=Paper=
{{Paper
|id=None
|storemode=property
|title=Ontology-Based Generation of Object Oriented Bayesian Networks
|pdfUrl=https://ceur-ws.org/Vol-818/paper2.pdf
|volume=Vol-818
}}
==Ontology-Based Generation of Object Oriented Bayesian Networks==
https://ceur-ws.org/Vol-818/paper2.pdf
Ontology-based generation of Object Oriented Bayesian Networks
Mouna Ben Ishak Philippe Leray Nahla Ben Amor
LARODEC Laboratory Knowledge and Decision Team LARODEC Laboratory
ISG, University of Tunis LINA Laboratory UMR 6241, ISG, University of Tunis
Tunisia, 2000 Polytech’Nantes, France Tunisia, 2000
mouna.benishak@gmail.com philippe.leray@univ-nantes.fr nahla.benamor@gmx.fr
Abstract reasoning under uncertainty. Ontologies allow logi-
cal reasoning about concepts linked by semantic re-
Probabilistic Graphical Models (PGMs) are lations within a knowledge domain. Even though they
powerful tools for representing and reasoning represent two different paradigms, PGMs and ontolo-
under uncertainty. Although useful in sev- gies share several similarities which has led to some
eral domains, PGMs suffer from their build- research directions aiming to combine them. Concern
ing phase known to be mostly an NP-hard for the majority of them was to extend ontologies in
problem which can limit in some extent their order to support uncertainty. This is either by adding
application, especially in real world applica- additional markups to represent probabilistic informa-
tions. Ontologies, from their side, provide a tion or by mapping the ontology into a PGM in order
body of structured knowledge characterized to enrich ontology reasoning with probabilistic queries.
by its semantic richness. This paper proposes Few works intend to construct PGMs using ontologies.
to harness ontologies representation capabil- In this area, Bayesian networks (BNs) (Pearl, 1988) are
ities in order to enrich the process of PGMs the most commonly used. Typically, concepts are as-
building. We are in particular interested in sociated to nodes, ontology relations are used to link
object oriented Bayesian networks (OOBNs) these nodes, and for some proposals, axioms are in-
which are an extension of standard Bayesian volved to express nodes or edges or to define the states
networks (BNs) using the object paradigm. of variables. However, given the restrictive expressive-
We show how the semantical richness of on- ness of Bayesian networks, these methods focus on a
tologies might be a potential solution to ad- restrained range of ontologies and neglect some of their
dress the challenging field of structural learn- components such as representing concepts properties,
ing of OOBNs while minimizing experts in- non taxonomic relations, etc. To overcome this weak-
volvement which is not always obvious to ob- ness, we propose to explore other PGMs, significantly
tain. More precisely, we propose to set up more expressive than standard BNs, in order to ad-
a set of mapping rules allowing us to gener- dress an extended range of ontologies.
ate a prior OOBN structure by morphing an We are in particular interested in object oriented
ontology related to the problem under study Bayesian networks (Bangsø and Wuillemin, 2000)
to be used as a starting point to the global (OOBN), which are an extension of standard BNs. In
OOBN building algorithm. fact, OOBNs share several similarities with ontologies
and they are suitable to represent hierarchical systems
as they introduce several aspects of object oriented
1 Introduction modeling, such as inheritance. Our idea is to bene-
fit from ontologies in order to address the challeng-
Knowledge representation (KR) is one of the principal
ing problem of OOBN structure learning known to
areas of Artificial Intelligence which was studied by
be an NP-hard process. To this end, we first estab-
different techniques coming from various disciplines.
lish the correspondence between OOBNs and ontolo-
In this work we will focus on probabilistic graphical
gies. Then, we describe how to generate a prior OOBN
models and ontologies which are considered within the
structure by morphing an ontology related to the prob-
most efficient frameworks in KR.
lem under study and then to use it as a starting point
Probabilistic graphical models (PGMs) provide an ef- to the global building OOBN algorithm. This latter
ficient framework for knowledge representation and will take advantages from both semantical data, de-
rived from ontology which will ensure its good start-up • OT is the set of output nodes. They are nodes
and observational data. from the class usable outside the instantiations of
the class and they can not have parents outside
The remainder of this paper is organized as follows:
t. An output node of an instantiation can be a
In sections 2 and 3 we provide a brief representation
reference node if it is used as an output node of
of our working tools. In section 4, we show how to
the class containing it.
benefit from knowledge provided by an ontology to
define the structure of an OOBN. In section 5 we rep-
Internal nodes, which are not instantiations of classes,
resent a survey on existing approaches trying to find a
and output nodes (except those that are reference
combination between PGMs and ontologies. The final
nodes) are considered as real nodes and they repre-
section summarizes conclusions reached in this work
sent variables. In an OOBN, nodes are linked using
and outlines directions for future research.
either directed links (i.e., links as in standard BNs) or
reference links. The former are used to link reference
2 Object Oriented Bayesian Networks or real nodes to real nodes, the latter are used to link
reference or real nodes to reference nodes. Each node
Probabilistic graphical models (PGMs) provide an effi- in the OOBN has its potential, i.e. a probability dis-
cient framework for knowledge representation and rea- tribution over its states given its parents. To express
soning under uncertainty. In the literature, we distin- the fact that two nodes (or instantiations) are linked
guish a panoply of PGMs sharing two common com- in some manner we can use construction links (− − −)
ponents: a graphical one (i.e. a set of nodes and which only represent a help to the specification.
links) and a numerical one allowing the quantifica-
When some classes in the OOBN are similar (i.e. share
tion of different links defined in the graphical com-
some nodes and potentials), their specification can be
ponent via probability distributions. Among the most
simplified by creating a class hierarchy among them.
used PGMs we can mention Bayesian networks (BNs)
Formally, a class S over (IS , OS , HS ) is a subclass of
(Pearl, 1988) which have been largely developed and
a class T over (IT , OT , HT ), if IT ⊆ IS , OT ⊆ OS and
used in several real world applications. Despite their
HT ⊆ HS .
great success, BNs are limited when dealing with large-
scale systems. Thus, several extensions have been pro- Example 1. Figure 1 represents the insurance net-
posed in order to broaden their range of application, work adapted to the OOBN framework (Langseth and
such as object oriented Bayesian networks (OOBNs) Nielsen, 2003). This network contains six classes (In-
(Bangsø and Wuillemin, 2000), (Koller and Pfeffer, surance, Theft, Accident, Car, CarOwner and Driver).
1997) which introduce the object oriented paradigm In this figure only the interfaces of the encapsulated in-
into the framework of BNs. Object Oriented Bayesian stantiations are shown, dashed ellipses represent input
Networks (OOBNs) are a convenient representation of nodes, while shaded ellipses represent output nodes.
knowledge containing repetitive structures. So they For instance, the class CarOwner describes properties
are a suitable tool to represent dynamic Bayesian net- of a car owner. It has no input nodes, the nodes
works as well as some special relations which are not Age, SocioEcon, HomeBase, AntiTheft, VehicleYear
obvious to represent using standard BNs (e.g., exam- and MakeModel operate as output nodes of this class.
ine a hereditary character of a person given those of Moreover, Driven characteristics are a part of the no-
his parents). Thus an OOBN models the domain us- tion of a car owner. Thus, an instantiation of the class
ing fragments of a Bayesian network known as classes. Driver is then encapsulated in the class CarOwner.
Each class can be instantiated several times within Note that the output node DrivQuality of the class
the specification of another class. Formally, a class Driver is used as output reference node of the class
T is a DAG over three, pairwise disjoint sets of nodes CarOwner as it is referenced in the Accident class.
(IT , HT , OT ), such that for each instantiation t of T: In the extreme case where the OOBN consists of a
class having neither instantiations of other classes nor
• IT is the set of input nodes. All input nodes are input and output nodes we collapse to standard BNs.
references to nodes defined in other classes (called
referenced nodes). Each input node have at most As all PGMs, OOBNs have two fundamental corner-
one referenced node, it has no parents in t and no stones: construction and reasoning. The construc-
children outside t. tion of an OOBN concerns both learning the graph
structure and parameters estimation. Few works have
• HT is the set of internal nodes including instan- been proposed in the literature to learn the structure
tiations of classes which do not contain instanti- (Bangsø et al., 2001), (Langseth and Nielsen, 2003)
ations of T . They are protected nodes that can’t and the parameters (Langseth and Bangsø, 2003) of
have parents or children outside t. such a model from data. Given an OOBN, reasoning
Insurance
Age Age
Age
SocioEcon
SocioEcon
D:Driver
DrivQuality
HomeBase RiskAversion
CO:CarOwner
DrivQuality
AntiTheft VehicleYear MakeModel
HomeBase VehicleYear MakeModel DrivQuality
T:Theft C:Car A:Accident
AntiTheft Cushioning Mileage Mileage
Theft CarValue CarValue RuggedAuto Antilock Antilock Accident
MedCost ThisCarDam
ThisCarCost ILiCost Other-
PropCost CarCost
Figure 1: The insurance network represented using the OOBN framework
stands for probabilistic inference and this requires to not always obvious to obtain. To overcome this lim-
translate the OOBN into a BN or a multiply sectioned itation we propose to use ontologies richness. Before
Bayesian network (MSBN) (Bangsø and Wuillemin, introducing our method, we give basic notions on on-
2000). tologies.
In this paper we are interested in the learning process.
The standard approach proposed by (Langseth and 3 Ontologies
Bangsø, 2003) is the OO-SEM algorithm. This algo-
rithm is based on an Object Oriented assumption Over the last few years, there has been an increas-
which states that all instances of a class are assumed ing interest in the application of ontologies in vari-
to be identical w.r.t. both parameters and structure. ous domains (e.g., linguistics, semantic web, bioinfor-
This algorithm is based on a prior expert knowledge matics). They represent not only a fixed structure
about a partial specification of the OOBN by group- but also the basis for deductive reasoning. For the
ing nodes into instantiations and instantiations into AI community, an ontology is an explicit specification
classes. Then, on the basis of this prior, the learning of a conceptualization (Gruber, 1995). That is, an
process adapts the SEM algorithm (Friedman, 1998) ontology is a description of a set of representational
in order to learn the OOBN structure that fits best to primitives with which to model an abstract model of
the data. Learning in object oriented domains allows a knowledge domain. Formally, we define an ontology
to reduce the search space, however it remains an NP- O = hCp, R, I, Ai as follows:
hard problem. In fact, the main computational phase
in the OO-SEM algorithm consists in finding the in- • Cp = {cp1 , . . . cpn } is the set of n concepts
terfaces of instantiations, which is exponential in the (classes) such that each cpi has a set of k proper-
number of instantiations. So, this information may be ties (attributes) Pi = {p1 , . . . pk }.
also elicited from domain experts. However, human
• R is the set of binary relations between elements
expertise, required to initiate the learning process, is
of Cp which consists of two subsets:
Loan requests Couple hand into the a prior OOBN structure. To this end, we
Amount Total income
Decision NbChildren first define the common points and similarities between
constituted of constituted of
these two paradigms, then we describe the main steps
of our proposal.
Man Woman
Military service Maiden name 4.1 OOBNs vs ontologies
is-a is-a
In this part, we highlight the common points and
Person
similarities between ontologies and object oriented
Name Bayesian networks. The main components of an ontol-
Age ogy (i.e., concepts and relations) may be viewed as a
Salary
Employment start-up to define the main components of an OOBN
(i.e., classes and relations among them).
Figure 2: The joint credit ontology
• Concepts vs classes
Ontology concepts are translated into classes of
– HR which describes the inheritance relations the OOBN framework. Hence, for each class so
among concepts. defined, concept properties will constitute the set
– SR which describes semantic relations be- of its random variables (real nodes). It is clear
tween concepts. That is, each relation that the set of the concept properties does not
cpi sR cpj ∈ SR has cpi as a domain and cpj cover the three sets of nodes of a class. Let:
as a range.
– cpi be the concept of the ontology trans-
• I is the set of instances, representing the knowl- lated to the class ci in the underlying OOBN,
edge base. where ci is a DAG over Ic , Hc and Oc .
• A is the set of the axioms of the ontology. A con- – Pi = {p1 . . . pk } be the set of properties of
sists of constraints on the domain of the ontology cpi .
that involve Cp, R and I. – Hc0 = Hc \ Hcinst , where Hcinst is the set of in-
ternal nodes which are instantiations of other
Axioms are of the form A ≡ B (A and B are equiva- classes.
lent), R1 ⊆ R2 (R1 is a subproperty of R2), R1(x, y) – Oc0 = Oc \ Ocref , where Ocref is the set of
(x is related to y by the relation R1), A(x) (x is of output nodes which are reference nodes.
type A), etc. Where A and B are concepts, R1 and
R2 are relations and x and y are instances. Pi allows us to generate Hc0 ∪Oc0 . Reference nodes,
namely, Ic ∪ Ocref , are pointers to nodes defined
Example 2. Figure 2 is an example of a joint credit in other classes. Consequently their set of states
ontology. as well as parameters are copied from the refer-
Cp = {Loan, Couple, M an, W oman, P erson}. enced nodes. These latter are properties of other
For instance PLoan = {Amount, Decision}. concepts in the ontology side. Reference nodes as
SR = {requests(Couple × Loan), constituted well as Hcinst will be derived from the semantic
of(Couple×M an), constituted of(Couple×W oman)}. relations.
Is-a relations represent HR and are equivalent to
subsumption axioms, e.g., Man⊆ Person. For in- • Inheritance relations vs class hierarchy
stance, we can have an instance p of the concept Man
As ontological inheritance relations already model
p {P aul, 30, 2000$, teacher, T }, p.Name = Paul, p.Age
a hierarchical feature, then all concepts connected
= 30, p.Salary = 2000$, p.Employment = teacher and
by an is-a relation in the ontology will be repre-
p.Military service = T.
sented by a class hierarchy in the OOBN frame-
work.
4 A new approach for OOBNs
building based on ontologies • Semantic relations vs links
Having two concepts {cpi , cpj } ∈ Cp2 related by a
Clearly PGMs and ontologies share several similarities semantic relation means that there is at least one
even they are derived from different frameworks. Thus property of one of them that affects at least one
our idea is to use the ontological knowledge in the property of the other, which means that the def-
OOBN learning process by morphing the ontology in inition of one of them depends on the existence
of the other. In the underlying OOBN, this al- 4.2 The morphing process
lows to set up dependencies among nodes from
different classes. Suppose that the property pk of To ensure the morphing process, we need to traverse
concept cpi affects the property pk0 of concept cpj . the whole ontology. To provide this, we assume that
Then, the node that represents pk in the class ci the ontology is a directed graph whose nodes are
will be either an output node connected directly the concepts and relations (semantic and hierarchical
using directed links to the internal node represent- ones) are the edges. Our target is to accomplish the
ing pk0 in the class cj , in this case cj could only mapping of the ontology graphical representation into
be an encapsulating class of the instance of ci , or an OOBN while browsing each node once and only
an output node referenced, using reference links, once. To this end, we propose to adapt the generic
by a reference node in the class cj , this reference Depth-First Search (DFS) algorithm for graph travers-
node is either an input node, parent of the node ing. The idea over the Depth-First Search algorithm is
that represents pk0 in cj or an output reference to traverse a graph by exploring all the vertices reach-
node of the class containing an instance of ci and able from a source vertex: If all its neighbors have al-
communicates with cj . ready been visited (in general, color markers are used
to keep track), or there are no ones, then the algorithm
Semantic relations might provide an information backtracks to the last vertex that had unvisited neigh-
about classes interfaces and instantiations organi- bors. Once all reachable vertices have been visited, the
zation in the OOBN. However, the link direction algorithm selects one of the remaining unvisited ver-
of the semantic relation can not provide a good tices and continues the traversal. It finishes when all
informer about dependence relations among the vertices have been visited. The DFS traversal allows
variables of the OOBN, which variable depends us to classify edges into four classes:
on the other? So, it is required that the seman-
tic relations be designed from the beginning of a • Tree edges: are edges in the DFS search tree.
causal or an anti-causal orientations. The choice
of a fixed orientation is a determining factor to • Back edges: join a vertex to an ancestor already
specify which instantiation Ii could be referenced visited.
from an instantiation Ij . Suppose that all seman- • Forward edges: are non-tree edges connecting a
tic relations are of causal orientation, the cause vertex to a descendant in a DFS search tree.
is then conceived as the direct explanation of the
fact and it is involved in its production. conse- • Cross edges: all other edges.
quently, the definition of the concept range de-
pends on the existence of the concept domain. In We use these classes of edges to determine actions
the OOBN side, this means that the definition of to do on each encountered concept. Tree edges al-
the class representing the concept domain is part low to define actions on concepts encountered for the
of the class representing the concept range. This first time, while forward and cross edges allow to de-
can be translated in the OOBN by instantiating fine actions to do on concepts that are already visited
the class representing the concept domain within crossing another path and so having more than one
the specification of the class representing the con- parent. According to their definition, back edges al-
cept range. low cycle detection, in our case these edges will never
be encountered. As our edges respect a causal orienta-
In what follows, we assume that all seman- tion having a cycle of the form X1 → X2 → X3 → X1
tic relations have a causal orientation. Thus, means that X1 is the cause of X2 which is the cause of
∀ {cpi , cpj } ∈ Cp2 related by a semantic relation, X3 so this latter can’t be the cause of X1 at the same
where cpi is the domain and cpj is the range, cpi instant t but rather at an instant t + . We are limited
is considered as the cause of cpj and this latter is to ontologies that do not contain cycles, because such
the effect. relationships invoke the dynamic aspect which is not
In fact, the ontology conceptual graph is simply considered in this work.
the result of the ontology components definition. A deep study of the similarities discussed above shows
Thus, we require that semantic relations defini- that the morphing process can be done in three main
tion to be, from the beginning, done following a steps, namely initialization, discovery and closing. At
causal reasoning that is considered as an intuitive each step, we define a set of actions that might be
reflexion of the ontologist. Then, if we require to done:
have all semantic relations to be anti-causal, we
just have to reverse their definitions (i.e., define i. Initialization step: All concepts are undiscov-
the domain as range and vice versa). ered, we generate the OOBN class and a class to
Algorithm 1: Generate OOBN Algorithm 2: Handling Process
Input: An ontology O Input: An ontology O, A concept S.
O is of an anti-causal orientation. We use color markers to keep track of which vertices
For all concepts, the color must be initialized to have been discovered: white marks vertices that have
”white” before running the algorithm. yet to be discovered, gray marks a vertex that is
begin discovered but still has vertices adjacent to it that are
CREATE OOBN GLOBAL ; undiscovered and black marks discovered vertex that
for each concept cp ∈ Cp do is not adjacent to any white vertices.
RECORD PREDECESSOR[cp]=NULL; begin
CREATE CLASS(cp) color[S]:= gray;
for each concept cp ∈ Cp do for each property p of S do
if color[cp]= white then ADD OUTPUT NODE(p, cS )
Handling Process(O, cp) for each V ∈ adjacent[S] do
if color[V ]=white then
RECORD PREDECESSOR[V ]=S;
Handling Process(O, V );
each concept: ADD INTERNAL NODE
(INSTANCE OF(cV ), cS );
CREATE OOBN GLOBAL : creates the OOBN if (S, V ) is an inheritance relation then
class. ADD CONSTRUCT LINK
INSTANCE OF(cV ),INSTANCE OF(cS ))
CREATE CLASS(Concept cp): transforms a con-
cept cp to a class ccp . if (S, V ) is a semantic relation then
for each node n ∈ GET OUTPUT(cV ) do
ADD REFERENCE LINK
ii. Discovery step: The classes of edges are used to
(n,ADD INPUT NODE(n,cS ))
determine actions to do on each encountered con-
cept. These actions allow us to define input, inter- if color[V ]=black then
nal and output sets for each class of the OOBN. if (S, V ) is an inheritance relation then
ADD INPUT NODE(Node n, Class c) : adds an ADD CONSTRUCT LINK
input node n to a class c. this action is invoked INSTANCE OF(cS ),INSTANCE OF(cV ))
on all properties of a concept which is related by if (S, V ) is a semantic relation then
an out edge to another one. Its properties are for each node n ∈ GET OUTPUT(cV )
considered as candidate input nodes of the class do
representing the second concept. ADD INPUT NODE(n, cS )
ADD OUTREF NODE
ADD INTERNAL NODE(Node n, Class c): adds (INSTANCE OF(cS ),INSTANCE OF(cV )
an internal node n to a class c. The set of internal
nodes of a class consists of instantiations of other color[S]:= black;
classes representing concepts that are related by if RECORD PREDECESSOR[S] = N ull then
an out edge to the corresponding concept of the ADD INTERNAL NODE
class c in the ontology and this edge is in the same (INSTANCE OF(cS ),GLOBAL OOBN CLASS)
DFS search tree.
ADD OUTPUT NODE(Node n, Class c): adds
an output node n to a class c. all properties of a
concept are transformed into variables of its cor- to be referenced by output reference nodes of the
responding class in the OOBN. These nodes are class containing it until reaching its second parent
considered as candidate output nodes of the class. (see figure 3).
ADD OUTREF NODE(Class c1, Class c2): adds ADD CONSTRUCT LINK(Class c1, Class c2): a
output reference nodes to classes containing c1 construct link appears between instantiations of
until reaching c2. In fact, some concepts might superclasses and instantiations of their subclasses
have parents coming from more than one DFS (see figure 4). All properties of the super-concept
search tree or from different paths. Let cpi be are considered as properties of its subconcepts.
a concept having two parents cp1i and cp2i com-
ing from two different branches. Then, ccpi would ADD REFERENCE LINK(Node n1, Node n2):
to be instantiated within the specification of only allows the communication between classes inter-
one of them. However, ccpi has its output nodes faces.
Cp1 painted gray and it has cp5 as adjacent concept, so on
cp1.1
cp1.2 cp4.1 cp4.1 until reaching cp9 . cp9 is grayed and all its properties
cp3.1
cp4.2
are declared as output nodes of the class representing
Cp2 Cp3 I3: C3 cp4.2
cp2.1 cp3.1 I4: C4 it in the prior OOBN (ccp9 ). As it has no adjacent, it
cp3.1 cp3.1
cp2.1
I2: C2 is instantiated within its ancestor ccp6 . As cp6 and cp9
cp1.2
are related by an inheritance relation then, we add a
Cp4 cp2.1
cp4.1
cp3.1 cp1.1
I1: C1 construction link between ccp6 and ccp9 and all proper-
cp4.2
ties of the super-class ccp9 are considered as properties
of its subclass ccp6 . The concept cp9 is finished and
Figure 3: An example of more than one parent blackened. We backtrack to the cp6 concept, it is gray
and it has finished his adjacent concepts so, it is in-
Cp1
cp1.1
stantiated within its ancestor ccp11 . As cp11 and cp6
cp4.1 cp4.2
are related by a semantic relation then, all its output
Cp2 Cp3 cp2.1 cp4.1 cp3.1
nodes are considered as input nodes of the ccp11 class
cp2.1
cp2.1 cp4.2
cp2.2
cp3.1
cp2.2
I4: C4
linked by reference links. cp6 is blackened and we go
cp2.2 I3: C3
I2: C2 back to cp11 it is gray and it has finished his adjacent
is-a is-a
cp1.1
I1: C1 concepts so, it is instantiated within its ancestor ccp5 .
Cp4
cp4.1 As ccp11 and ccp5 are related by an inheritance relation
cp4.2
then, we add a construction link between them. cp11 is
blackened and we go back to the second adjacent of the
Figure 4: An example of inheritance relation cp5 concept. cp5 is gray and cp9 is black, so (cp5 ,cp9 ) is
a cross/forward edge, means that cp9 has already been
iii. Closing step: We check whether the vertex is instantiated so, we add output reference nodes from
a root (having no predecessor), if it is, we add ccp6 until reaching the ccp5 class. cp5 is gray and it
an instance of its class to the global OOBN class has finished his adjacent concepts so, it is instantiated
using the ADD INTERNAL NODE action. within its ancestor and so on until backtracking to the
concept ccp1 , it is gray and it has not ancestors, so it
is blackened and instantiated within the specification of
We also define the INSTANCE OF (Class c)
the Prior OOBN class. The first DFS tree is finished,
which allow to instantiate a class c and the
so we choose an undiscovered node from the remain-
GET OUTPUT(Class c) which returns all output
der nodes and we apply the algorithm until discovering
nodes of a class c.
all the concepts. The result of this process is shown in
All these actions are used in Algorithms 1 and 2. The figure 5.(b)) shows the final result.
Handling Process function (see algorithm 2) provides
actions to do at each vertex.
5 Related work
Example 3. We assume that all random variables are
modeled in the corresponding ontology 5(b) as concepts In recent years, a panoply of works have been proposed
properties and that all semantic relations present in the in order to combine PGMs and ontologies so that one
ontology are of an anti-causal orientation. can enrich the other. We can outline two main direc-
We will follow the steps of the Generate OOBN algo- tions for these proposed approaches. The first aims to
rithm (see algorithm 1)to generate our prior OOBN enhance ontologies capabilities to support probabilis-
structure. tic inference. While the second aims to enhance PGMs
construction by integrating ontologies.
First of all, we start by generating the Global OOBN
class Prior OOBN. Then we create a class to each Ontologies provide a support for logical reasoning, but
concept of the ontology, that is, we create 11 classes they do not support uncertainty. Hence, several exten-
ccpi , i = {1, . . . 11} which are initially empty. their sions have been proposed to overcome this limitation.
sets of nodes will be discovered during the generation One line of research aims to extend existing ontology
process. languages, such as OWL1 , to be able to catch uncer-
tainty in the knowledge domain. Proposed methods,
Initially, all concepts are white. cp1 is the source con- such as BayesOWL (Ding and Peng, 2004), OntoBayes
cept, it is grayed and all its properties are declared as (Yang and Calmet, 2005) use additional markups to
output nodes of the class representing it in the prior represent probabilistic information attached to indi-
OOBN. Then, each concept adjacent to cp1 is recur-
sively visited if it is white and its properties are treated 1
ttp://www.w3.org/TR/2004/REC-owl-features-
in the same way. cp1 has cp2 as adjacent concept, it is 20040210/
Cp1 Cp2 Cp3 Cp4
cp1.1 cp2.1 cp3.1 cp4.1
cp1.2
Cp5 Cp6 Cp7 Cp8 Cp10
cp5.1 cp6.1 cp7.1 cp8.1 cp10.1
cp6.2 cp10.2
is-a is-a is-a is-a
Cp11 Cp9
cp11.1 cp9.1
cp9.2
(a) The ontology to morph
Prior OOBN
cp9.1
cp2.1 cp3.1
cp2.1 cp7.1
cp9.1 cp9.2
I7
I9 cp9.2
cp1.1 Cp7.1
cp6.2 I3
I6 cp6.1
cp1.2 cp11.1 cp6.1
Cp11.1 cp6.2
cp9.2
cp9.1 cp9.1 cp10.1 cp10.2
cp9.2 cp9.2 cp9.1 I10
cp5.1
I11
cp4.1 cp10.1
I5 cp cp9.1 cp9.2
5.1 cp8.1 cp10.2
I2 cp8.1
I4 I8
I1
(b) The resulting OOBN
Figure 5: An example of ontology morphing to a prior OOBN structure
vidual concepts and properties in OWL ontologies. structure of causal Bayesian networks (i.e. BNs with
The result is then a probabilistic annotated ontology causal relations) (Pearl, 2000) and improve the causal
that can be translated into a BN to perform probabilis- discovery.
tic inference. Other works define transition actions in
However, all these solutions are limited to a restrained
order to generate a PGM given an ontology with the
range of PGMs, usually BNs. So, they neglect some
intention of extending ontology querying to handle un-
ontology important aspects such as representing con-
certainty while keeping the ontology formalism intact
cepts having more than one property, non taxonomic
(Bellandi and Turini, 2009).
relations, etc. In our approach we used OOBNs which
On the other hand, some solutions proposed the use of are much richer graphical model than standard BNs.
ontologies to help PGMs construction. Some of them They allowed us to address an extended range of on-
are designed for specific applications (Helsper and Van tologies, we focused on concepts, their properties, hi-
der Gaag,2002), (Zheng et al., 2008), while some oth- erarchical as well as semantic relations and we showed
ers give various solutions to handle this issue. We how these elements would be useful to automatically
can mention the semi-automatic approach provided generate a prior OOBN. Our proposal concerns exclu-
in (Fenz et al., 2009) to create BNs and the Sem- sively the OOBN structure definition through the use
CaDo (Semantical Causal DiscOvery) algorithm (Ben of ontologies.
Messaoud et al., 2009) (Ben Messaoud et al., 2011)
which ensure the integration of ontological knowledge,
more precisely, subsumption relationships, to learn the
6 Conclusion and future work ference on Symbolic and Quantitative Approaches to
Reasoning with Uncertainty, 168–179. Verona, Italy.
The crossing-over of PGMs and ontologies can allow Z. Ding and Y. Peng (2004). A probabilistic extension
us to improve relevant tasks related to each of them. to ontology language OWL. Proceedings of the 37th
In this paper, we showed how we take advantage of Hawaii International Conference On System Sciences.
the semantic richness provided by ontologies to gen- Big Island, HI, USA.
erate a prior OOBN structure and this is by explor-
ing similarities between these two paradigms. The S. Fenz, M. Tjoa and M. Hudec (2009). Ontology-
use of the OOBN framework has enabled us to han- Based Generation of Bayesian Networks. Proceed-
dle an extended range of ontologies unlike works which ings of the Third International Conference on Com-
were limited to the use of standard Bayesian networks, plex, Intelligent and Software Intensive Systems, 712–
which brings us to say that this work is an initia- 717. Fukuoka, Japan.
tive aiming to set up new bridges between these two N. Friedman (1998). The Bayesian structural EM al-
paradigms. gorithm. Proceedings of the Fourteenth Conference on
The final structure resulting from the learning process Uncertainty in Artificial Intelligence, 129–138. Uni-
may also be useful to make the initial ontology evolve, versity of Wisconsin Business School, Madison, Wis-
and this is by trying to find how the new relations dis- consin, USA:Morgan Kaufmann.
covered by the learning process can affect the (semi) T. Gruber (1995). Toward Principles for the Design of
automatic ontology enrichment process. Thus, as an Ontologies Used for Knowledge Sharing. International
ongoing work, we aim to analyze the elements that are Journal Human-Computer Studies 43 (5–6): 907–928.
common to both tasks and provide a two-way approach
that uses ontology power in representing knowledge to E. M. Helsper and L. C. van der Gaag (2002). Build-
help the hard process of OOBN structure learning by ing bayesian networks through ontologies. Proceedings
proposing new metrics, based on ontological knowl- of the 15th European Conference on Artificial Intelli-
edge, allowing to assess better the choice of the best gence, 680-684. Amsterdam.
structure. Then, uses novel relations discovered by the J. Pearl (2000). Causality: Models, reasoning and in-
learning process in order to improve the hard activity ference. Cambridge.: MIT Press.
of ontology enrichment.
J. Pearl (1988). Probabilistic reasoning in intelligent
systems, San Franciscos: Morgan Kaufmann.
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