Causal modelling is a branch of complex systems modelling approaches. Causal modelling methods are common in statistics, econometrics, cybernetics, computer science, data science and other complexity sciences to study cause-effect relationships, and constructing causality driven models to predict and to control the possible dynamics of the systems.

Causal knowledge and causality are two of the key concepts in our approach. A causal knowledge is a type of knowledge, next to declarative, procedural, and relational knowledge. A causal knowledge is “a description of causal links among a set of factors … which provides a means for organizations … how best to achieve some goal” (Zack, 1999). The awareness of the theory of domain causality is the prerequisite to gain deep knowledge (i.e. causal dependencies) by analysis. This deep knowledge problem formulated in a good regulator theorem in cybernetics: “any regulator (if it conforms to the qualifications given) must model what it regulates” (Conant and Ashby, 1970). The Internal Model (IM) is a model of the subject domain. The Internal Model is created in advance using prior knowledge, i.e. IM is a predefined model, based on knowledge of the essential properties of the domain. In other words, IM is a causal knowledge model. The internal model first was articulated as the internal model principle of control theory in 1976 (Francis and Wonham, 1976).

Causality as a theoretical concept is discussed in Schurz and Gebharter (2016). According to Glymour (2004), Schurz and Gebharter (2016) causality should be understood as a theoretical concept (in analogy to the concept of force in Newtonian physics). A general theory of causation was developed by J. Pearl (2000, 2009), which underlies the theory of causal nets (TCN) developed in Spirtes et al. (2000), Pearl (2009). There are distinguished two notions of causality – type causality (so-called general causality) and actual causality (called specific causality) (Halpern, 2015). Actual causality focuses on particular events, while type causality is looking for common regularity (law). The understanding of causality in systems modelling can be quite different according to the nature of the knowledge used.

From the point of view of our approach, if the external modelling paradigm is applied, then external observation of some domain is a source of knowledge. Such way of modelling is the analysis of “the particular events”, and the actual causality discovered in that way. If we follow the internal modelling paradigm, then the regularity inherent to a type of domain (causality) is already perceived, this deep knowledge determines the final model.

The domain (or subject domain) here is a real world area – a content of what the learning object (LO) is about. The paper is on how to align the existing learning content and current (new) knowledge of the domain using the same causality driven viewpoint and the described models (frameworks).

Some examples of different domain types and causality. In enterprise modelling, causality is defined as dependencies of the enterprise goals upon components of the enterprise, such as processes, services, systems, etc. (Lagerström et al., 2009). Causality in the risk management is to be considered as the relation of the event directly to a risk situation (influence relation) (Sienou et al., 2008). Influence relation is a causality relation between causal events of risk situations. In physical system causality is a dependency between causes (impacts, events, faults, etc.) and changes of a system (state, transition, parameter values, etc.). The captured domain knowledge specified in the knowledge base is the internal domain model (e.g. the cause-consequence rules, equations, ontology, meta-model or other structures of causal knowledge) (Grundspenkis, 1998).

By the way of contract, data analytics (data mining, process mining) is a discovery of actual causality seeing that it is revealed by analysis of observable associations between elements of the domain using the Bayesian nets (causal graphs), conditional probabilistic dependencies of processes are counted (model content is data analysis based). Examples are causal nets and Bayesian nets (Glymour, 2004; Francis and Wonham, 1976). However, it should be recalled that conditional probabilistic dependencies (correlation) do not imply causation. In domain related theory based causality modelling the pre-condition is a deep knowledge of domain causality, e.g. exploring of the underlying theory of the subject domain, which defines a system of causal dependencies (regularities).

A learning object (LO) is “a collection of content items, practice items, and assessment items that are combined based on a single learning objective” (Sicilia et al., 2005). LO’s have granular structure (are modular units). Modules can be assembled together to form the study subject – study program, course, lessons, or concept (Convertini et al., 2006).

The learning object content predefines a set of capabilities to handle the subject domain, which was obtained by studies (Xu et al., 2005). This viewpoint is inherently fitting with the role of the LO metadata as “function-enabler” and instructional design based on knowledge objects in Merrill (2000). In other words, the validity of learning object content (i.e. validity of the domain knowledge) is a decisive factor. IT-supported LO content renewal (adaptation) using a causal knowledge is promising, rational considering the changing business requirements and their impact on educational content (Stuikys et al., 2017).

We are dealing with the subject domain summarized by the term “organizational system” and related to a wide range of industries, e.g. manufacturing, military, healthcare, energy, communication enterprises, and other. Such subject domain is a type of complex systems referred to as “enterprise” in systems engineering.

The concepts “management functional dependency” (MFD), “management transaction” (MT), and “elementary management cycle” (EMC) were introduced for enterprise causal modelling in information systems engineering (Gudas, 2012; Gudas and Lopata, 2016). Conceptual representation of MT and EMC can be considered as transactional workflows, which associated with conceptual models is as follows: Action Workflow model (Rusinkiewicz and Sheth, 1994; Medina-Mora et al., 1992), Deming’s PDCA cycle of business management (Deming, 1993), ITIL Framework (Persse, 2012), or the autonomic computing component (Kephart and Chess, 2003). The unified representation (normalization) of captured knowledge is a reasonable condition for comparison of distinct knowledge structures. Normalization in this approach is based on the usage of MT and EMC frameworks (Gudas and Valatavicius, 2017) as the pre-defined causal models of the subject domain.

This method is suitable for discovering causal relationships in domains that are characterized by internal circular causality – control and management, regulatory processes, self-regulation, renewal. These are not just organizational systems (i.e. enterprise) or cyber-social systems, but also biological systems (organisms), ecological systems, content of education systems and other complex systems.

A subject domain may be of different nature: real-world activities or documented content. A brief example of the real-world domain causality modelling for learning content renewal is presented. The normalized model of a subject domain reveals a set of MTs to be included in the learning content. There is also a detailed example of the causal modelling of the study content and content renewal process. The existing (old) learning content (LO, course, or study programme A) and the subject domain (i.e. content of advanced (best) study programme B) – both are reconstructed using the same frameworks MT and EMC. The mandatory normalization of the content (knowledge structures) occurs due to clustering of content items (dimensionality reduction). This normalization reveals the causality of the domain, helps the analyst to capture and compare knowledge structures. Then, the causal model of the existing learning content is compared to the causal model of the subject domain for adapting LO content.

The remainder of the paper is structured as follows: Section 2 reviews causal knowledge modelling concepts, stressing the causality driven paradigm. The learning content renewal assumptions are stated, and the key concepts of the causality driven modelling are discussed. Section 3 introduces the subject domain – an enterprise, and the causal knowledge structures: MT – a management transaction, and EMC – an elementary management cycle. A detailed model of the management transaction (MT) and a particular version of EMC for the enterprise modelling is laid out in Section 4. In Section 5, the knowledge normalization and renewal algorithms are described. A case study of the content renewal of two study subjects is laid out in Section 6. Traceability matrixes are introduced to specify the mismatch of the different knowledge objects and illustrated. Classification of the content discrepancies are introduced and illustrated. The LO content repository model is discussed. Conclusions in Section 7 summarize the key features of the causality driven approach to the subject domain (i.e. enterprise) modelling and knowledge discovery.

In this approach, the management functional dependency (MFD) is defined as a primary cause that creates a causal behaviour between activities of the subject domain (a chain of causal dependencies) defined as Gudas (2012), Gudas and Lopata (2016). MFD denotes the causal dependencies of some activities, processes, operational capabilities or organizational units required by particular business needs (i.e. strategic plan or actual business event). MFD is a real-world phenomenon, which could be revealed by managers or domain analysts (or not perceived in case of incompetence). The perceived MFD is visualized using the Management Transaction (MT) and the Elementary Management Cycle (EMC) frameworks (Gudas, 2012; Gudas and Lopata, 2016).

As an example, look at Porter’s Value Chain Model (VCM) (Porter, 1985) from the internal modelling viewpoint (Gudas, 2012). The transformed VCM view in Fig. 3 is a system of MFDs (MFD tsub11, MFD₁₂, …, MFD₅₅), where MFDij is a pair of interacting Support Activities (Administration (i=1) , HRM (i=2) , Finance Management (i=3) , Product and Technology Development (i=4) , Procurement (i=5) ) and Primary Activities (Inbound Logistics (j=1) , Operation (j=2) , Outbound Logistics (j=3) , Sales and Marketing (j=4) , Servicing (j=5) ).

The discovered by experts set {MFD11,MFD12,…,MFD55} is conceptualized from the viewpoint of information processing as the management transactions (MTs). By definition, MTij={Fi,Pj,(A,V)} includes two types of activities: Pj – an enterprise process, Fi – an enterprise management function which is linked together by a feedback loop comprising information flows A and V (Gudas, 2012). Therefore, an internal model of VCM is presented in Fig. 4 as a set of the management transactions {MT11,…MT55} . We provide concepts from other fields of engineering and science describing causal dependencies – analogs of MFD and MT, for instance:

The internal model of Porter’s VCM (in Fig. 4) consists of a set of MTs, which are clarified as follows:

Two level granularity of the domain causal knowledge is presented in Fig. 5:

The concept “the management transaction” (MT) is explored in this approach for the first step of LO content modelling – MT conceptualizes the management information transformations inherent for the subject domain.

The internal model of MT is an elementary management cycle (EMC) – a more detailed knowledge granule in Fig. 5 (Level 2).

EMC is considered as an essential (unified) building block of an enterprise as a self-managed system, i.e. EMC is a deep knowledge component (Gudas, 2012). The similar interpretation of the deep knowledge component (“a molecule”), which is defined as a transaction, is in enterprise ontology described in DEMO (Grundspenkis, 1998).

A particular version of EMC in Fig. 6 is developed for the needs of the knowledge-based business process modelling and software engineering in Gudas (2012), Gudas and Lopata (2016). The elementary management cycle (EMC) explicitly specifies the enterprise management transaction. EMC framework includes components as follows: a management Goal (Gw), a goal-driven management function Fj (G), enterprise process Pi (G), and connecting management information flows. Management function Fj(G) is a complex structure, which consists of a set of goal-driven procedural components IN, DP, DM, and RE (four types of the information transformation steps) and the management information flows (A, B, C, D, V) (data/knowledge), and S (impacts of goal G) (Gudas, 2012; Gudas and Lopata, 2016).

A semantics of EMC procedural components is as follows:

A semantics of the management information flows in Fig. 6 is as follows: A is the “process state attributes”, B is the “systematized raw data”, C is the “processed data”, D is the “management decisions”, and V is the “controls” of the Process Pi (G). The specific semantics of EMC procedural components (steps) and flows depends on the nature of the particular enterprise.

The causal knowledge analysis includes two steps: the first step is based on the MT framework (Fig. 5), and the next step is the more detailed analysis based on the EMC framework (Fig. 6).

The specific semantics of EMC procedural components (steps) and information flows depend on the nature of the subject domain. In the enterprise domain the EMC steps are defined as the clusters of knowledge (Gudas, 2012):

In the context of LO renewal issue, the semantics of the management information flows in Fig. 6 is as follows:

Unified representation (normalization) is the obligatory pre-condition for comparison of the different knowledge structures (contents): old knowledge (LO content) and captured new knowledge (current state of subject domain). Normalization of knowledge representation is achieved in two steps by mapping different knowledge structures to the same causal frameworks: (phase 1) content transformation to the MT framework (normalization) and next (phase 2) – normalized content detailing by transformation to EMC framework (see Fig. 5 and Fig. 6). The set of identified MT in the context of specialty studies means the main topics of the study (chunks of knowledge) which form the basis of specialty, provide required abilities. Process of the study subject content analysis and renewal is as follows:

The algorithm of LO content renewal includes two phases and is presented in Fig. 7 (phase 1), and in Fig. 8 (phase 2).

Phase 1 is MT-based knowledge acquisition and renewal of main topics of the study subject (renewal of the scope of study program or course). The phase 2 involves deepening of the knowledge captured in phase 1, when MT-based knowledge objects are decomposed to detailed EMC-based representation.

It is important to notice that subject domain may be of different nature: real-world activities or documented content. In both cases, the described method of knowledge discovery is suitable for transforming perceived knowledge into normalized specifications. The need to extract new knowledge and update the known content is constant, the reasons and the goals of the renewal may vary.

The following are actually possible and realistic:

a) Learning content needs to be updated because new types of phenomena (processes, transactions, technologies) are not taught in the study program or study subject.

b) The ministry of the country seeks to harmonize the similar (analogous) programs and their content at different universities.

c) The University seeks to bring it into line with the best study program in the field of science (leading university).

The normalized view of learning content makes it easy to identify the differences and similarities (discrepancies of knowledge) of the different study programs or courses.

Let’s take an example of the first case (a) are new types of phenomenon (processes, transactions, systems) linked by the 4th Industrial revolution, such as augmented reality, genome editing, smart materials, blockchain technology, 3-D printing and 4-D printing, autonomic systems, cyber-systems, Internet of Things and other (Gartner, 2018).

A new emerged knowledge needs to be described, and new content created using the method discussed above, i.e. the key topics are specified as management transactions (MT) (see Fig. 4), and then each key topic is specified in detail as EMC (see Fig. 5).

For example, normalized (existing) software engineering (SE) course covers key topics MT₁–MT₁₅. A normalized representation of the SE course is as follows: SE (old) = (MT₁, MT₂, …, MT₁₅). Performing problem domain analysis, the result is a normalized domain model: SE (new) = (MT₁, MT₂, …, MT₁₅, MT₁₆, MT₁₇, MT₁₈, MT₁₉), where the new needs to be identified and modelled as the management transactions (MTs) MT₁₆ – Block Chain Technology, MT₁₇–3-D Printing and 4-D Printing, MT₁₈ – Cyber Systems (CPS, CSS, CPSS), MT₁₉ – Internet of Things.

The second case (b) is described in more detail, a specific case from our experience, confirmed by real documents. An example of the normalized view of the learning contents of two study subjects (Study program SP1, and Study program SP2) presented in Table A.1 (Appendix A). The learning content of study programs is specified on the level of courses. Our assumption is that the subject domain of SP1 and SP2 is the same, and its causality has a theoretical basis described by EMC framework (see Fig. 6) in detail. Table A.1 illustrates the normalized view of the learning content of both study programs by mapping to EMC framework.

The EMC-based content normalization of the study program (SP2 – Software engineering, Bachelor of Informatics engineering, University B) depicted in Fig. 9. This normalized view reveals the particular goal G of SP2, and the clusters of learning content (i.e. clusters of courses) as follows: IN – courses on data/information capture (methods, techniques and tools) in SE, DP – courses on data processing methods, techniques and tools in SE, DM – courses on decision making methods, techniques and tools in SE, and RE – courses on decision implementation methods, techniques and tools in SE. The causal links (flows A, B, C and D) between the clusters of courses (Acquirements 1–4), and the impact S of goal G to the content of each cluster and causal link are defined. Suppose each course of the study program implemented by LO (one or more LOs) in the learning system.

The presented method considers other normalization step – the disclosure of the causality dependencies within the each cluster of courses of study program. In this case, the courses are specified at the level of lessons (topics). The causal modelling of courses should be done by analogy with the study program normalization. Note: the successful case is to assume the appropriate causality framework (specific to the course or cluster of courses) (see Fig. 1).

An example of the normalized content of course “B014 Fundamentals of Software Engineering” (Study program SP2) is presented in Table 1. The learning contents of course B014 correspond to the methodology of software engineering described in Sommerville (2016). For conciseness, Table 1 describes the content of EMC steps, the graphical representation corresponds to EMC representation in Fig. 5.

This normalized view reveals the particular goal G of course B104 focused on the software engineering of sociotechnical systems (Sommerville, 2016), the clusters of topics as follows: IN – topics on data/information capture (methods, techniques and tools), DP – topics on data processing (methods, techniques and tools), DM – topics on decision making (methods, techniques and tools) and RE – topics on decision implementation (methods, techniques and tools).

Content normalization helps to systematize course content, create causal relationships between lecture topics according to selected engineering methodology (development technology) stages.

The third case (b) is also possible for a qualitative leap if there is sufficient resources. In this case, the modelling process is similar to case(b); only the role of the subject area is the best study program in the world leading university. Further modelling, as in the case (b), does not have any fundamental differences.

Traceability matrixes specify the results of comparison – discrepancies of the old knowledge (the normalized LO content) and captured actual knowledge (current state of subject domain). Several options identified: 1) LO content is actual (S – sameness); 2) LO content should be restructured or supplemented by new knowledge items (C – change); 3) a new LO content item (a new knowledge) is required (N – new); 4) the exclusion of LO content item – LO no longer meets requirements (D – delete). Therefore, the traceability matrix elements indicate discrepancies, which can have values as follows: (1) R={S,C,N,D}.

The mismatch of knowledge structures could be checked on the two levels of granularity: a) using the MT-based knowledge clustering (MT-based normalization), and b) using the EMC-based clustering (EMC-based normalization).

An example of the traceability matrix using the MT-based SP content clustering is depicted in Table 2. The MT-based normalized learning content (from Table A.1, Appendix A) is evaluated in Table 2 on the top level of (knowledge) granularity, where the study program SP1 is to be improved, and is compared against study program SP2.

The most complicated part is the evaluation methods of the likelihood and difference of content. It can be done by experts or it can be supported by software tools using data science (knowledge discovery, data mining, text mining, domain ontologies) (Wowczko, 2015; Embley and Campbell, 1998; Ye and Chua, 2006; Zhai and Liu, 2005; Dou and Hu, 2012) or process mining methods (Bolt et al., 2018; Mannhardt et al., 2018).

In this example, experts have fixed the following changes to the study program SP1 in MT-based traceability matrix (Table 2): the purpose of SP1 need to be adjusted (goal G), capabilities provided (Process P), skills obtained, core knowledge of SP1 restructured or supplemented (F) and skills of SP1 provided. Another example of an expert evaluation is in Table 3.

The evaluation of content discrepancies using software tools is the most promising solution. Some attempts of using data mining methods for development of content (text) analysis software systems are discussed in Wowczko (2015), Embley and Campbell (1998), Ye and Chua (2006), Zhai and Liu (2005), Dou and Hu (2012). Data mining based method for the similar content (skills and vacancy) analysis is proposed in Wowczko (2015), the prototype tool is developed using RapidMiner and R. Ontology based methods Embley and Campbell (1998) use heuristics and domain ontologies to identify data, but the disadvantage is that the method requires the predefined object-relationship model.

The detection and evaluation of content discrepancies applying the process mining approach is more in line with the causal modelling principles as the reconstructed process model is based on current domain data (event log) (Bolt et al., 2018; Mannhardt et al., 2018). The proposed Guided Process Discovery (GPD) technique (Mannhardt et al., 2018) is a close causal modelling based PM. The core of the GPD technique is the relation between high-level activities and low-level events. GPD need to translate low-level events into high-level activities that are recognizable by stakeholders (Mannhardt et al., 2018). In case when the higher-level activities model is an adequate model of the domain causality (regularity inherent to some type of domain), we have causality-based process mining. In this case, a content assessment tool can be created on basis of GPD technique.

Here top-level event log corresponds to the EMC-based structure, consisting of few knowledge clusters (i.e. groups of courses). The content of each cluster (i.e. the course group) can also be arranged (i.e. normalized) according to known causal dependencies model. Thus getting a lower level event log. The evaluation of similarities and differences between process models provides initial data to the content discrepancies assessment. The method for comparing the two process models is described in Bolt et al. (2018). This process variant comparison approach can serve to content evaluation software development. Such tool would greatly help to process the knowledge that is structured into Table A.1 and obtain the values of the evaluation column.

The more detailed comparison of the study programs SP1 and SP2 (on the level of courses) can be specified using the EMC-based traceability matrix. Due to limited space of the article the column “Evaluation” in Table A.1 is added to specify the results of comparison. An example of the EMC-based traceability matrix of only one knowledge cluster “Raw data gathering and systematizing process” (the step IN of EMC) is presented in Table 3. The normalized learning content in Table 3 is evaluated on the level of courses.

The following required modifications of SP1 content have been fixed by experts: the course B101 Physics 1 is deleted (Delete), course B001 Mathematics 1 is clarified (Change) using the content of SP2 courses, and course B002 Mathematics 2 is replaced (New) by new content from SP2.

The LO repository model in Fig. 10 is designed by integrating the study subject requirements with the LO content repository. The structure of LO content repository is based on the causal knowledge models, i.e. it is based on the definitions of MT and EMC frameworks. The LO content repository prototype is developed using the IBM Rational RequisiteProTM tool.

Thus, the deep characteristics of subject domain are captured (note: in the case under consideration the domain type is an enterprise) using the causal knowledge frameworks MT and EMC. The LO knowledge repository is designed to store clusters of knowledge (matching MT and EMC elements): Goals (G), Processes (P), Functions (F), also internal elements of F structure: steps Interpretation (IN), Data Processing (DP), Decision Making (DM), and Decision Realization (RE), Flows (S), Flows (I). The LO content repository is integrated with the repository of study subject (study program, course) requirements.

The causality driven modelling approach is applied for the domain knowledge discovery and learning object content analysis. The theory of the subject domain causal dependencies is the prerequisite to gain deep knowledge by analyst. The domain here is a real world area – a content of what the LO is about – and is considered as a complex system. The paper is on how to align the existing learning content and current (new) knowledge of the domain using the described models (frameworks).

The provided method is suitable for discovering causal relationships in domains that are characterized by internal circular processes of control and/or management, self-regulation, adaptation. Such circular causality is characteristic not just of organizational systems (i.e. enterprise) or cyber-social systems, but also common to biological systems (organisms), ecological systems, and other complex systems.

Two level granularity of modelling is introduced. The causal model of subject domain (content of what LO is about) is conceptualized using MT and EMC frameworks in two steps. The top-level causal dependencies are revealed and visualized as a set of the management transactions. Secondly, a deep knowledge is captured using the elementary management cycle (EMC) framework for decomposition of the identified set of MT’s. These frameworks are used here to transformation (normalization) and renewal (adaptation) of the learning objects (study program content).

The normalization of LO content is used for clustering of content items. Normalization is obtained by mapping LO content items onto the causal knowledge framework. Such normalization of knowledge structure is valid only when the relevant causal knowledge frameworks are used, e.g. causality models are inherent to the subject domain. Provided algorithms describe the renewal process of LO content in two phases. Phase 1 reveals the scope of causal knowledge within the subject domain. Phase 1 of the knowledge capturing is based on the management transaction (MT) framework. Phase 2 involves deepening of the MT-based knowledge using the EMC framework. Phase 2 of content normalization is based on the EMC framework, which represents an internal model of MT.

A case study of learning content renewal showed that the causal modelling is useful for clustering the knowledge, discovering the logical sequences, systematic comparison of the different knowledge objects. The comparison of two knowledge structures is carried out at different levels of detail. We used two levels of granularity: a top level is the MT-based normalization, and a more detailed level – using the EMC-based normalization. An example of the study programs (learning content) causal modelling is presented. Traceability matrixes have been developed to assess discrepancies between different knowledge structures and to compare study programs used here.

The main outcome is the effectiveness of discovering deep knowledge in the subject domain, but only when the domain causality frameworks are theory based. The presented causal models can be applied to modelling information transactions of any type of goal-driven complex systems (characterized by internal circular causality). One of these types of complex systems is enterprise (organizational system), for which MT and EMC models have been developed. Causal models (modified) can also be applied to the analysis of educational content by teaching the deep knowledge (domain causality) of different subject domains (e.g. eco-systems, bio-systems, organizational systems, economical systems, etc.).

This causal modelling method allows you to effectively update complex knowledge structures (training content) using software tools. The creation of such tools is a development perspective for knowledge-based e-learning systems. The causality driven knowledge modelling is suitable for analysis of various domains, and not only for the educational content analysis. It may be the objective of further works.