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