=Paper=
{{Paper
|id=Vol-1665/paper3
|storemode=property
|title=Automatic Generation of Probabilistic Ontologies from UMP-ST Model
|pdfUrl=https://ceur-ws.org/Vol-1665/paper3.pdf
|volume=Vol-1665
|authors=Diego M. Azevedo,Marcelo Ladeira,Laécio L. Santos,Rommel N. Carvalho
|dblpUrl=https://dblp.org/rec/conf/semweb/AzevedoLSC16
}}
==Automatic Generation of Probabilistic Ontologies from UMP-ST Model==
https://ceur-ws.org/Vol-1665/paper3.pdf
Automatic generation of Probabilistic Ontologies
from UMP-ST model
Diego M. Azevedo1 , Marcelo Ladeira1 , Laécio L. Santos1 , and Rommel N.
Carvalho1,2
1
Department of Computer Science
University of Brası́lia
Campus Universitário Darcy Ribeiro
Brası́lia, Distrito Federal, Brazil
diegomarques.azevedo@gmail.com
laecio@cic.unb.br,{mladeira,rommelnc}@unb.br
http://www.cic.unb.br
2
Department of Research and Strategic Information
Brazilian Office of the Comptroller General (CGU)
SAS, Quadra 01, Bloco A, Edifı́cio Darcy Ribeiro
Brası́lia, Distrito Federal, Brazil
rommel.carvalho@cgu.gov.br
http://www.cgu.gov.br
Abstract. The Uncertainty Modeling Process for Semantic Technolo-
gies (UMP-ST) is an incremental and iterative approach that covers
the difficulty in maintaining and evolving existing POs [5]. It is a gen-
eral methodology for the majority of the existing semantic technolo-
gies which support uncertainty. One of them is the Probabilistic OWL
(PR-OWL), which is a language for representing Multi-Entity Bayesian
Networks (MEBN). The modeling of a PO using UMP-ST methodol-
ogy and MEBN/PR-OWL representation is supported by UnBBayes, a
framework for building probabilistic graphical models and performing
plausible reasoning. Although there is a guidance described by UMP-ST
to model a PO, the implementation of a PO is painful and repetitive.
Nowadays, the user needs to build the ontology from the zero in a specific
technology, even if the user models the PO in UMP-ST. A proper inte-
gration that helps the user to implement the PO such as an intermediate
structure makes implementation easier than build the PO from the zero
and speeds up the modeling process. This paper proposes an algorithm
to generate POs based on the mapping of elements of an UMP-ST model
into a MEBN/PR-OWL representation. This approach is basically an ex-
tension of the UMP-ST to generate POs to an specific formalism, that is,
the MEBN/PR-OWL language. The algorithm proposed is implemented
as a Java plug-in for the UnBBayes.
Keywords: Automatic Generation, Probabilistic Ontology, Uncertainty
Modeling Process, UMP-ST, POMC, Fraud Detection, MEBN, UnBBayes.
1 Introduction
The limitation of OWL in representing uncertainty are covered by many ap-
proaches based on different formalisms, one of them is the Probabilistic Web
Ontology Language (PR-OWL) [2]. PR-OWL is based on Multi-Entity Bayesian
Networks (MEBN), a formalism that joins the expressiveness power of First Or-
der Logic to represent a domain and the ability to perform plausible reasoning
of Bayesian Networks.
Although probabilistic reasoning is one of the most promising approaches to
deal with uncertainty in ontologies, little support was giving because of the diffi-
culty level to execute and replicate probabilistic ontologies. Carvalho [1], focusing
on how to design this kind of probabilistic ontologies, proposes a methodology
based on the Unified Process (UP) to make the working related to build this mod-
els less complex. The Uncertainty Reasoning Process for Semantic Technologies
(URP-ST) is a framework that guides this working process though a series of
steps as modeling, populating the knowledge base, and making inferences on the
model.
The Uncertainty Modeling Process for Semantic Technologies (UMP-ST) is
an incremental and iterative approach to model probabilistic ontologies though
a set of disciplines. Carvalho defines Probabilistic Ontology Modeling Cycle
(POMC) as a project lifecycle composed by four disciplines to handle the un-
certainty modeling and reasoning processes. These disciplines are composed by
Requirements, Analysis & Design, Implementation, and Test [1]. The URP-ST
methodology is supported by UnBBayes [1, 6].
UnBBayes 1 is an open source framework with support to plug-ins that offers
support to many methods with different formalisms based on Bayesian Networks
(BN) [7]. One of them gives support to UMP-ST modeling process. Basically, the
UMP-ST plug-in supports the Requirements and Analysis & Design disciplines
[5]. The Implementation and Test disciplines as well as others steps of the URP-
ST, such as populating the knowledge base and making inferences, can be done
in UnBBayes using the MEBN/PR-OWL plug-in.
Although UnBBayes gives support to URP-ST, it does not have a link be-
tween modeling and implementing disciplines. This makes the developing pro-
cess more painful because the effort needed to build the same model switching
between the UMP-ST and in PR-OWL/MEBN plug-in, without a proper in-
tegration. This paper presents in detail how elements defined in UMP-ST are
mapped to PR-OWL/MEBN elements and how is made the automatic genera-
tion of probabilistic ontology in PR-OWL from the UMP-ST plug-in extension.
This paper is organized as follows: Section 2 presents fundamental knowledge
of URP-ST, UMP-ST, PR-OWL and MEBN. Section 3 describes UnBBayes and
the plug-ins developed for PR-OWL and UMP-ST. Section 4 defines how it is
possible to generate PR-OWL 2 ontologies with UMP-ST models and uses the
Fraud Detection proposed by Carvalho [1] as a case study. Section 5 presents
some concluding remarks.
1
http://sourceforge.net/projects/unbbayes/
2 Fundamental Knowledge
This section presents basic concepts related to URP-ST, UMP-ST, PR-OWL/PR-
OWL 2 and MEBN, providing an approach about these formalisms and their
application in the PO context.
2.1 URP-ST
Uncertainty Reasoning Process for Semantic Technologies was proposed by Car-
valho [1] as an approach for modeling a probabilistic ontology and using it for
plausible reasoning in applications that use Semantic Technologies. It is divided
into three steps: modeling the domain, populating the model with data, and
using both the model and the data available, i.e Knowledge base, for reasoning.
The model describes how different concepts in our ontology interact under un-
certainty by knowing facts that will guide the construction process. Once the
model is available, reasoning can be done when the model is populated with
data, i.e entities and evidence. Then it is possible make inferences to answer
queries from the users.
2.2 UMP-ST
Uncertainty Modeling Process for Semantics Technologies was proposed by Car-
valho [1] as an iterative and incremental methodology for modeling POs. It
describes the first phase of the URP-ST and it is compounded by four major
disciplines: Requirements (functional and non-functional), Analysis & Design,
Implementation, and Test. The modeling process described by UMP-ST is also
consistent with the bayesian network modeling methodology [9][10].
Like in the UP, all disciplines in each iteration of the UMP-ST cover a set of
requirements, building deliverable versions of the model. The idea behind every
iteration is to take advantage of what has been learned during the modeling of
earlier versions. It comes from discovering new requirements, rules, entities, and
relations from previous versions.
Following the steps described by the UMP-ST, it is possible to build a Re-
quirements Traceability Matrix (RTM) defined by traceability of work products
of different disciplines. It can describe which requirement item is being imple-
mented in each design object or implementation object. I.e, an entity and rela-
tionship defined in Analysis & Design discipline can be linked to goal described in
the first discipline. Traceability promotes an easy identification of objects that
should be analyzed or modified when implementing changes and also ensures
that all requirements are covered.
The interaction process covered by the UMP-ST is depicted in Probabilistic
Ontology Modeling Cycle (POMC), illustrated in Figure 1. This cycle defines
the major outputs from each discipline and the natural order in which outputs
are produced. Although there is a modeling order, it is not necessary to occur
in a rigid and sequential way like the waterfall model. The interactions between
the disciplines are not restricted to the arrows presented.
Fig. 1. POMC flow.
The Requirements discipline defines objectives that must be achieved by
reasoning in PO. For each goal, it is necessary to define queries that will be
answered with the aid of evidence.
Analysis & Design discipline defines classes of entities, their attributes, rela-
tionships, and rules. It will be grouped to isolate characteristics of the domain
and to facilitate the visualization of dependencies that will guide implementation
of the PO model in the next step.
In the Implementation discipline, entities, relationships, attributes, rules, and
groups will be mapped to their corresponding concepts in a specific formalism
that allows uncertainty representation. In our case study, the mapping is done
to PR-OWL 2 format.
In the Test discipline, the user will validate and verify the model, in which it
is observed whether the resulting ontology has an expected behavior and whether
all requirements have been implemented.
2.3 MEBN and PR-OWL
Multi-Entity Bayesian Networks (MEBN) was proposed by Laskey [4] as a lan-
guage for representing probabilistic knowledge. It extends Bayesian networks by
incorporating the expressive power of first-order logic, and expands first-order
logic by adding a way to specify probability distribution through its random
variables. Thus, MEBN expands Bayesian network approach to a domain where
the number of random variables (RVs) involved is unknown.
MEBN describes knowledge as a collection of MEBN Fragments (MFrags),
organized into MEBN Theories (MTheories). Each MFrag represents a repeat-
able pattern of knowledge that can be instantiated as many times as needed to
form a BN addressing a specific situation. Thus, it can be seen as a template for
building fragments of a Bayesian network. MFrags are instantiated by binding
their arguments to domain entity identifiers to create instances of RVs. Each
MEBN fragment has three kinds of RV: context, resident, and input. Context
RVs are conditions that guarantee the consistency of the distributions defined
in a MFrag. Input RVs influence the distributions of other RVs in a MFrag, but
their distribution are defined in their home MFrag. Resident RVs are defined
by specifying their Local Probability Distribution (LPD) in their home MFrag.
Each LDP of Resident RV is conditioned on the values of instances of its parents.
An MTheory is a set of MFrags that collectively satisfy conditions of con-
sistency ensuring the existence of a unique joint probability distribution over
instances of its random variables.
The instantiation of its RVs by biding their arguments to domain entity
identifiers results in a Situation-Specific Bayesian Network (SSBN), where the
RVs of MFrags will become RVs in an ordinary Bayesian network. Then, these
SSBNs can use regular BN inference engines to answer the query.
PR-OWL is a language for representing uncertainty knowledge in a princi-
pled, structured, and shareable way proposed by Costa [2]. It was developed as
an extension of OWL, using MEBN to allow applications to perform plausible
reasoning and requiring MEBN inference engine to process additional syntax
based on Bayesian network probabilistic inference. This language consists of a
set of classes and subclasses that collectively form a framework for building
probabilistic ontologies [6].
PR-OWL 2 is an extension of PR-OWL proposed by Carvalho [1], providing
a consistent mapping between OWL concepts and data types and PR-OWL. It
facilitates the construction of hybrid ontologies with deterministic and proba-
bilistic statements.
3 UnBBayes and the plug-in for UMP-ST
UnBBayes is an open-source JavaT M application distributed in GPL license. It
has been developed since 2000 and was created for building probabilistic graph-
ical models and performing plausible reasoning [7]. In mid-2010, UnBBayes had
its architecture modified to give support to plug-in extension form. This fa-
cilitates its expansion into new formalisms. In core version, UnBBayes imple-
ments Bayesian network (BN) and Inference Diagrams (ID). Multiply-Sectioned
Bayesian Network (MSBN), Object-Oriented Bayesian network (OOBN), Hy-
brid Bayesian Network (HBN), MEBN, PR-OWL, and PR-OWL 2 as others
formalisms are supported by adding plug-ins extension.
MEBN implementation in UnBBayes is saved using the PR-OWL format. It
was the first implementation of MEBN formalism in the world. In order to pop-
ularize PR-OWL language and MEBN formalism, UnBBayes provides a GUI for
editing ontologies making inference through the creation of SSBNs. PR-OWL
2 was implemented to allow the creation of probabilistic ontologies from deter-
ministic ontologies in OWL. PR-OWL 2 plug-in was developed to allow the user
to edit both probabilistic and deterministic parts of ontologies. It is possible
because Protegé has been integrated into UnBBayes to design the deterministic
part.
UMP-ST plug-in was implemented to solve three problems: the complexity
in creating POs; the difficulty in maintenance and evolution of existing POs; and
the lack of a centralized tool for documenting POs [5]. One of the key features
in this plug-in is the implicitly creation of the traceability matrix by linking the
objects created during the disciplines to the requirements they relate to. The
plug-in allows the user to work with the Requirements and Analysis & Design
disciplines. However, to allow the automatic generation of a PO from the UMP-
ST model, it is necessary select a specific language and formalism that will be
mapped in the Implementation discipline. MEBN and PR-OWL 2 were chosen
because UnBBayes has support to both formalisms as well a plug-in for UMP-ST.
4 Automatic generation of probabilistic ontologies from
UMP-ST models
After the modeler defines the elements in the Analysis & Design discipline, it
is necessary to choose a specific language that allows uncertainty representation
in semantic technologies to implement the model designed. This work describes
how to generate a PO in PR-OWL 2 using UnBBayes from the model designed
in UMP-ST plug-in. One of the main advantages is the traceability between the
elements defined in the Requirements and Analysis & Design disciplines and the
PR-OWL elements in the Implementation discipline.
To automatic generate a model in PR-OWL 2, it is necessary to start by
mapping the entities, their attributes, and relations to the chosen language.
Figure 2 presents how the elements created in UMP-ST can be mapped to PR-
OWL 2, which essentially uses MEBN terms [1]. The designed model needs to
be simplified, since UnBBayes has some limitations. E.g., the lack of support for
a type hierarchy.
As represented in Figure 2, the elements of UMP-ST (in blue) at the left
side are mapped to MEBN terms present at the right side by considering the
limitations of UnBBayes. Thus, the entities in the model will be mapped to an
entity in PR-OWL 2. The attributes and relationships of the model are charac-
teristics that may be uncertain. In MEBN, it is represented by defining random
variables (RVs), which can be a kind of context RV (in green), input RV (in
gray) or resident RV (in yellow).
To define a RV in UnBBayes PR-OWL, first we need to define its home
MFrag. However, it is not necessary with the PR-OWL 2 plug-in, because RVs
are independent of MFrag and are defined globally. This makes the RVs definition
easier compared with UnBBayes PR-OWL definition process [1].
Fig. 2. Mapping of UMP-ST elements to PR-OWL 2.
In UMP-ST, the attributes and relationships as others elements defined in the
Analysis & Design discipline are separated in different groups. Also in MEBN,
each RV has a home MFrag into which it is defined the local probability distri-
bution. So on, in Figure 2 the groups (on the left side) will be mapped as MFrags
(on the right side).
As described in Figure 3, relationships in UMP-ST (on top) can be defined as
a relation of one or more entities, being a predicate or a function, depending of
their context, e.g, livesAtSameAddress(Person, Person). In MEBN theories,
a RV (in yellow) takes arguments that refer to entities of the domain of applica-
tion [4]. These arguments in UnBBayes have OrdinaryVariable type and they
are represented by a Context RV (in green) with Boolean range as the built-in
RV isA(resource, class). resource, in this type of RV, represents individ-
uals of OrdinaryVariable and class represents entities related to the domain
of application [8, 1].
Relationships defined in the UMP-ST will be mapped to (input or resident)
RVs (in yellow) and for each entity present in relationship, context RVs (in green)
with Boolean range will be created as the built-in RV isA(resource, class).
This will be necessary to guarantee the unique joint probability distribution over
the RVs when the model is instantiated.
Even though UMP-ST is a generic modeling process for the majority of exist-
ing semantic technologies which support uncertainty representation, the chosen
language does not offer a formal link between these terms. It is impossible for
reasoners to identify that these terms are even linked. At best, it could only
“guess” they are the same, since they have similar syntax [1].
Fig. 3. Mapping a relationship in UMP-ST to a RV in PR-OWL 2.
Once all RVs are mapped, their relations and constraints can be defined by
analyzing RVs dependencies described by the rules in the UMP-ST model [3, 1].
It is important to capture local consistence of the model by testing these rules
even before implementing the model in a specific language by creating simple
probabilistic model to evaluate whether it will behave as expected. However,
rules in UMP-ST are basically described in textual form [3], which makes an
automatic identification of the rule structure more complexity and subject to
errors.
To make the rule structure understandable by computer and less subject to
errors, an extension of the rule definition is proposed during the Implementation
discipline. It is based on four steps. In the first and the second steps, the rule
context (ordinary variables and necessary conditions) is specified. In the third
and last steps, a casual relation to describe the dependence of RVs is defined.
Figure 4 presents an example to illustrate this form of extension.
Considering the rule and the group description in the Analysis & Design
discipline, each rule is related to only one group and each group can have one or
more rules. Therefore, the relation of dependence over the RVs described by the
rule is restricted to the group in which it is declared. This relation of dependence
defined in a specific group will contribute to set the local probability distribution
over the RVs by describing who it is cause and who it is effect.
The new rule definition extension allows mapping the ordinary variables and
the necessary conditions to context RVs and the cause and the effect to (input
or resident) RVs. For instance, in Figure 4 the ordinary variables person and
enterprise are both related to the class Person and Enterprise. Thus, they are
mapped in an MFrag to the isA(person, Person) and the isA(enterprise,
Enterprise) context RVs. The necessary condition can be described by a first-
order logic and also can be a RV as isResponsibleFor(person, enterprise)
which is mapped to a context RV. This condition, in the MEBN fragment, will
restrict the application of the probability distribution over its RVs to instances
of Person that are responsible for the instances of Enterprise.
With all elements defined in the Analysis & Design already mapped to the
PR-OWL 2 language, now it is necessary to distinguish input and resident RVs.
An algorithm to select RVs based on their home MFrag and their relation of
dependence is proposed. This algorithm is composed by three criterion of selec-
tions.
The First criteria of selection defines as resident RV the RV present
only in its home MFrag and does not influence a probability distribution of
other RVs as a possible input RV. E.g., ownsSuspendedEnterprise(person) in
Owns Suspended Enterprise MFrag illustrated by Figure 5. This is done by the
algorithm, by identifying the relationships that there are in just one group.
The Second criteria of selection defines as input RV in a MFrag the
RV that also is defined as resident RV in another MFrag. E.g, in Figure 5,
isSuspended(enterprise) has input type in Owns Suspended Enterprise MFrag,
but first it is defined as resident RV in Enterprise Information MFrag.
In the Second criteria of selection, the algorithm analyses the rules of each
group and identify where the RVs are the cause and where they are the effect.
If there is a RV that is cause and in other group it is defined as effect by a rule,
then this RV which is cause will have input type and the other which is effect will
have resident type. This is possible because in MEBN an input RV influences
the local probability distribution of resident RV like a cause and effect relation,
but first the RV which has input type needs to be a resident RV in its home
MEBN fragment.
After analyzing the causal relation defined by the rules, it is possible to ex-
ist some RVs that still have undefined type. This kind of RVs can be identified
by analyzing the RVs which are not defined by a rule but they still partici-
pate in a MFrag. E.g, in Figure 5 in Enterprise Information MFrag, the RV
isResponsibleFor(person, enterprise) is not defined by some rule because
in the group related to its MFrag, it is not a cause or effect. In this case, the
algorithm considers that this kind of MFrag is the home MFrag of the RV ana-
lyzed and it will be defined as resident RV. Nevertheless, if there are RVs that
still do not have a type, they will be added in a list of doubts.
The Third criteria of selection analyzes whether after first and second
criterion of selection may exist some RVs that still have undefined type. So on,
if there are RVs in the list of doubts, then each RV in doubt will be presented
to the user decides manually whether this RV has input or resident type. The
type of RV decided by the user will be added to a list of hypothesis and it will
be saved in UMP-ST plug-in file.
Carvalho [1] proposes the probabilistic ontology for procurement fraud and
detection and prevention in Brazil. This case study is modeled in PR-OWL 2
with URP-ST and it will be used to illustrate the generation process using the
algorithm proposed.
To explain the problem described by Carvalho in the fraud and detection
model, it is necessary to have in mind the principles established by Brazil’s Law
among equality of bidders. This Law prohibits the procurement agent from dis-
crimination among potential suppliers. Therefore, the procurement agent cannot
Fig. 4. Group and rule representation.
be related to the bidder or might feed information in order to favor the bidder’s
enterprise. Also, the committee for a procurement must be well prepared and
must has a clean history with no criminal or administrative convictions. These
constraints give rise to a set of goals, queries and evidences which will guide the
modeling process.
During the Analysis & Design discipline, one of the goals covered by Carvalho
identifies whether some person ownsSuspendedEnterprise. This relationship is
defined as a relation between Person and Enterprise entities. However, to know
whether some person ownsSuspendedEnterprise, it is necessary to known also
the probability of the enterprise analyzed isSuspended. This rule only will be
valid whether the person isResponsibleFor the enterprise. Figure 4 illustrates
this rule in extension form.
This goal can be analyzed and designed in two groups. isSuspended and
isResponsibleFor can be grouped as Enterprise Information which also
will contain the entities that they relate to. The other group will contain the
elements necessary to describe the rule defined before. So on, it needs to have
isResponsibleFor, isSuspended and ownsSuspendedEnterprise as relation-
ships and Person and Enterprise as entities.
After modeling the elements during Analysis & Design discipline, to generate
the PO, first each element will be mapped as described in Figure 2. Then, the
algorithm will run the sequence of steps presented below to define the RVs type
based on rules and groups distribution.
i It is identified whether the model had already been generated by analyzing
the list of hypothesis.
ii Case the list of hypothesis is not empty, then each RV listed will have the
type defined by the user hypothesis.
iii First criterion of selection is executed and the RVs present in just one MFrag
will be defined as resident.
Fig. 5. MFrag generated after mapping elements of Analysis & Design stage.
iv Second criterion of selection is executed. If the RV is defined as cause in a
rule and in other group it is defined as effect, then it will have input type
in MFrag that it was cause and in the other that it was effect, it will have
resident type.
v Case there are RVs that were not declared in any rule, but they were defined
in a group, then they will have resident type.
vi Third criterion of selection will define the type of the RVs that still are in
doubt by presenting them to the user decides.
The PR-OWL 2 format generated by the algorithm does not define the lo-
cal probability distribution presents in each resident RVs. Therefore, the model
generated is not complete. The user needs to define the local probability distri-
bution by editing the code generated in MEBN plug-in supported by UnBBayes.
After that, the PO is validated and verified by analyzing whether the ontology
has a expected behavior and whether all requirements have been implemented.
Case one requirement has not been implemented, the user will edit the PO in
the MEBN plug-in, but if it is necessary to change some rule, then it is possible
to generate other PO in PR-OWL 2 format from the UMP-ST plug-in extension.
5 Conclusion
It is possible to generate automatically a PO in PR-OWL 2 format able to be
read and edited by UnBBayes. Although there is not a formal link between the
UMP-ST elements and the output format, the proposed mapping of the elements
defined in Analysis & Design discipline to PR-OWL 2 format was based on the
related concepts of each element of both representations.
The new definition of the rule during the generation process is necessary to
make its format understandable by a computer. This is possible by defining the
ordinary variables, the necessary conditions and the causal relation over its RVs.
These elements will be mapped to MEBN/ PR-OWL 2 and, by executing the
algorithm, the model defined by UMP-ST plug-in will generate a MEBN theory.
The generation of the PR-OWL 2 code by the extension of the UMP-ST plug-
in speeds up and facilitates the creation of a MEBN model (PR-OWL 2 PO).
The development of this extension is on implementing phase. It is developed in
JavaT M and riles on Java Plugin Framework2 (JPF) version 1.5.1.
References
1. R. N. Carvalho, ”Probablistic ontology: Representation and modeling methodology,”
PhD, George Mason University, Fairfax, VA, USA, 2011.
2. P. C. G. Costa, ”Bayesian semantics for the semantic web,” PhD, George Mason
University, Fairfax, VA, USA, Jul. 2005.
3. R. M. de Souza, ”UnBBayes plug-in for documenting probabilistic ontologies using
UMP-ST,” B.S., University of Brası́lia, Brası́lia, Brazil, 2011.
4. K. B. Laskey, ”MEBN: a language for First-Order bayesian knowledge bases,” Ar-
tificial Intelligence, vol. 172, no. 2-3, pp 140-178, 2008.
5. R. N. Carvalho, M. Ladeira, R. M. de Souza, S. Matsumoto, H. A. D. Rocha, and G.
L. Mendes, “UMP-ST plug-in: A tool for documenting, maintaining, and evolving
probabilistic ontologies.” in URSW, ser. CEUR Workshop Proceedings, F. Bobillo,
R. N. Carvalho, P. C. G. da Costa, C. d’Amato, N. Fanizzi, K. B. Laskey, K. J.
Laskey, T. Lukasiewicz, T. Martin, M. Nickles, and M. Pool, Eds., vol. 1073. CEUR-
WS.org, 2013, pp. 15–26.
6. R. N. Carvalho, K. B. Laskey, P. C. G. da Costa, M. Ladeira, L. L. Santos, and
S. Matsumoto, “UnBBayes: modeling uncertainty for plausible reasoning in the
semantic web,” in Semantic Web, gang wu ed. INTECH, Jan. 2010, pp. 1–28.
7. S. Matsumoto, R. N. Carvalho, M. Ladeira, P. C. G. da Costa, L. L. Santos, D. Silva,
M. Onishi, E. Machado, and K. Cai, “UnBBayes: a java framework for probabilistic
models in AI,” in Java in Academia and Research. iConcept Press, 2011.
8. S. Matsumoto, ”Framework based in plug-ins for reasoning with probabilistic on-
tologies,” M.Sc., University of Brası́lia, Brası́lia, Brazil, 2011.
9. K. B. Laskey and S. M. Mahoney, “Network engineering for agile belief network
models,” IEEE Transactions on Knowledge and Data Engineering, vol. 12, no. 4,
pp. 487–498, 2000. [Online]. Available: http://portal.acm.org/citation.cfm?id=
628073
10. K. B. Korb and A. E. Nicholson, Bayesian Artificial Intelligence, 1st ed. &
Hall/CRC, Sep. 2003. Chapman
2
JPF homepage: http://jpf.sourceforge.net/