayesian analysis on the obtained Net from

effective for each pair of user objects. Each

Galois lattice [8], [25].

places in table 4 represents 768 users of the

The principal objective of this analysis is to

software that we have put in place.

find all the possible oriented dependence

instance, in the first places, corresponding to

existing between different user objects: the

the couple of objects 'the Sign' and 'the

knowledge of some will determine - it such or

number', 100 users have used the word 'the

such others. To reply to this objective, we

Sign' to each time that they have used the

have considered the following user objects:

word 'the number' to designate a system's

The number, The Sign, The letters, The

object. 30 other users have used the word 'the

numbers, The Characters and Substantive.

number' without used the word 'the Sign'. 85

These user objects represent synonymies by

have used the word 'the Sign' without using

novice users to designate the following

the word 'the number' and 553 remainder of

system’s objects: Char, Word and Key shown

the total effective have not used neither the

in table 2. To determine the different binary

word 'the Sign' nor the word 'the number' to

relationships

designate system's object.

between

each

couple,

the

Descriptive Inductive Analysis

For

analysis consists to study the implicative

For each of these crossed sorting, we

structure to

calculate the Loevinger’s indication H [3], [4]

each

couple,

then

to

all

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Eighth international Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems.

associated to the four possible error squares.

presents relationships of q-exclusion and

Positive indices are represented in fat (table

tendency to the q-exclusion.

4). If we consider the two values-mark htend=0,40 and hquasi=0,60 we have to respect

3.2

next conclusions:

Analysis

H < htend htend ≤ H

absence of q-implication ≤ hquasi tendency to the q-

implication H ≥ hquasi q–implication

Processing by Inductive Bayesian

This stage consists in determine with the help of the IBA [2], [3], observed oriented relationships

descriptively

that

can

be

certified inductively, among all relationships

The suitable figure 3 shows two possible

in order that the indication H ≥ 0,20. The

cases. The first case, constituted following

objective of this analysis can be seen as an

user objects: Substantive, The number, The

operation

Sign, The letters, and The numbers. Positive

descriptive graph (figure 3).

connection following q-implication from The

In order that, we are going to calculate, to

number to The Sign. From The Sign to The

each places in the table 5 above (H < 0,20),

letters with tendency to the equivalence, q-

the inferior credibility limit, for a guarantee -

implication with equivalence between The

mark δ=90, for the corresponding indication

Sign and The numbers, tendency to the q -

dress η.

implication from The Sign to The numbers

have used a recent version of the software

and between The number and Substantive

IBA-2 developed in the Cognitive Psychology

with tendency to the equivalence. The second

Laboratory of the Paris8 University and that

case constituted by the number user objects,

is going to be published later. Results of these

Substantive, The Characters and The Sign

calculations are presented in the following table 6.

of

filtering

of

the

obtained

To realize these calculations, we

Negative values are not taken in

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Eighth international Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems.

account and therefore it does not appear in

allows identifying the unknown novice user

table 5.

request of the share of the device used. This

The results of this filtering allow

determining

relationships

that

can

be

can serve as basis for our research so as to

generalized, among the totality of observed

elaborate a general methodology to diagnosis

relationships descriptively.

the purpose goal of the subject, applicable to

According to the graph of the figure 4, we can

a large diversity of devices. The objective

certify on the one hand, a q-implication with

being to find the totality of compatible

tendency to the equivalence between The Sign

purposes with actions of the users, the trip of

and the letters user objects and a q-

such graphs facilitates grandly the research.

implication from The Sign to The number. We

The development of this method would have

can also certify, on the other hand, a tendency

to allow a best approximation of the category

to the q-implication from Substantive to The

of the purpose aimed by the user and best

number. For the implication from the letters

approaches the diagnosis. We think that it

to The Characters and from this last to the

would be interesting to strengthen this tool of

numbers, we notices that there is an absence

softening with the notion of similarity

of q-implication with tendency to the

between two Objects (respectively two Goals)

exclusion.

so as to establish connection between user Object (or Goal) and system Object (or

4

system Goal) in the semantic Net. This makes

Conclusion Although the approach presented in this

only increase performances of the system in

paper, that consists of a learning of new word

the course of the identification of user

in natural language

requests.

in a fuzzy semantic

Networks, represent a particular methodology to diagnosis the goal query’s novice users and

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Eighth international Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems.

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BackWardWord [Direction(Backward) ]

Word Choose* Unit [direction(Direction)] select*

ForWardWord [direction(Forward)] The letters

Key press

Object

BackWardChar [direction(Backward)]

Char choose*

ForWardChar [direction(Forward)] Backward choose* Direction

The number Forward choose*

« How to Gum Letters ? »

Figure 1: The Semantic Network of Novice Users.

P rocedure P i

(P roperties) Y

Z (properties )

Procedure P j

X (properties)

P rocedure P k

In clu sio n r e la tio n ( X is a k in d o f

Y)

Figure 2: Procedural Semantic Net representation with inclusion relations. Procedural and declarative semantics of the device merges in regard of applied procedures. Classes Y and Z inherit of procedures of superordinate classes as class X inherits of procedures of both Y and Z classes (multiple inheritance).

Table 1: Key Direction (Forward) Direction (Backward) Choose Select Press

Forward-Word X

Backward-Word

Forward-Char X

X X X

X X

Backward-Char X X X

X X

Char X X X X

Word X X X X

Unit X X

Direction

X X

X

Table 2. Example of symbolic table. Char Word Key

Novice User 1 The number The numbers The Characters

Novice User 2 The Sign The letters Substantive

Novice User 3 The letters Substantive Substantive

Novice User 4 The numbers The Sign The Characters

Novice User 5 The number The Sign The letters

Table 3. Galois lattice corresponding to the table 2. The number Char Word Key

1 0 0

The Sign 1 1 0

The letters 1 1 1

The numbers 1 1 0

The Characters 0 0 1

Substantive 0 1 1

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Eighth international Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems.

The Sign

The Characters

The letters

The numbers

The number

Substantive

Figure 3. The user’s objets Net corresponding on the table 2. Table 4: Table of staffs crossed to each couple of user objects. The Sign The number

100 85

The letters 30 553

50 143 150 43

The Sign

The numbers

80 495 35 540

The letters

The Characters

Substantive

49 100 49 100

81 538 136 483

38 70 43 65

92 568 142 518

66 50 46 70

64 588 139 513

49 100

144 475

78 30

115 545

26 90

167 485

49 59

100 560

29 87 38 78

120 532 70 582

The numbers The Characters

Table 5: Table of Loevinger’s indices to each couple of user objects. The Sign The number

The letters

The numbers

The Characters

Substantive

-2,19

0,7

-0,53

0,18

-0,94

0,22

-1,08

0,18

-2,36

0,42

0,45

-0,14

0,11

-0,04

0,19

-0,05

0,22

-0,04

0,48

-0,09

-2,23 0,71

0,75 -0,24

0,57 0,12

0,09 -0,03

-0,65 0,21

0,11 -0,03

-0,65 0,2

0,11 -0,04

-0,3 0,1

0,07 -0,02

-1,87 0,18 -1,34 0,32

0,31 -0,1 0,22 -0,05

0,11 -0,04 -0,23 0,07 -1,33 0,22

-0,02 0,01 0,05 -0,01

The Sign The letters The numbers The Characters

0,24 -0,04

Table 6 : Table of inferior credibility limit for each indication H with the guarantee 0.90. The Sign The number

The letters

The numbers

The Characters

Substantive

0,156

0,414

0,168

0,634 0,397

The Sign

0,36

0,698 0,658

0,135

The letters

0,264

The numbers

0,171 0,253

The Characters

0,174 0,159

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Eighth international Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems.

0.48

The number 0.42 0.45

0.22

Substantive

0.42 0.22

0.22

The numbers

0.70 0.45

0.57

0.24

0.22 0.32

The letters

0.75 0.71

The Sign

0.31 The Characters

0.21

Figure 4: The implicative descriptive graph of relationships with the indication H ≥ 0,20.

The Sign 0,698

0,634 0,658 0,397

The letters 0,264 The Characters

The number 0,360

0,414

Substantive

0,253

The numbers

Figure 5: The implicative inductive graph of relationships with the indication H ≥ 0,20.

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