2.1 Methods based on a Reference Entity

These methods allow the extraction of dependencies between rules based on a reference entity (a pattern, a rule, etc.). [¹⁸] propose a system to improve rapid decision-making in software defined networks. The proposed method defines different patterns for the basic rules. The analysis of the dependencies between the rules is thus ensured by analyzing these patterns. The method is based on the organization of the rules in a hierarchical form. Thus, the authors defined dependencies in the form of direct dependencies and complex dependencies. These notions made it easier to update the dependency graph when deleting a rule. [⁵] propose an approach to maintain rule bases.

They represented them with a dependency graph according to calculated dominance criteria. To do this, they propose to define a dominant rule for the base, and then calculate the degree of dominance of the latter for each of the other elements of the base. This allows to possible to define the succession relationships between the elements of the base. [²⁸] present a tool called S2REd to assist in the development of a rule base. Their main aim is to facilitate the creation, editing and understanding of rules by representing each rule in a graph. The proposed tool offers the end user semantic assistance by modelling the knowledge represented by the rule processed and that expressed by the other elements of the rule base. This is based on loading (or defining) and matching meta-model rules.

2.2 Methods based on the Analysis of Usage Data

These methods are based on analyzing the results of the rule base application on one or more fact bases.

[²⁵] introduce a Framework to modify the transfer policies installed in the distributed switches of a network. The authors extracted the dependency relationships between the rules to eliminate unnecessary updates. Dependency graph generation is achieved incrementally along the compilation process.

In [²⁰], the authors present an approach to ensure a clear visualization of the rule bases. Their proposal refers to usage data provided to find frequently used rules and highlight their dependencies. [⁹] propose a system based on dependencies between rules in order to manage large bases of rules. These dependencies are determined as a function of the execution frequencies of the rules calculated by the application of the rules on a dataset. [²⁷] propose an approach for the visualization of rule bases using their usage data which take the form of proof trees. This approach mainly aims to help the user while evaluating the quality of the rule base and while modifying it. The collection of usage data is done through requests introduced either during the tests, either during the system specification phase or during its use.

2.3 Methods based on Consequent-Antecedent Analysis

These methods are the most used. They are based on the fact that if a rule Ry depends on a rule Rx, then Rx must provide data which will be used by Ry. These methods therefore analyze the relationships between the consequent atoms of the first rule and the antecedent atoms of the second. They are divided into two groups: syntactic methods and semantic methods. Syntactic methods seek syntactic dependency relationships. They are then based on relations of equality and equivalence between the atoms predicates. Semantic methods seek semantic dependency relationships. Indeed, they have improved syntactic methods by adding the use of hierarchical relationships defined between entities referenced by the predicates of atoms.

Slider-p [⁸] is a reasoner proposed to manage the data of a dynamic knowledge base. It is based on a rule dependency graph.

[¹⁰] suggest reducing the decision-making time based on grouping rules and variables, and on the dependencies extracted between the rules. In this work, the extraction of dependencies is based on the fact that some consequent atoms of the first rule are invoked in the antecedent of the second. In [¹], the authors have based their proposal on dependencies between the elements of the rule base. They proposed a tool ensuring the response to the queries posed to ontologies. Dependency extraction is based on the search for equality relations between the atoms predicates and on their variables unification. This work uses the notion of k-dependency to check if the dependency between two rules can last.

[¹⁵] offer a rule base representation tool called Axiomé. Axiomé is based on referencing the same classes and the same object properties without taking into account the analysis of the variables. In 2010, the second version of Axiomé was proposed in [¹⁴] to enrich the first version by analyzing the domain and the range of object property type atoms. Hierarchical relationships between classes and between properties defined in the ontology are also considered.

[¹¹] propose a bottom-up approach to govern workflows ^fn in business processes. This work presents a model for workflows components built based on the dependency graphs between the consequents and the antecedents of the business rules. [²³] propose an approach which exploits dependency graphs to represent solutions to constraint systems. They are also used in this same work to represent the execution of protocols by detecting the causal dependencies between the rules.

Our study of the art allowed us to draw Table 2. We classified these methods according to the aim of each work. The first type of methods are based on the reference to an entity, the second type of methods are based on the analysis of usage data. The first type of method did not provide an understandable representation of the base while the second type of method approach did not improve the speed of decision-making.

The third type of approach for extracting dependency relationships are syntactic methods. These methods analyze the dependency relationship between the rule base elements by analyzing the dependency relationship between their atoms. The last type of methods are semantic ones. They actually represent an extension of syntactic ones. Syntactic and semantic methods failed to provide a sufficient number of correct dependencies.

Overall, we noticed that the representations of the base provided by existing work are not clear. In addition, the results of dependency relationships extraction are not sufficient to be able to properly manage a large rule base. Confronted with these problems, we propose a method for improving the results of extracting dependency relationships. Our method provides an understandable representation adapted to the needs of the expert.In the following section, we present a method to deal with the cited gaps.

3.1 Analyzing Dependency Relationships

RuDES begins its processing with analyzing the dependency relationship between two rules Rx and Ry using two different techniques. Each of them is implemented in a sub-module. The first is called CADA for Consequent-Antecedent analysis based on Different-type Atoms. As its name suggests, this sub-module analyzes the dependency from Rx to Ry by analyzing the dependency between the consequent of the first rule and the antecedent of the other. This stems from the fact that if Ry depends on Rx, certainly Ry will make use, in its antecedent, of knowledge inferred by consequence from Rx. In addition, this sub-module is also based on the analysis of atoms having different types.

The second sub-module is called CCA for Consquent-Consequent Analysis. It is based on a principle different from the previous sub-module. It mainly uses the relationships between the facts inferred by the first rule and the facts inferred by the second. This sub-module, unlike the other sub-module, is not based solely on facts expressed by the ontology Ω. It also uses knowledge based on the rule base Σ itself [⁴].

3.2 Dependencies Filtering

After analyzing the dependency relationship between two rules Rx and Ry, each of the sub-modules CADA and CCA provide a dependency which may be different from the other. The Dependencies Filtering sub-module role consists in keeping the most appropriate dependency. This choice is made using the confidence degrees DC_i (i ∈ {CADA, CCA}) of each dependency and the sub-module that generated it (Algorithm 2).

Algorithm 2 Dependencies Filtering 

The highest coefficient (c_{_CCA} = 1) is assigned to the CCA sub-module because it is based on knowledge extracted from the definition of the ontology Ω and those extracted from the rule base Σ. The other two sub-module is based only on knowledge extracted from Ω. Then its coefficient c_{_CADA} is lower than c_{_CCA} (c_{_CADA}=0.8 and c_{_CCA}=1). These coefficients are chosen after carring out some experiments that proved them.

3.3 Rules Grouping

Most rule bases decompose into groups of rules, each of which is responsible for accomplishing a task. As example we cite the rule base associated to the ontology Vehicul Ontology [³] which includes a group of rules responsible for determining a vehicle position in relation to others. It also includes another group responsible for proposing actions appropriate to a danger situation, etc. On the other hand, there are rule bases where each task is accomplished by one rule.

We cite the example of the base associated to the ontology Autism Ontology [²⁶]. The elements of its rule base define how each phenotype should be derived from a set of clinical outcomes.

Each rule is based on knowledge defined in the ontology to infer new knowledge without using any other rule.

In our proposal, the Rules Grouping module build the groups in order to facilitate and optimize inference processes and rule base verification. Rules Grouping module is based on dependency relationships already extracted. The rules belong to the same group take, as input, facts that relate to the same classes. They also produce facts concerning the same classes. Thus, the rules of the same group have the same incoming edges and the same outgoing edges. The groups are saved in DepKB.

3.4 Saving Rule Dependencies

The DepKB knowledge base is represented by an ontology. As shown in Figure 3, it is composed of a fact base, a rule base and an instance base. The fact base is detailed in Table 3. It has three classes, three object properties and one data property. A dependency relationship is represented using the classes Dependency and Rule, connected by the object properties beginsFrom and endsAt. The confidence degree of a dependency relationship is expressed using the data property hasWeight (see Figure 4).

Fig. 3 DepKB architecture 

Fig. 4 D_Rx→Ry representation in DepKB 

Each instance of the Dependency class has only one instance of the properties beginsFrom, endsAt and hasWeight.

Rule groups are represented using the class Group linked to the class Rule by the object property belongsTo (see Figure 4). Each instance of the Rule class has only one instance of the belongsTo property. In Figure 4 we show show to represent the dependency relationship D_Rx→Ry in the ontology DepKB. This representation can be simplified for the experts as presented in Figure 5.

Fig. 5 Simplified representation of D_Rx→Ry 

The DepKB ontology also includes the rule R-Trans, represented in Figure 6. It expresses transitivity property of dependency relationships. This rule can be read as follows: if there is a rule Ry which depends on a rule Rx, and if there is a rule Rz which depends on the rule Ry, then the rule Rz depends on the rule Rx (see Figure 7). DepKB also includes the DepG part which contains all the instances of the Dependency class representing the saved dependency relationships.

Fig. 6 RTrans: rule expressing the transitivity property of dependency relationships 

Fig. 7 Transitivity property of dependency relationships 

4.1 Ontologies used for Evaluation

We applied our approach on rule bases associated to three ontologies from various fields: Web service security field, medical field and road safety field.

4.1.1 WebService-SecurityPolicy Ontology

WebService-SecurityPolicy (WS-SP) [⁷] is an ontology from Web service security field. Its primary role is to specify and match web service security policies between a requester and a web service provider. This base includes 79 rules. The developers of this rule base divided it into five groups, each of which has a specific task (see Figure 8a). These tasks must be performed in a specific order. The first group instantiates the semantic relationships that may exist between the requester’s atomic security properties and those of the service provider.

Fig. 8 Rule groups provided by ontologies designers (a:WS-SP, b:DFO, c:VO) 

The elements of the second group instantiate the semantic relationships that can exist between the complex security properties of the requester and those of the service provider. Then the third group matches their security assertions. The fourth group makes the connections between their security alternatives. Finally, the last group decides the degree of security correspondence between their assertions (Perfect match, close match, possible math and no match).

4.2 CADA and CCA Sub-Modules Performance

To evaluate the performance of both dependency extraction sub-modules (CADA and CCA), we applied them separately on the study cases already mentioned. Then we compared the obtained results to those provided by the rule bases developers. Thus, we were able to define the number of correct dependencies, the number of false dependencies and the number of non-extracted (missed) dependencies.

The CADA sub-module extracts dependencies by analyzing pairs of different type atoms. One atom comes from the consequent of the first rule and the other from the second’s antecedent. Table 7, Table 8 and Table 9 present the dependency relationship rates found compared to those missed. They also show the rates of false dependencies extracted compared to all of those found.

These tables show that CADA actively contributed to the extraction of the correct dependencies in DFO and VO cases. In return, the number of false dependencies is high. In the WS-SP case, CADA has extracted a small number of correct dependencies. It also extracted a large number of false dependencies compared to the other module. These results show that this sub-module sometimes contributes to the increase in the number of correct dependencies, but it helps to extract a large number of false dependencies. We also noticed that it contributed to detect the dependencies missed by CCA. To take advantage of this sub-module, we eliminated its drawback by the Dependencies Filtering sub-module.

Besides, the CCA sub-module allowed the extraction of a large number of correct dependencies. It generated only a small number of false dependencies in all of the case studies. In the case of the WS-SP database, CCA extracted more than 23 of correct dependencies.

In the cases of the DFO and VO databases, it extracted almost half. This result proves its efficiency. This fact is due to its use of knowledge expressed by the fact base and those expressed by the rule base.

All these results prove that both CADA and CCA participate, in some cases, in increasing the number of correct dependencies. In other cases, they help reduce the number of false ones. This proves that these modules are complementary.

4.3 RuDES Performance

To position ourselves vis-a-vis existing work interested in dependencies extraction, we compared our method to Axiomé. Axiomé is the most complete existing semantic method. It includes all the techniques of semantic ones. It is available as a plugin in Protégé^fn, an ontology development environment.

We applied RuDES and Axiomé to the study cases already presented. The results are shown in Figure 9 and Figure 10. These values are computed in the same way as that used to calculate the results presented in the previous section.

Fig. 9 All dependencies extracted by Existing Methods and RuDES 

Fig. 10 Correct dependencies extracted by Existing Methods and RuDES 

Figure 9 presents the numbers of correct dependencies versus the numbers of false extracted ones. Figure 10 shows, for each case, the number of correct dependencies extracted versus the number of missed ones. The figures show that in the case of WS-SP base, the existing methods have extracted a small number of dependencies among which nearly 30% are false. Whereas RuDES has extracted practically all the requested dependencies with almost perfect precision (small number of false dependencies).

These results are due to a large number of WS-SP base rules using atoms whose types are not considered by existing methods. In the case of the DFO and VO bases, the rule bases do not include these atoms. Thus, existing methods did not extract false dependencies in DFO case and a small number in the VO case. They managed to extract almost half of the number of dependencies requested.

RuDES extracted almost all the requested dependencies with a small number of false ones. This results improvement is owing to the facts that RuDES (i) extends the existing methods with analyzing a larger number of atoms and (ii) uses a new technique as shown before.

4.4 Rules Grouping Module Performance

The developers of each of the studied ontologies provided the rules in groups (as described in subsection 4.1). Figure 8a presents the rule groups provided by the WS-SP ontology designers, whereas Figure 8b shows the rule groups provided by the DFO ontology designers. The elements of each group are responsible for a well-defined task during the inference process. The rules of the same group can be applied in any order. Yet, rules from different groups must execute in a well-defined order to infer correct and consistent knowledge. In this subsection, we choose to prove the efficiency of our method by comparing the resulting groups to those provided by the ontologies designers. The clustering algorithm is based on extracting the rules groups from the rules dependency graph DepG. The elements of the same group have the same incoming edges and the same outgoing ones.

As shown in Figure 11b, in the case of the DFO ontology, the extracted dependencies between the groups are all correct. In addition, the dependencies to be extracted are all present. Thus, RuDES succeeded in extracting the dependencies allowing to guarantee a correct and a consistent inferred knowledge. Besides, in the WS-SP ontology case (Figure 11a), the dependencies between groups are all present and their performance order is close to the one specified by the designers. On the other hand, in all three cases (Figure 11) there is a coincidence between the extracted groups and those provided by the ontologies designers. This proves that RuDES succeeded in determining which rules would be responsible for the same task.

Fig. 11 RuDES Rule groups (a:WS-SP, b:DFO, c:VO)