Towards Simplification of ME-Maps

Abstract

As knowledge increases tremendously each and every day, there is a need for various means to manage and organize it, so to utilize it when needed. For example, for finding solutions to technical and engineering problems. An alternative for achieving these goals is through knowledge mapping that aims at indexing the knowledge. Recently, we devised an approach called ME-MAP for mapping out know-how, so to facilitate knowledge indexing. However, the challenge of handling large maps still exists. In this paper, we address this challenge by proposing a simplification mechanism for ME-maps. In particular, we define the meaning of simplification in ME-MAP, set simplification rules, and develop an algorithm for simplifying ME-maps. In addition, we confirm the correctness of the algorithm and its scalability, as well as its support for understanding domain maps through a preliminary user study.

This research was partially supported by the Israel Science Foundation (Grant No. 495/14).

1 Introduction

Knowledge, especially in technology and engineering domains, is developing at a tremendous pace. In such domains, we are especially concerned with know-how, the kind of knowledge that guides action towards practical objectives, prescribing solutions to technical problems, and evaluating alternative solutions [24]. Know-how management can provide various benefits such as: domain review, trade-off analysis, and support for decision making. While there is almost instant access to published know-how on-line, to the best of our knowledge, there has been little advance in how a body of know-how is organized for easier access, understanding, and reasoning.

One way of addressing the know-how management challenge is through knowledge mapping. “A knowledge map - whether it is an actual map, ‘yellow pages’ or cleverly constructed database - points to knowledge but it does not contain it. It is a guide not a repository” [6]. The need to refer to explicit knowledge structures for complex information seeking situations has been discussed in e.g., [9], in which the authors refer to the case of exploratory search which cannot be achieved through simple keyword search. Other usages of knowledge maps also include enhancing the results of search engines [4] and increasing the efficiency of creativity and invention [20]. We believe that know-how mapping will increase knowledge accessibility and its utilization, improve exploratory search, facilitate exploratory reading, and assist in decision making processes.

Fig. 1.

A partial ME-map for the Goal Modeling Language specification domain.

Fig. 2.

A simplification of the map appears in Fig. 1.

Following the advantages mentioned above, we devised a mapping approach, ME-MAP (Means-End Map), that leverages on Goal-Oriented Requirements Engineering (GORE) conceptual structure to organize and manage a body of know-how for technology and engineering domains. The ME-MAP approach has been evaluated both for the ease of construction [28] and for the ease of understanding [22] of maps and found to be useful in both cases. An example of such a map appears in Fig. 1 that partially maps out the domain of defining a goal modeling language. In constructing the map, we consult several works in the GORE domain.

A major problem that arises during know-how modeling/mapping is that the maps become increasingly large and complex. Therefore, it becomes difficult to understand, inspect and modify such maps due to the potentially many inter-relationships and elements that may exist. In the ME-map in Fig. 1, although represents a fraction of the domain, there are a lot of elements and inter-dependencies, which make it difficult to grasp and understand the domain. To address these concerns, there is a need for a “zoom-out” technique that executes simplification operations over the maps and transforms the maps into high-level ones. Figure 2 presents a simplification of the ME-map in Fig. 1.

Simplification can be used for two major purposes: (1) Understandability: The accuracy of comprehending the domain. (2) Reasoning efficiency: A simplified map that keeps the reasoning properties under interest, improves the efficiency of the reasoning process, as there are fewer elements to deal with. Our conjecture is that the simplification would indeed improve the understandability and reasoning. It should be noted that by simplification we refer to a view over the map rather than to its modification. Thus, the users can navigate within the various views.

In this paper we elaborate on the simplification of ME maps and provide algorithms for generating simplified maps (views) that preserve the original semantics. We further evaluate the simplification for its performance and usability.

The paper is organized as follows. Section 2 details the simplification task and presents the algorithms. Section 3 details the implementation and evaluation of the simplification algorithms. Section 4 reviews related works and positions those with respect to this study. Finally, Sect. 5 concludes and outlines plans for future research.

2 Simplification of ME-Maps

The ME-MAP approach draws its core concepts from the goal-oriented requirement engineering (GORE) paradigm [31]. A main objective of ME-MAP is to take advantage of the inherent means-ends relationship that characterizes know-how, where the identification of problems and development of feasible solutions is a key concern. The approach aims at presenting problems identified in a domain, properties of problems that are particularly relevant in the domain, and offers a systematic review of proposed solutions. Formally, a ME-map is a tuple $ME=\langle \mathcal {E}, \mathcal {L}nk \rangle$, where $\mathcal {E}$ is a non-empty set of elements such that $\mathcal {E}= \mathcal {T}\cup \mathcal {Q}$, $\mathcal {T}\cap \mathcal {Q}=\emptyset$, where $\mathcal {T}$, $\mathcal {Q}$ are set of tasks and qualities, respectively. $\mathcal {L}nk$ is a set of pairs of elements representing the links between them. The semantics of the ME-MAP language is defined as the set of all alternative solutions to the main problems. The detailed syntax and semantics of the ME-MAP appear in [17]. It is important to note that achieved-by links indicate alternatives from which only one of these can be selected for a legal instance (XOR) whereas consists-of links indicate parts that are required to be selected for a legal instance (AND).

Simplification deals with the reduction of information by retaining essential properties and removing insignificant details deemed unimportant by the user [8]. Map simplification helps in dealing with the map complexity, scalability, improves the map understandability, and might also support the validation tasks compared to existing larger ME maps. For example, assume that for the ME map in Fig. 1, we are only interested in the tasks (called initial user tasks), Define Grammar, Define Meta-Model, Define Textual Syntax, Use Propositional Logic. Then, removing the other tasks and “collapsing” the links between the selected tasks produces the ME map in Fig. 2. This simplified map explicates that the Use Propositional Logic task contributes positively to the qualities Support for Semantics Analysis and Precision.

The ME-Map simplification procedure involves identifying a set of tasks that should remain on the map. Based on this set, the simplification is performed. Egyed in [8] showed that a major challenge in simplification is recomputing the hiding information in the context of the remaining, non-hidden map elements. For example, removing contribution links between two non-hidden qualities may require adding a new link whose label is the composition of the labels of the removed links. Egyed uses a set of abstraction rules to remove classes and group relationships into one relationship. In this paper, we adopt a similar approach. In the following we refer to simplification validity, simplification rules, the simplification method and finally the simplification algorithm.

2.1 Valid Simplification

Simplification uses a set of initial tasks provided by the user. The simplification process creates a partial, concise map that includes the initial tasks and possibly additional tasks between the root and the initial tasks. Simplification should preserve semantic properties we will discuss later (soundness and completeness). Otherwise, the simplified map may be misleading and not preserve reasoning properties such as consistency. Consider a simplification of the ME-map in Fig. 3a with initial tasks $X,T_7,T_8, T_9$. Figures 3b, 3c present possible simplifications. Figure 3b presents $achieved-by~$relationships between T and $X, T_7, T_8$ and $T_9$ respectively. However, the ME-map in Fig. 3a does not include $achieved-by~$paths between T to these three tasks. The map can mislead the user because $X, T_7, T_8$, and $T_9$ are not alternatives (direct or indirect) for achieving T. In addition, the semantics enforce an xor constraint on the $achieved-by~$relationships. A legal instance of the simplified map can include only one task. On the other hand, in the original ME-map, a legal instance might include both tasks $T_7$ and $T_9$. Task X is inconsistent in Fig. 3a but is consistent in Figs. 3b, 3c. The simplification in Fig. 3b loses semantic properties that existed in the original model. Thus the use of the maps in Fig. 3b for consistency verification is incorrect. The ME-map in Fig. 3d introduces an improvement over the incorrect version in Fig. 3c. Any relationship between two tasks in the simplified map also exists in the original map directly or indirectly. For example, for the $achieved-by~$relationship between $T_1$ and $T_7$, there exists a path of relationship $T \xrightarrow {achieved-by}^+ T_7$ in the original map.

Fig. 3.

A map with three possible simplifications

Based on these observations we require the simplified map to satisfy the following properties:

• Soundness requires that any relationship implied by the simplified map must also be implied by the original map.

• Completeness requires that any relationship between the root and an initial task in the original map must be implied by the simplified map.

Removing any task requires ensuring that the removed task does not alter map soundness and completeness properties. The removal of tasks requires adding new links that preserve the implied relationships between the remaining tasks. For instance, an $achieved-by~$sequence $T_1 \xrightarrow {achieved-by} T_2$, $T_2 \xrightarrow {achieved-by} T_3$, might be replaced by one “achieved-by” link $T_1 \xrightarrow {achieved-by} T_3$. Nevertheless, its implied semantics is unchanged: , $T_1$ is “achieved by” $T_3$. A contribution link sequence ${elm}_1 \xrightarrow {{cont}_1} q_1$, ${q}_1 \xrightarrow {{cont}_2} q_2$, might be replaced by a single contribution link ${elm}_1 \xrightarrow {{cont}} q_2$ in which cont reflects the implicit contribution of $cont_1$ with $cont_2$.

Definition 1 (Valid simplification)

A valid simplification of $ME=\langle \mathcal {E}, \mathcal {L}nk \rangle$ and initial tasks S is a ME-Map $ME_{\downarrow {[S]}}=\langle \mathcal {E'} \subseteq \mathcal {E}, \mathcal {L}nk' \rangle$ that satisfies the following properties:

• 1. The initial tasks S are the leaf tasks of $\mathcal {E'}$.

• 2. Soundness

  • (a) For each two tasks $T_1,~T_2 \in \mathcal {E'}$ being $lnk= achieved-by/consists-of$, if $T_1 \xrightarrow {lnk} T_2$ holds in $ME_{\downarrow {[S]}}$, then $T_1 \xrightarrow {lnk}^+ T_2$¹ holds in ME too.

  • (b) For each element elm and quality q in $ME_{\downarrow {[S]}}$ if $elm \xrightarrow {cont} q$ holds in $ME_{\downarrow {[S]}}$, then $elm \xrightarrow {cont}^+ q$ holds in ME too.

• 3. Completeness

  • (a) For each two tasks $T_1,~T_2 \in \mathcal {E'}$, if $T_1 \xrightarrow {lnk}^+ T_2$ holds in ME, then $T_1 \xrightarrow {lnk}^+ T_2$ holds in $ME_{\downarrow {[S]}}$ too.

  • (b) For each tasks $T_1,~T_n \in \mathcal {E'}$, for each interleaved path of $achieved-by~$/$consists-of~$relationships between $T_1$ and $T_n$, $T_1 \xrightarrow {\alpha _1}^+T_2$, $T_2 \xrightarrow {\alpha _2}^+T_3,\dots ,$ $T_{n-1} \xrightarrow {\alpha _n}^+T_n$ in ME where $\alpha _i \in \{$achieved-by $,$consists-of $\},~ i=1,n~\text {and}~\alpha _i \ne \alpha _{i+1}$, there exists a similar interleaved path (possibly shorter) with same tasks $T_1,~T_2,\dots ,T_n$ and the same interrelationships $T_1 \xrightarrow {\alpha _1}^+T_2$, $T_2 \xrightarrow {\alpha _2}^+T_3,\dots ,$ $T_{n-1} \xrightarrow {\alpha _n}^+T_n$ in $ME_{\downarrow {[S]}}$.

  • (c) For each element elm and quality q in $\mathcal {E'}$ if $elm \xrightarrow {cont}^+ q$ holds in ME, then $elm \xrightarrow {cont}^+ q$ holds in $ME_{\downarrow {[S]}}$ too.

2.2 Simplification Rules

The simplification cannot be applied without considering the context in which the paths belong. If the task T belongs to two paths of different types, $\alpha _1= T_1 \xrightarrow {achieved-by} T$, $T\xrightarrow {achieved-by} {T_2}$ and $\alpha _2 = {T_3} \xrightarrow {consists-of} T$, $T\xrightarrow {consists-of} {T_4}$, then T is therefore an intermediate task of an interleaved path of $achieved-by~$and $consists-of~$links ${T_1} \xrightarrow {achieved-by} T$, $T\xrightarrow {consists-of} {T_4}$. Therefore T is not eliminated and the later two paths $\alpha _1, \alpha _2$ will not be reduced even though they are paths of links of the same type. Based on these observations we present the notion of a mandatory task and a mandatory quality.

Definition 2 (Mandatory tasks and qualities)

Let $ME=\langle \mathcal {E}, \mathcal {L}nk \rangle$ be a ME-map and $S \subseteq \mathcal {E}$ a set of initial tasks.

(1) Mandatory task. A task T is called a mandatory task if it satisfies one of the following conditions

• 1. T is the root task or $T \in S$

• 2. There exists a sequence $<T_1 \xrightarrow {consists-of} \boldsymbol{T}$, $\boldsymbol{T} \xrightarrow {achieved-by} T_2>$ or a sequence $<T_1 \xrightarrow {achieved-by} \boldsymbol{T}$, $\boldsymbol{T} \xrightarrow {consists-of} T_2$ that belongs to some path of $achieved-by~$and $consists-of~$links between the root and a task in S.

A task that does not satisfy any of the above conditions is called non-mandatory task or alternatively removable task.

(2) Mandatory qualify. A quality q is called a mandatory quality if its owner task [17] is a mandatory task. It is called a non-mandatory quality or removable quality if its owner is non-mandatory or it is not a quality of any task.

Let $T_{removable}$ and $q_{removable}$ be removable task and quality respectively. Then:

R1.:

${source} \xrightarrow {achieved-by} T_{removable}$, $T_{removable}\xrightarrow {achieved-by} {target}$ $\Rightarrow$ source $\xrightarrow {achieved-by} {target}$

R2.:

${source} \xrightarrow {consists-of} T_{removable}$, $T_{removable}\xrightarrow {consists-of} {target}$ $\Rightarrow$ source $\xrightarrow {consists-of} {target}$

R3.:

$elment_{source} \xrightarrow {cont[l_1]} q_{removable}$, $q_{removable} \xrightarrow {cont [l_2]} q_{target}$ $\Rightarrow$ $elment_{source} \xrightarrow {cont} [min(l_1,l_2)$²$]q_{target}$

The Simplification Algorithm

Algorithm 1 produces a simplified map based on an initial set. It includes two major steps, as we have already shown. Step 1 produces a simplified map without the qualities while the second step updates the map from step 1 with qualities, association and contribution links.

Contribution links can only differ in their labels; therefore, two successive contribution links can be reduced to a single link. The new link must, however, have a new label that represents the combined contribution labels of the two links. In addition, when a new contribution link ${elm} \xrightarrow {{cont}} q$ is created between some element elm and some quality q, no other additional contribution link between elm and q is created. But rather, the label cont is updated to reflect the contribution of the two links together (aggregation operation). The way we combined the joined contribution labels was by choosing the minimum label. We have adopted a conservative approach by placing greater weight on the lowest value of contribution links in a series of successive labels or groupings of labels than on the higher values. This is, however, a domain-specific problem, and other joined contribution policies can be used.

3 Implementation and Evaluation

We implemented the simplification algorithm together with other reasoning methods presented in [17] within a MEMapReasoner prototype tool we developed [18]. The tool gets as an input a JSON file exported from the ME Map web-based tool [27] and MEMapReasoner provides the related output as a JSON file.

Based on the implemented prototype, we evaluate the work with respect to its two purposes. The first refers to the algorithm scalability and reasoning efficiency and the second to the impact of ME-map simplification on understandability.

3.1 Scalability Evaluation

To evaluate the simplification algorithm we test it with several maps following different characteristics in terms of elements and related links. As mentioned earlier, the graph-based techniques used in our paper have exponential worst-case time complexity. Therefore, we need to show that in actual maps, this method scale well. Thus, it is appealing to test the method on large-scale maps. However, currently, such maps are not available. To address this, we follow solutions proposed in other domains and generated large maps automatically. In the following, we report on the evaluation setup, the execution, and the results of the evaluation we performed.

Table 1. Average time for the simplification tasks

Setup and Execution. First, we performed the tests on four limited-size ME-maps. The advantage of these maps is that they represent real domains. They were built by our group and their size range from 20 to 30 tasks on each map. Second, we generated synthetic ME-maps. The sizes of these maps were 500–2000 tasks. To generate the maps, we started with a seed of tasks and links, and iteratively generated layers of child tasks with randomly selected $achieved-by~$and $consists-of~$links. Moving backward on the paths of the generated map, we added qualities, association links, and contribution links so to develop realistic maps. Although the number of qualities is much lower than the number of tasks, we believe that the way the maps were built enforces the algorithm to consider the implications of abstracting qualities as well.

For each of the tested maps we apply the simplification algorithm. For the initial user (important) tasks, we selected randomly 30% of the leave tasks. The independent variables are: number of tasks, number of qualities number of $achieved-by$ number of links, number of $consists-of~$ links and number of contribution links, whereas the dependent variables are the decreased percentage of elements and the time needed to perform the simplification. We executed each task 5 times and computed the average of all runs. The evaluation was performed on a Aacer computer laptop, Windows 10 64 bits, Intel(R) Core™ i5-1035G1, 8GB RAM and 512GB SSD.

Results and Discussion. Table 1 introduces the results of the evaluation. The left-hand side of the table provides descriptive information about the maps: number of Task (Ta), number of Qualities (Qu), number of achieved-by links (AB), number of consists-of links (CO), number of contribution links (Con) and the total number of Elements (El). The right-hand side of the table details the decreasing percentage of the number of elements in the simplified maps (%Dec) and the time in milliseconds it took to perform the simplification. The table shows that applying the simplification algorithm reduces over 55% of the elements in most maps. In addition, it shows that the algorithm works efficiently and we got results in less than four seconds even for a large map with 2000 tasks. The results also indicate that the overall number of elements is not enough to analyze performance. The domains of Sentiment Analysis and DPSL have almost the same number of elements, with sizes of 62 and 63, receptively. However, there are differences in the overall performance. The performance of the simplification task in the Design Patterns map is about 12% higher than the Sentiment Analysis map. Since the maps are actually graphs, the performance of the algorithm is significantly affected by the number of contribution paths. As shown in the table, the number of contribution links in the DPSL map is around triple more than the Sentiment Analysis map.

To check the implication of the simplification results, we execute a consistency check [17] over the maps and their corresponding simplifications. The column ConsBefore in Table 2 shows the times in milliseconds of running the consistency algorithm on the synthetic maps evaluated in the previous section augmented with a consistency problem. The results show that the performance is expensive and the consistency check lasted between 11 s for the map of 500 tasks and 15 min for the map with 2000 tasks. The column ConsAfter in the table shows the time it last to apply the same consistency check on the simplified maps. The results show significant improvements (Improvement column) compared to the performance of the algorithm on the original maps. Note that in both cases for each map the same consistency problems were identified.

Table 2. Improvement in applying consistency check

Threats to Validity. The results of the experiments we conducted should be taken cautiously due to the following threats to validity. First, we perform the experiments on a small number of maps. In addition, as we develop the maps, it might be that the way the maps are constructed is biased. Yet, the “real” domain maps were carefully reviewed by several of our group members to reflect the actual domain knowledge. Nevertheless, these maps were relatively small and larger “real” domain maps are required.

3.2 Understandability

To check the support of the ME-map simplification with respect to understanding a domain, we conducted a user study by means of a preliminary controlled experiment. In the following we shortly elaborate on the experiment design, execution, and results.

Hypotheses. We checked the comprehension of a domain by means of question answering, in which we checked the correctness, the time to answer the questions, and the confidence we had in their answers.

Our conjectures are that using simplification would lead to more correct answers as many unrelated details are avoided and thus the quest for answers is easier. For that reason, we also believe that the confidence in the answers will increase. As for time to answer the questions, there is a trade-off between finding all answers in one place and the need to navigate over or execute multiple simplifications. Yet, when the number of simplifications is limited we believe that the time to answer the questions will be shorter than when searching for the answer in a complete/unified map. In case of many simplifications, finding the right one may take time. Similarly, deciding on the appropriate simplification may also take time.

Design. We next describe the variables, the participants, and the tasks.

The independent variable in the experiments is the way the domain map was presented. Either as a unified map or two separated simplified maps that jointly represent the entire domain. We decided upon this design to make sure that the answers were achieved by following the provided simplifications. The independent variables are the following: (1) the correctness of the answers, measured by their relative alignment with the gold standard on a scale of 0-1. We classified the questions into three categories of task identification, screening, and analysis. These categories refer to different capabilities required by the participants. (2) the time it takes to answer the question, measured in minutes; and (3) the confidence a participant had in her answers, measured on a scale of 1 to 7 (indicates the highest confidence). We also checked the perception of the participants.

The participants in the experiment were nine senior undergraduate and graduate students at Ben-Gurion University of the Negev. They were recruited by a call for participation posting and were offered monetary compensation. They were not familiar with the domain and with the ME-MAP approach.

The experiment form consists of three parts: (1) a pre-questionnaire that checks the background and knowledge of the participants; (2) the main task, in which participants received either a single domain ME map or two simplified ME maps and were required to answers a set of questions regarding the domain; (3) the last part of the form reflects upon the participants’ perception on ME map and their form. The domain that was introduced in the experiment is the domain of Software Design Pattern Specification Languages (DPSL) and consisted of knowledge extracted from [15]. The experiment forms can be found in [19].

Execution. The execution of the experiment took place in a special session that lasts approximately 1 h. Before the experiment started, we briefly introduced ME-MAP and its semantics for about 10 min. Then, the participants were asked to sign the consent form detailing their rights. They were randomly divided into two groups. Form A in which the subjects received a unified ME map of the DPSL domain was assigned to 4 subjects. Form B in which the subjects received two simplified ME maps of the DPSL domain was assigned to 5 subjects. In both forms the students were asked the same 9 questions. For each question, they wrote their answer, the time it took them to arrive at that answer, and the confidence they had in that answer. Next, they filled out the post questionnaire.

Results. In Table 3 we present the results of the main task performed by the participants. We present the results in four categories: Total, which accumulates all answers; Task identification, which accumulates the answers to questions 1–2; Screening, which accumulates the answers to questions 3–4 and refers to comparison among tasks; and Analyze Concrete Contributions, which accumulates the answers to questions 5–9. The $\overline{x}$ columns indicate the average and the $\sigma$ indicate the standard deviation. In terms of correctness, it seems that using the simplified maps achieved better results, in particular, in comprehending complex tasks such as trade off analysis. The same hold for the confidence the participants had in their answers, in particular, when analyzing specific contributions. A deviation from that trend refers to the time it took the participants to arrive at their answers. It appears that the screening task took much more time when using the simplified maps.

Table 3. Descriptive statistics

From analyzing the participants’ subjective preferences, we found out that there are benefits of having both the unified view (to see all the details) and the simplified views (to focus on specific aspects).

Discussion. The results indicate that for simple comprehension questions, there is no difference in using either the unified or the simplified maps in both correctness and confidence. This is probably due to the minimal cognitive effort required for detecting related tasks. Nevertheless, in most cases the time to reach the answers is shorter when using the simplified maps. This is probably due to the focused information appears on those maps. The most observable difference between the two representations occurs in the complex task of analyzing concrete contributions. Here, using the simplified maps results in more correct answers that gain higher confidence. It also took less time to reach these answers. We attribute these differences to the way the simplified maps are organized in terms that they presented concise information which was easy to grasp with respect to the same information that was spread all over the unified map.

Another issue that requires further attention is the time it took to perform the screening tasks. It seems that the participants who use the simplified maps switched among the maps trying to answer the questions as it was not clear, where the relevant information can be found. This is actually quite important. In the experiment, we defined the simplification in advance. However, in a regular situation, we expect the users of a knowledge map to perform their own simplification based on their searching and exploration needs (using the proposed algorithm), and thus they would skip the need to navigate across multiple simplifications to allocate the relevant information.

Threats to Validity. Here again, the results of our study need to be considered in view of several threats to validity. First, we examined two alternatives for knowledge representation. As the experiment is quite simple in its design, there might be a chance for mono operation bias, in which we did not explore or test a range of simplifications. Second, in the experiment we used a hard copy of the maps, whereas in reality we expect the participants to work with an on-line platform that ease the search and simplifications. Third, the conclusions we arrived at should be taken with caution, as we got no statistical support for their validity. Yet, they provide an indication of the supremacy of the simplification. Fourth, we had a limited number of participants, thus, it is challenging to draw a definite conclusion. In addition, we experiment with only one domain a fact that also challenges the generalization of the results.

4 Related Work

Abstraction plays a crucial role in dealing with model complexity. It deals with simplifying information by retaining essential properties and removing insignificant details. Indeed, numerous works on reducing model complexity have been presented in various modeling languages and domains and for various purposes like increasing comprehension or verification purposes [5, 7, 8, 14, 25, 30].

de Lara et al. [7] identified four types of abstractions: (1) Merge techniques in which one element of the same type replace a set of model elements, collecting the merged elements’ properties [8]; (2) Aggregation techniques which suggest grouping low-level model elements into higher-level elements, e.g., [25]; (3) Delete techniques that delete elements which are not considered relevant or modify some observed properties of a model. e.g., [30]; and (4) View techniques in which a new model is created (called view) using the same language or a different one and that discard the original model features that are irrelevant for the desired abstraction, e.g., [11].

Egyed presented in [8] an algorithm for abstraction (simplification) of UML class diagrams. The presented algorithm uses abstraction rules to remove intermediate classes and group intermediate relationships (such as associations and class hierarchies). The author evaluated the abstraction technique on over a dozen real-world case studies ranging from in-house-developed models to third-party models. Other approaches used a set of rules for class model simplification presented in [1, 12].

Shoval et al. presented in [25] a method for creating a hierarchy of entity-relationship diagrams (HERD) from a “flat” ER diagram. The method uses packaging operations that aggregate entities and relationships into higher-level ER diagrams called structures. A structure is a partial ER diagram with external relationships to related structures that might group two or more specific relationships (Aggregate). Other approaches in ER that use the aggregation can be found in [3, 13, 21, 29]. Villegas and Olive present in [30] a method that uses a set of elements provided by the user (called user focus set), and the method filters (simplifies) the conceptual schema by producing a subset of the elements of the original schema taking into account the importance of each entity type in the schema and its closeness to the entity types the user focuses on. The method might create new entities and use the hierarchy to produce a more abstract model.

Other modeling languages have used different abstraction techniques such as aggregation into higher-level elements or removing unnecessary elements to reduce the model’s complexity, such as workflow languages [23, 26]. Some of these languages use already built-in hierarchical primitives that enable element aggregation.

As the language we are using in this paper is a subset of $i^*$ [31] we refer to studies dealing with its complexity management. We found out that scalability is considered one of the important challenging problems that have been treated only to a limited extent [2, 10, 16]. Most solutions focus on increasing the modularity of the $i^*$ language by providing modularization mechanisms. These approaches require extending the languages with new modeling constructs that encapsulate the internal structures of the model. A detailed survey can be found in [16]. In contrast to the works presented by the $i^*$ community, in this work we chose to remain with the existing language and not extend the language with new constructs that naturally require a steeper learning curve. Our aim is to simplify the maps to enable better understanding, inspecting, and managing the maps while preserving their semantics. In that sense, we adopt a similar direction to the work of Egyed who introduced abstraction rules for class models and an algorithm for applying them [8].

5 Conclusion and Future Work

We develop a simplification algorithm for know-how maps and found it improving knowledge reasoning efficiency as well as knowledge understandability. We examined the reasoning efficiency and scaleability using large scale maps and the understandability via a controlled experiment. The importance of the map simplification is high as knowledge, in particular know-how, is developing at a fast pace, so the need to manage and reason about it is increased. Even know-how maps that index the existing knowledge are complex and tend to scale fast, and thus required further simplification. We believe that by applying the simplification algorithm over the maps, stakeholders can better manage and navigate throughout the maps, and better be supported for decision making.

In the future, we plan to further investigate and evaluate the mechanism we developed and look for additional mechanisms that facilitate various simplification capabilities, so to better manage ME maps. We also plan to test the simplification of ME maps for industrial/practical purposes. In particular, as the ME-MAP approach is derived from GORE, we plan to apply the simplification mechanism to goal modeling techniques.