The Uncertainty Modeling Process for Semantic Technologies (UMP-ST) is an incremental and iterative approach that covers the di culty in maintaining and evolving existing POs [5]. It is a general methodology for the majority of the existing semantic technologies 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 methodology 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 speci c technology, even if the user models the PO in UMP-ST. A proper integration 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 extension of the UMP-ST to generate POs to an speci c formalism, that is, the MEBN/PR-OWL language. The algorithm proposed is implemented as a Java plug-in for the UnBBayes.
The limitation of OWL in representing uncertainty are covered by many
approaches based on di erent formalisms, one of them is the Probabilistic Web
Ontology Language (PR-OWL) [
Although probabilistic reasoning is one of the most promising approaches to
deal with uncertainty in ontologies, little support was giving because of the di
culty level to execute and replicate probabilistic ontologies. Carvalho [
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 de nes Probabilistic Ontology Modeling Cycle
(POMC) as a project lifecycle composed by four disciplines to handle the
uncertainty modeling and reasoning processes. These disciplines are composed by
Requirements, Analysis & Design, Implementation, and Test [
UnBBayes 1 is an open source framework with support to plug-ins that o ers
support to many methods with di erent formalisms based on Bayesian Networks
(BN) [
Although UnBBayes gives support to URP-ST, it does not have a link between modeling and implementing disciplines. This makes the developing process more painful because the e ort needed to build the same model switching between the UMP-ST and in PR-OWL/MEBN plug-in, without a proper integration. This paper presents in detail how elements de ned in UMP-ST are mapped to PR-OWL/MEBN elements and how is made the automatic generation 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 de nes how it is
possible to generate PR-OWL 2 ontologies with UMP-ST models and uses the
Fraud Detection proposed by Carvalho [
This section presents basic concepts related to URP-ST, UMP-ST, PR-OWL/PROWL 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
Carvalho [
UMP-ST
Uncertainty Modeling Process for Semantics Technologies was proposed by
Carvalho [
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 Requirements Traceability Matrix (RTM) de ned by traceability of work products of di erent disciplines. It can describe which requirement item is being implemented in each design object or implementation object. I.e, an entity and relationship de ned in Analysis & Design discipline can be linked to goal described in the rst discipline. Traceability promotes an easy identi cation of objects that should be analyzed or modi ed 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 de nes 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.
The Requirements discipline de nes objectives that must be achieved by reasoning in PO. For each goal, it is necessary to de ne queries that will be answered with the aid of evidence.
Analysis & Design discipline de nes classes of entities, their attributes, relationships, 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 speci c 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 [
MEBN describes knowledge as a collection of MEBN Fragments (MFrags), organized into MEBN Theories (MTheories). Each MFrag represents a repeatable pattern of knowledge that can be instantiated as many times as needed to form a BN addressing a speci c 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 identi ers 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 de ned in a MFrag. Input RVs in uence the distributions of other RVs in a MFrag, but their distribution are de ned in their home MFrag. Resident RVs are de ned 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 consistency 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 identi ers results in a Situation-Speci c 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
principled, structured, and shareable way proposed by Costa [
PR-OWL 2 is an extension of PR-OWL proposed by Carvalho [
UnBBayes is an open-source JavaT M application distributed in GPL license. It
has been developed since 2000 and was created for building probabilistic
graphical models and performing plausible reasoning [
MEBN implementation in UnBBayes is saved using the PR-OWL format. It was the rst implementation of MEBN formalism in the world. In order to popularize 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 deterministic 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 Protege 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 di culty in maintenance and evolution of existing POs; and
the lack of a centralized tool for documenting POs [
After the modeler de nes the elements in the Analysis & Design discipline, it is necessary to choose a speci c 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 de ned 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
PROWL 2, which essentially uses MEBN terms [
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 characteristics that may be uncertain. In MEBN, it is represented by de ning random variables (RVs), which can be a kind of context RV (in green), input RV (in gray) or resident RV (in yellow).
To de ne a RV in UnBBayes PR-OWL, rst we need to de ne its home
MFrag. However, it is not necessary with the PR-OWL 2 plug-in, because RVs
are independent of MFrag and are de ned globally. This makes the RVs de nition
easier compared with UnBBayes PR-OWL de nition process [
In UMP-ST, the attributes and relationships as others elements de ned in the Analysis & Design discipline are separated in di erent groups. Also in MEBN, each RV has a home MFrag into which it is de ned the local probability distribution. 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 de ned 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
application [
Relationships de ned 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
existing semantic technologies which support uncertainty representation, the chosen
language does not o er 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 [
Once all RVs are mapped, their relations and constraints can be de ned by
analyzing RVs dependencies described by the rules in the UMP-ST model [
To make the rule structure understandable by computer and less subject to errors, an extension of the rule de nition is proposed during the Implementation discipline. It is based on four steps. In the rst and the second steps, the rule context (ordinary variables and necessary conditions) is speci ed. In the third and last steps, a casual relation to describe the dependence of RVs is de ned. 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 de ned in a speci c group will contribute to set the local probability distribution over the RVs by describing who it is cause and who it is e ect.
The new rule de nition extension allows mapping the ordinary variables and the necessary conditions to context RVs and the cause and the e ect 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 rstorder 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 de ned 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 selections.
The First criteria of selection de nes as resident RV the RV present only in its home MFrag and does not in uence 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 de nes as input RV in a MFrag the RV that also is de ned as resident RV in another MFrag. E.g, in Figure 5, isSuspended(enterprise) has input type in Owns Suspended Enterprise MFrag, but rst it is de ned 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 e ect. If there is a RV that is cause and in other group it is de ned as e ect by a rule, then this RV which is cause will have input type and the other which is e ect will have resident type. This is possible because in MEBN an input RV in uences the local probability distribution of resident RV like a cause and e ect relation, but rst the RV which has input type needs to be a resident RV in its home MEBN fragment.
After analyzing the causal relation de ned by the rules, it is possible to exist some RVs that still have unde ned type. This kind of RVs can be identi ed by analyzing the RVs which are not de ned by a rule but they still participate in a MFrag. E.g, in Figure 5 in Enterprise Information MFrag, the RV isResponsibleFor(person, enterprise) is not de ned by some rule because in the group related to its MFrag, it is not a cause or e ect. In this case, the algorithm considers that this kind of MFrag is the home MFrag of the RV analyzed and it will be de ned 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 rst and second criterion of selection may exist some RVs that still have unde ned 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 le.
Carvalho [
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 discrimination among potential suppliers. Therefore, the procurement agent cannot 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 identi es whether some person ownsSuspendedEnterprise. This relationship is de ned 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 de ned before. So on, it needs to have isResponsibleFor, isSuspended and ownsSuspendedEnterprise as relationships and Person and Enterprise as entities.
After modeling the elements during Analysis & Design discipline, to generate the PO, rst each element will be mapped as described in Figure 2. Then, the algorithm will run the sequence of steps presented below to de ne the RVs type based on rules and groups distribution. i It is identi ed 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 de ned by the user hypothesis. iii First criterion of selection is executed and the RVs present in just one MFrag will be de ned as resident. iv Second criterion of selection is executed. If the RV is de ned as cause in a rule and in other group it is de ned as e ect, then it will have input type in MFrag that it was cause and in the other that it was e ect, it will have resident type. v Case there are RVs that were not declared in any rule, but they were de ned in a group, then they will have resident type. vi Third criterion of selection will de ne 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 de ne the local probability distribution presents in each resident RVs. Therefore, the model generated is not complete. The user needs to de ne the local probability distribution by editing the code generated in MEBN plug-in supported by UnBBayes. After that, the PO is validated and veri ed 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.
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 de ned in Analysis & Design discipline to PR-OWL 2 format was based on the related concepts of each element of both representations.
The new de nition of the rule during the generation process is necessary to make its format understandable by a computer. This is possible by de ning 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 de ned 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 plugin 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 J avaT M and riles on Java Plugin Framework2 (JPF) version 1.5.1.