<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Formation and Application of Transformation Knowledge within Dynamic Enterprise Architecture</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>ny Zin</string-name>
          <email>E@Zinder.ru</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>FOSTAS Foundation</institution>
          ,
          <addr-line>Moscow, Russian Federation</addr-line>
        </aff>
      </contrib-group>
      <abstract>
        <p>The study presents the current state of the discipline "Enterprise Architecture" (EA) in the context of digital transformations and architectural models for full-fledged work with these transformations. It is shown that the search for new EA capabilities is associated not with the task of creating EA artifacts but with supporting managers in managing enterprise transformations through the use of EA capabilities. The possibilities of using various EA approaches to reflect the life history of an enterprise as one of the most critical factors in the dynamics of enterprises are analyzed. The approaches "3D-enterprise" and its extension "nD-enterprise", which increase the expressive power of using the resources of time in the life history of the enterprise, are highlighted. Modeling concurrent flows of change is one of the useful properties for managing transformations. The article describes the formation of a scheme of factual, procedural, conceptual, and metacognitive knowledge as a part of EA which includes knowledge not only about the states of the enterprise, but also about the methods and procedures for performing transformations of these states with a reference to the dimension of time. The study shows the use of "nD-enterprise" for solving problems of transformations management of the enterprise based on the indicated knowledge of EA. The actual tasks of EA are considered: the creation and use of the capabilities of the EA for managing the transformation of the enterprise, the flexible but stable implementation of the enterprise strategy, the support of the integrity of EA and some others.</p>
      </abstract>
      <kwd-group>
        <kwd>Enterprise dynamics</kwd>
        <kwd>Enterprise architecture knowledge</kwd>
        <kwd>Enterprise transformation</kwd>
        <kwd>3D-Enterprise</kwd>
        <kwd>nD-Enterprise</kwd>
        <kwd>Architectural model</kwd>
        <kwd>Dimension of time</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>1.1</p>
    </sec>
    <sec id="sec-2">
      <title>Introduction and context analysis</title>
      <sec id="sec-2-1">
        <title>Background. An overview of the situation</title>
        <p>High enterprises variability requires significant abilities of EA in the sphere of
seeking and justification of decisions about introducing changes in the enterprise
arrangement and these decisions implementation control. At the same time, dealing with
changes should consider not only the change drivers generated by the environment
and inner enterprise intentions, but also particularities and limitations of real
enterprise structure. Thereby the primary attention of this paper is focused on complex and</p>
        <p>large-scale changes of an enterprise as a system which will be denoted by the word
‘transformation’. Local changes in the case of changing something in EA are also
covered by the examined methods.</p>
        <p>
          It is helpful to consider EA and its models in the context of general turbulence of
understanding and of rational application evaluation of both informational
technologies and EA discipline. Several years ago, global appeals to across-the-board digital
transformation along with cloud computing and agile style propaganda motivated
many authors to claim that EA paradigm requires cardinal replacement. Even “EA
father”, J. Zachman, caved in to this pressure in the publication [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ] as his EA
framework was under sharp criticism (though in the author’s opinion, this criticism was
caused by a too primitive interpretation of Zachman’s suggestions).
        </p>
        <p>
          However, not long after, EA discussions became constructive again. The author of
this paper conducted the analysis of EA development stating [
          <xref ref-type="bibr" rid="ref2">2</xref>
          ] that we deal not with
the radical replacement but with the permanent expanding of EA. This conclusion is
being justified by growing attention and the number of publications about the
necessity and new methods of EA for solving current problems of an enterprise dynamics,
in particular, using Zachman Framework (ZF) [
          <xref ref-type="bibr" rid="ref3">3</xref>
          ] and its later versions.
        </p>
        <p>One particularity of the moment is the contrariety of classical requirements for EA
and the way of practical implementation of these requirements. Zachman suggested
regarding EA as the means of accumulation of knowledge about an enterprise, but
despite some exceptions, sustainable knowledge forming and management is not
observed. It was also suggested that EA should reflect an enterprise change. However,
although changes happen with the passage of time, using full value dimension of time
in EA is rather an exception than a rule.
1.2</p>
      </sec>
      <sec id="sec-2-2">
        <title>Recent studies and EA tasks</title>
        <p>
          It is specified in [
          <xref ref-type="bibr" rid="ref4 ref5 ref6">4-6</xref>
          ] that introducing EA discipline in organizations is expanding. At
the same time, technological destructors and their impact persistently stimulate
largescope transformations in business ecosystems, business units and functions. In these
conditions, EA research is still often limited by abilities of ordering the concrete
organization resources. However, it is highlighted in the works [
          <xref ref-type="bibr" rid="ref4 ref6">4,6</xref>
          ] that EA is not just
needed as such, but as an ability to quickly solve the problems of enterprise change
management and transformation governance and not to just accumulate artifacts.
        </p>
        <p>
          The papers [
          <xref ref-type="bibr" rid="ref7 ref8 ref9">7-9</xref>
          ] also indicate EA benefits especially in the area of an enterprise
dynamics and its information systems (IS) support. It is recommended in [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ] to
provide profound understanding of key enterprise components dynamic behaviour and
formal control of architectural descriptions integrity by means of EA. The studies
consider characteristics of a model of an enterprise endeavoring to “change business”
in contradistinction to its routine running, and ZF by J. Zachman serves as a
framework. The study [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ] also builds on ZF and aims at meaty support of the strategic
management of small and medium-sized enterprises starting with their business
architecture. It should be noted that despite former critical comments many researchers and
practices keep using ZF as the conceptual basis.
        </p>
        <p>
          While considering the corporate IT-architecture, advantage of EA for supporting
dynamics looks more evident, especially for IT-infrastructure. Thus, EA examined in
[
          <xref ref-type="bibr" rid="ref9">9</xref>
          ] is intended for dynamic redefining of optimal cloud allocation of applications and
data.
        </p>
        <p>
          The paper [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ] is useful in that it indicates an inadequacy of applying any
“extreme” approach in EA. It is noted that AP is often at a point of collision, for example,
between proponents of agile approaches and adherents of “nonagile”, “conservative”
AP practices, but both of these approaches are just radical simplifications of the real
circumstances of the organization. Practice, however, more often requires not one
"extreme" ideology, but a set of different approaches meeting different urgent tasks of
the enterprise. At the same time, it is indicated in [
          <xref ref-type="bibr" rid="ref11 ref12">11,12</xref>
          ], as in the publications noted
above, that the structures of the EA remain mostly informal in nature, and the
interference from the complexity of the enterprise architecture is especially strong with the
growth of enterprise variability.
        </p>
        <p>
          At the same time, there are works aimed at radically more complex and dynamic
architectures. So, in [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ] the dynamics is extended not only to enterprises, but also to
units of its transformable cyber-physical products even after the release of the latter.
Note that this can lead to attempts to simulate the dynamics of not only EA as such,
but also all the changing elements of reality included in the enterprise environment,
which can be quite redundant in practice. Note also that the framework [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ] is
intrinsically multidimensional; it defines ten architectural dimensions, but there is no time
dimension among them. At the same time, the authors admit that many real situations
are only intended for study yet.
        </p>
        <p>
          The paper [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ] classifies schools and methods of EA and indicates the qualitative
differences of EA at the current stage of "cognitive revolution", and at the stages of
previous "revolutions". To reflect the dynamics, the authors, on the one hand, use a
conservative division of work with EA into phases, and on the other hand, replace the
analysis of the classical EA transition from "as-is" to " to-be " by so-called
continuously conducted analysis. Note that this having no alternative replacement seems too
“revolutionary”, and that even in the radical work [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ] it is reported that the proposed
suggestions do not replace, but expand existing architectural schemes and methods.
        </p>
        <p>
          It is also essential to note a substantially updated revision of the standard
fundamental for EA [
          <xref ref-type="bibr" rid="ref15">15</xref>
          ] that has recently become operative, where the definitions and
requirements for EA and for modelling the enterprise and its EA, including the use of
elements of the GERAM approach, are confirmed and refined.
        </p>
        <p>As for EA as a repository of enterprise knowledge, the occurring attempts to
consider EA as a discipline of knowledge management or as a means of transforming
knowledge in the work of architects indicate the insufficient fullness and readiness of
the EA content [16] and low readiness of many specialists [17] to fully use EA as an
important system of enterprise knowledge management. J. Zachman's thesis about EA
as a means of accumulating knowledge is confirmed [18], but it is insufficiently
developed, as is the formation of the normative ordering of this knowledge.</p>
        <p>The described context substantiates the direction of this work which proposes a
natural order of knowledge categories in EA focused on their use in the tasks of
enterprise transformation. The rationality of the proposed order is justified by
demonstrating the way of its application for solving current problems of enterprise
transformation.
2
2.1</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>Methodology and structure of the rest of the paper</title>
      <sec id="sec-3-1">
        <title>Used interpretations of concepts and their interconnections</title>
        <p>Understanding of dynamics is used in the article as changes in any characteristics of
an enterprise under the influence of external or internal factors ("drivers"). In EA,
changes are considered at the architectural level of description, that is, at the level that
is sufficiently specific to take into account the specifics of the enterprise, but which is
possibly partly aggregated and generalized. The level of aggregation and
generalization of EA entities is determined by the enterprise itself. This level is supposed to
provide the enterprise with the abilities for effective achievement of its goals, but
retains the necessary freedom for engineering decisions for EA implementation.</p>
        <p>Transformation means complex changes:
 of material and ideal objects of the enterprise; the changes which are understood by
the people of the enterprise, and, on this basis, explicitly accepted by the
enterprise;
 leading the enterprise to a new qualitative state which includes visible changes in
the enterprise business model proposed to achieve the declared goals;
 having speed and volume which are sufficient to be included in the sphere of
meaningful conceptual and architectural design.</p>
        <p>With this in mind, the complete methodology of the study included the following
steps:
1. analysis and fixation of constraints of transformation time display, first of all, in
the approaches of ZF, GERAM and ISO 15704;
2. determining requirements of real enterprises life stories for the full dimension of
time in the approach of 3D/nD-enterprise;
3. definition of categories of knowledge about the enterprise, their place in the
models of its architecture and the role in transformations placed in the EA itself;
4. definitions and formalized representations of parallel flows of changes
(transformations, their parts) in enterprises;
5. eliciting modern problems of managing EA changes including those described in
the publications given in subsection 1.2;
6. consideration of approaches to solving these problems based on the approach of
3D/nD-enterprise and knowledge of EA structured within its framework.
The results of steps 1, 2, and partly of step 4 were described in [19,20] but are also
indicated here.
2.2</p>
      </sec>
      <sec id="sec-3-2">
        <title>Structure of the rest of the paper</title>
        <p>Section 3 reflects the limitations of the main approaches that formed the EA discipline
in part of the dimension of the time of enterprise changes. Section 4 specifies the
main features of the 3D/nD-enterprise approach, introduces definitions of the
knowledge categories about transformations associated with EA, and specifies some
EA entities required for transformation management. In Section 5, the approach
described in section 4 is discussed through the prism of current EA problems and tasks.
In Conclusion, the result of organization of EA knowledge in the 3D/nD-enterprise
approach is formulated and the directions for further research and their application are
determined.
3</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>Limitations of the approaches that formed the dimension of time in EA</title>
      <p>3.1</p>
      <sec id="sec-4-1">
        <title>Architectural schemes and models of explicit work with time</title>
        <p>At the end of the last decade of the 20th century, the first group of approaches,
models, and standards was proposed explicitly working with the dimension of the time of
enterprise transformation [19-22]. Also in an explicit form, the ISO 15704: 2000
standard [22] fixed the term "life history" of an enterprise which defines an ordered
description of a set of enterprise change events tied to a time axis and including many
life cycles of transformations. However, the introduction of the dimension of time in
these approaches provided different, often insufficient levels of architectural
capabilities which will be discussed below.</p>
        <p>Much later, a second group of approaches and models emerged suggesting
different tools for describing temporal aspects. In works [23,24], the extension of DoDAF
framework with universal descriptors of temporal aspects was considered for using
them in different EA entities. In [25,26] temporal aspects were proposed for the
retrospective analysis of changes in the enterprise performance indicators, as well as for
searching and correcting incorrectness in the descriptors of the enterprise's activities.
However, these proposals cannot be considered widely spread. It can be assumed that
in the case of [23,24], the path from the entities in formal ontologies reflecting
primitive temporal concepts to the practical use of the dimension of time by economists,
market experts, and other enterprise professionals involved in EA development is too
long. In the case of [25,26], each of the proposed approaches aims at solving an
important, but a single particular problem. The foregoing is the reason why the abilities
of the first group of approaches, models, and standards [19-22] will be considered
here, especially as they are actualized nowadays.
3.2</p>
      </sec>
      <sec id="sec-4-2">
        <title>Limitations of J. Zachman's framework, GERAM methodology, and ISO 15704</title>
        <p>
          The ZF framework and Zachman's rules are often interpreted in a simplistic way, as
almost mechanical filling the rows of cells in the corresponding table strictly from top
to bottom [
          <xref ref-type="bibr" rid="ref3">3</xref>
          ]. However, this interpretation contradicts to what Zachman wrote later
about his framework application in practice. Besides, the Zachman’s framework
remains, as shown in Section 1, a meaningful approach to structuring and discussing an
enterprise representation, with the ability to move easily from integrated EA models
to an in-depth consideration of partial models, aspects, and viewpoints.
        </p>
        <p>Despite its value, this framework has serious limitations and contradictions. The
transformation time of the enterprise is represented practically by only two states
("asis" and "to-be") and the sequence of the EA design phases implicitly related to the
time axis, but only within one time slice of EA. A detailed discussion of the
shortcomings of time representation in ZF can be found in [27 part 1].</p>
        <p>
          The GERAM framework [21] is more accomplished due to the explicit use of the
time axis as the dimension to which the events of the enterprise life history are
attributed, which is also included in ISO 15704 [22]. However, this time axis is
considered mostly as an illustration and is not graded as needed by architects in particular
cases, but only by reflecting on it the standardized phases of the EA transformation
life cycle. Thus, the {Views, Life-cycle phases} plane of the GERAM framework
carries limitations similar to those of ZF. These limitations are also inherited by ISO
15704 standard in all editions up to [
          <xref ref-type="bibr" rid="ref15">15</xref>
          ].
4
        </p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>3D/nD Enterprise Approach and Model</title>
      <p>The limitations and contradictions of the Zachman Framework described above
prompted the author of this work to propose a more developed approach and
framework to reflect the time of enterprise transformations in the late 1990s. After several
discussions and experimental applications in 1997-1999, this approach description
was published in 2000 in the article [19] and, in a more complete form, on the
resource "CIT-Forum" as the article "3D-enterprise - a model of the strategy of a
transforming system" [20]. These publications included the possibility of increasing the
number of dimensions of the framework which gives rise to the nD-enterprise
approach. The main abilities of using the 3D/nD model are also described in [27 part 1].
For this reason, the main features of this approach will be only briefly named below,
and the essence and principles of knowledge organization in EA, related to the time of
its transformations, will be presented in more detail.
4.1</p>
      <sec id="sec-5-1">
        <title>3D/nD-enterprise</title>
        <p>In the 3D/nD approach, EA is represented by a set of states of the EA model ordered
by reference to the full-fledged dimension of time. Distinctive features of the
3D/nDenterprise approach are:
 Description of not two, but many states of an enterprise in time as a set of
logically integral sets of its cell models (these cell models are similar to cells in the ZF)
for different moments and/or intervals of time by explicitly introducing the axis of
astronomical time.
 Reflection of the enterprises dynamics for different echelons of management at
different time horizons by splitting the dimension and axis of time into two or three
sub-axes on which states and events of short-term, medium-term and long-term
plans and actions respectively are located.
 Reflection of real multithreading of making changes to EA in which different
working parts of the architecture (WP - working parts of the EA, EAWP) are
changing each with their own speeds and, conditionally, in their own streams of
time, partially in parallel - synchronously or asynchronously - with other parts of
the architecture, but while maintaining the ability to synchronize actions and
control the integrity of the EA content.
 The approach openness, in particular, to changing the set of project phases or
stages of the enterprise development program and to possibilities of expanding the
number of dimensions by adding important for managing the running of the
architectural process and the development of the enterprise as a whole. Examples of
such dimensions are "Generalization-concretization", "Specialization and
competence of personnel" (including subject experts, IS developers and enterprise
architects), "Methods and tools for modeling", "Technological units and agents"
(including people, industrial robots, software agents), etc.</p>
        <p>One of specific problems solved due to the described differences is the use of
forecasts fragments of EA state in the long-term horizon to form the EA state in the
shortterm horizon. The purpose of this is to increase the validity and sustainability of
architectural solutions in general. An illustrative scheme for solving this problem is given
in [27 part 2, Fig. 2]. The dimensions of nD-models can support work with investment
support for the development of an enterprise (for example, in the form of analysis of
an investment projects portfolio), with an analysis of the effectiveness of the proposed
IS and IT blocks, for example, determining the degree of usefulness of specific
services to ensure the work of an end user or services of other levels.</p>
        <p>For nD-models, the requirement was introduced to define the links of each
modelcell with the nearest cells reflecting the previous and future states of the architecture
component to reflect the actions and the overall progress of the transformation. On
this basis, we can talk about the change in EA in time both at a large-aggregated level
of phases and stages of development and at the micro level of changes in particular
elements of EA.
4.2</p>
      </sec>
      <sec id="sec-5-2">
        <title>Formation of knowledge components categories about transformations for including them into models of 3D/nD-enterprise</title>
        <p>The definition of the EA knowledge components is given using a number of working
architecture constructs.</p>
        <p>The state of the EA model at the moment t(n) is considered as an integrated model
EAM(t(n))={cemi,j,t i =1 ... I, j=1 ... J, t=t(n)}. Here cemi,j,t is an analogue of a primitive
model or cell in ZF (row and column intersection) or the intersection of the life cycle
phase and aspect on the Vies axis in GERAM. The main differences in 3D/nD are the
ability to flexibly define a set of such cells and assign time points t(n).</p>
        <p>The components of the EA knowledge with the purpose of their application in the
dynamic EA transformation are associated with the cell models cemi,j,t, with the
procedures for transforming the model cell from one state to another, with the procedures
for monitoring the integrity of the entire EA model or the EAWP selected from it, as
well as procedures for solving specific problems of enterprise transformation.
Considering the amended categorization of Bloom [28], as well as the ways of applying
knowledge in the processes of enterprise transformation, the following categories
stand out as the main ones from all EA knowledge.</p>
        <p>Specific knowledge for cemi,j,t(n):
 • model cemdi,j,t(n) of factual knowledge - a description of the representation of EA
or EAWP state fragment reflected by this model-cell;
 • model cemp-Ti,j,t(n) of procedural knowledge - a prescriptive model of
transformation of cemi,j,t(n) into the next time-controlled state EAM(t(n+1));
 • model cemp-Ci,j,t(n) of procedural knowledge - a prescriptive model for controlling
the correctness of connections cemi,j,t(n) with adjacent models-cells within the point
of view j, aspect i, time stream in which a specific transformation is performed.</p>
        <p>
          Conceptual (generalized according to GERAM) knowledge related to cemi,j,t:
 generalized for t(n) model-description cemdi,j,t(0) for representing the admissible
states of the EA and EAWP, reflected in the model cemi,j,t in its dynamics (for
example, the general procedure for choosing and describing the data location scheme
in the corporate network of the enterprise);
 generalized for t(n) prescriptive model cemp-Ti,j,t(0) for representing the rules of
possible transformations cemi,j,t from the state t(n) to the next states in time;
 generalized for t(n) prescriptive model cemp-Ci,j,t(0) for checking the correctness
of connections cemi,j,t with adjacent cell models within the selected point of view j,
aspect i, and time flow (for example, a set of unified procedures for calculating the
truth of compliance with the rules of connectivity of elements in cell models and
between them);
 similarly, generalized for t(n) prescriptive models cemp-Ei,j,t(0) for solving other
possible dynamic problems of enterprise development management (for example,
in the style of dynamic capabilities of EA [
          <xref ref-type="bibr" rid="ref3">3</xref>
          ] and as competencies management).
For integrated models and different EAWPs, similar units of knowledge are formed,
associated with subsets composed of cemi,j,t(n), covered by the corresponding
integrated model, a specific EAWP, or the entire EA model. The category of metacognitive
knowledge is used to expand the amount of EA knowledge. Models of such
knowledge can be related with any primitive or integrated model of EA through their
specific subject and are not described here.
        </p>
        <p>One EA transformation stream is defined as the union of elementary
transformation streams of all cell models affected by one planned transformation and related
to one EAWP.</p>
        <p>The elementary transformation stream is defined as a set {cemi,j,t} ordered by t in
which i and j are constants that determine the occurrence of cemi,j,t in one EAWP, and
the rule t(m) ≤ t ≤ t(m+k) holds, where [t(m);t(m+k)] is the minimum time interval
that contains the given stream in one definite transformation.</p>
        <p>Multithreading is defined as the possibility of partially parallel execution of
transformation streams for one or different EAWPs.
5
5.1</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>Discussion of actual EA problems and conclusion</title>
      <sec id="sec-6-1">
        <title>Examples of current EA problems and discussion of their solutions based on EA knowledge</title>
        <p>The publications discussed in Sections 1 and 3 pose a number of partly classical and
partly new problems and tasks related to enterprise transformation management for
EA. These include the following:
 • support for flexible strategic management of enterprises;
 • support for the dynamic capabilities of EA as its transforming abilities;
 • dynamic search and analysis of incorrectness in the EA model;
 • support for the dynamic digital transformation of the enterprise, taking into
account the heterogeneous values systems of the stakeholders;
 • building EA providing dynamic changes and consistent use of actual working
knowledge of different contents and forms by individuals as actors of different
types.</p>
        <p>The methods of solving the first three problems are discussed in more detail below,
and general features associated with the other two tasks are commented. The issues of
support for extreme options of an enterprise behavior are considered separately.
5.2</p>
      </sec>
      <sec id="sec-6-2">
        <title>Supporting flexible strategic enterprise management</title>
        <p>This problem can be divided into two separate problems, and the first one is to apply
the knowledge of EA to form an architecture that implements a mission and a new
strategy. The principles of solving this problem in the 3D/nD-enterprise approach are
stated in [19,20,27 part 2]and are indicated here in subsection 4.1. The second one is
the use of EA methods for flexible but sustainable management of the implementation
of the formed strategy. The scheme of such management, based on separation and
linking of models and facts of strategy and tactical actions, is proposed in [29]. This
scheme itself and the method of its use refer to the generalized prescriptive
knowledge about EAWP or EA in general.
5.3</p>
      </sec>
      <sec id="sec-6-3">
        <title>Support for dynamic EA capabilities as its transforming abilities</title>
        <p>
          It is shown in [
          <xref ref-type="bibr" rid="ref3 ref5">3,5</xref>
          ] that it is important to move away from the interpretation of EA as
a method of creating its artifacts to dynamic decision making by managers based on
EA discipline. To this end, the “dynamic capabilities of the EA”, including
procedures and actions defined for managers in order to support their decision-making
based on EA are explored. The solution to this problem in the 3D/nD-enterprise
approach can be based on combining prescriptive knowledge (like cempi,j,t(n) models)
and other required related knowledge in EA with knowledge elements in the
normalized competency model [30]. Then the following is assumed:
 inclusion in the nD-enterprise scheme of the dimension of managers abilities and
abilities of the enterprise as a whole according to the rules [30], and the
prescriptive knowledge of the EA, aimed at fast involving managers in the work to
implement the dynamics of the enterprise;
 inclusion of relationships in the descriptions of potentially affected by the
transformation of architectural elements and prescriptive knowledge of EA, aimed at
solving a specific type of problem or task (for example, the problem of assessing
the cost of enterprise transformations, the task of detecting the redundancy of
stored data or organizational structures, etc.).
5.4
        </p>
      </sec>
      <sec id="sec-6-4">
        <title>Dynamic search for logical incorrectness and control of the EA model integrity</title>
        <p>The logical integrity of EA or EAWP models control at the time t(n) can be
performed according to different control policies. An example of the main idea of using
the EA knowledge for such control is:
 calculation of the truth of the compliance with the mutual correspondence rules at
the level of consistency of cells in EAWP provided by the models cemp-Ci,j,t(0 and
cemp-Ci,j,t(n) (possibly also{cemp-Ci,j,t(k) k=n-1,n,n+1});
 expansion of these calculations to cell-models included in EA and EAWP as a
subset of EAMWP(t), selected from the set EAM(t1,tN) of all cell-models {cemi,j,t }
for the moments t(n), t(n +1) and possibly for later ones.
5.5</p>
      </sec>
      <sec id="sec-6-5">
        <title>General possibilities for solving two other problems</title>
      </sec>
      <sec id="sec-6-6">
        <title>The need to support the dynamic use of working knowledge of different content</title>
        <p>
          and forms. Many works, including [
          <xref ref-type="bibr" rid="ref13 ref14">13,14</xref>
          ], indicate the need for semantic support for
different actor types in part of working with heterogeneous information. Control of
EA representations by means of combined ontologies and logical inference
(reasoning) is often considered. In this regard, it is necessary to point out the conclusions of
the works [31,32] about barriers on the way of combining ontologies of different
authors or formulated for different situations. At the same time, [31] shows the direction
of solving such problems by applying the proposed principles of dynamic enterprise
knowledge management and multimodal knowledge storages development. Such
architecture is quite compatible with the nD-enterprise approach in which there are no
restrictions on the means of description or the level of knowledge formalization.
The need to support the dynamic integration of different parties of the enterprise
ecosystem based on the axiological approach. The digital transformation of
enterprises based on values is considered important in many works. Naturally, the question
arises about the “digitalization of values”. However, axiology is a very broad and
"shaky" field for digitalization; therefore, it is better to carry out digitalization of
values with a focus on solving specific problems. An example of such a problem is the
search in the ecosystem of the enterprise and beyond those parties that are compatible
with the enterprise needs and values [33]. To solve this and a number of other
problems, the model of the space of digital values representations has been developed in
[34]. Such a model can be included in the nD-enterprise by adding to nD the
necessary dimensions of the values proposed in [34].
5.6
        </p>
      </sec>
      <sec id="sec-6-7">
        <title>Support for extreme versions of enterprise behavior</title>
        <p>
          The work [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ] mentioned above expands EA dynamics not only to the enterprise, but
also to the units of production which, similarly to assemblies of operating systems,
can be modified at any moment t after their release. Assuming that such an upgrade
must also be accompanied by a change in the enterprise, the architect can plan
changes that are not only broad in the composition of objects, but also continuous. Taking
into account the processing claims of products consumers, the enterprise will have to
support a variety of product architectures and enterprise states. The EA knowledge
structures fundamentally described in Section 4 and approaches to knowledge
application discussed in this section do not show any barriers to support such extreme
decisions. Still, it can be assumed that for most enterprises this may be quite redundant
in practice.
        </p>
        <p>In this regard, in this work, the concept of so-called "Continuous Architecture"
from [35] is not applied to the entire life history of the enterprise, but is deliberately
limited to EAWP and selected time intervals [t(n);t(n+k)]. Such a solution is aimed at
more reliable control of EA integrity with the planned allocation of control points in
time for checking and ensuring formal and meaningful criteria for EA integrity.
6</p>
      </sec>
    </sec>
    <sec id="sec-7">
      <title>Conclusion</title>
      <p>Analysis of current works in the field of enterprise architecture confirmed the
usefulness of EA as a discipline and showed the need for its development for the conditions
of increasing variability of enterprises and their environment. This need is associated
with solving old and new types of enterprise transformation problems. For the
specified conditions, this work shows the effectiveness of introducing the dimension of
time, proposed earlier in the 3D/nD-enterprise approach. For this approach, the
formation of a schema of factual, procedural, conceptual, and metacognitive knowledge
of EA is shown. This includes knowledge not only about the states of the enterprise,
but also about the methods and procedures for performing these states transformations
with an interrelation to the dimension of time. Besides, ways of using this knowledge
for solving modern problems of enterprise transformation are demonstrated.</p>
      <p>The main directions of further research and development of the 3D/nD-enterprise
approach and work with knowledge about transformations should consider embedding
rich knowledge management functions in architectural processes and in EA tools, in
particular, search and selection of EA knowledge management tools, taking into
account the multimodal architecture of the knowledge previously proposed in [31].
16. Schweers, F.: The role of enterprise architecture in knowledge conversion. Via Nova
Architectura. Internet resource
http://vianovaarchitectura.nl/page/the-role-of-enterprisearchitecture-in-knowledge-conversion, last accessed 2020/09/30 (2009)
17. Evernden, R.: EA as a Knowledge management discipline. Orbussoftware-com (2014).
Internet resource
https://www.orbussoftware.com/blog/enterprise-architecture-as-aknowledge-management-discipline/#, last accessed 2020/09/30.
18. Wibowo, A.: Knowledge management support for enterprise erchitecture development.
International Journal of Knowledge Engineering, Vol. 3, No. 1, June 2017. Pp. 25-31. Doi:
10.18178/ijke.2017.3.1.082 25 (2017)
19. Zinder, E.Z: "3D-enterprise" - a model of a transforming system (in Russian). Chief
Information Officer, № 4 (2000).
20. Zinder, E.Z: "3D-enterprise" - a model of a strategy of transforming system (in Russian).</p>
      <p>CIT-Forum (2000). URL: http://citforum.ru/seminars/cbd2000/cbd_day2_01.shtml, last
accessed 2020/09/30.
21. Generalised enterprise reference architecture and methodology. IFIP—IFAC Task force on
architectures for enterprise integration GERAM, Version 1.6.3 (1999).
22. Industrial automation systems — Requirements for enterprise-reference architectures and
methodologies. ISO 15704:2000 (2000).
23. Hause, M. and Kihlstrom, L.-O.: Architecting in the fourth dimension temporal aspects of
DoDAF. INCOSE International Symposium, June 2013, 23(1). Journal of Battlefield
Technology (2014). DOI: 10.1002/j.2334-5837.2013.tb03097.x
24. Feodoroff, R.: Intentional Enterprise Architecture - Temporal safety justifications over</p>
      <p>TOGAF/DoDAF models. (2015). DOI: 10.13140/RG.2.1.1647.1521
25. Bhat, M., Reschenhofer, T., Matthes, F.: A Model-based approach for retrospective
analysis of enterprise architecture metrics. In Proceedings of the International Conference on
Enterprise Information Systems, S. Hammoudi et al. (Eds.): ICEIS 2015, LNBIP 241, pp.
595–611 (2015).
26. Xavier, A., Vasconcelos, A., Sousa, P.: Rules for validation of models of enterprise
architecture - rules of checking and correction of temporal inconsistencies among elements of
the enterprise architecture. In Proceedings of the 19th Int. Conf. on Enterprise Information
Systems (ICEIS 2017), Volume 3, pages 337-344 (2017)
27. Zinder, E.: Enterprise architecture in the context of business reengineering (in Russian).</p>
      <p>Intelligent Enterprise, Part 1 in №4(180), Part 2 in №7(183) (2008).
28. Anderson, L. W., &amp; Krathwohl, D. R.: A taxonomy for learning, teaching, and assessing: a
revision of Bloom's taxonomy of educational objectives. New York: Addison Wesley
Longman (2001).
29. Zinder, E.Z.: Managing the balance of strategy and tactics in digital enterprises and
electronic governments implementation (in Russian). Information Society, No. 2, pp. 9-22
(2017).
30. Zinder, E.Z. and Yunatova, I.G.: Conceptual framework, models, and methods of
knowledge acquisition and management for competency management in various areas. In:
Proceedings of the 4th International Conference on Knowledge Engineering and the
Semantic Web (KESW 2013). St.Petersburg, Springer, vol. 394, pp. 228-241 (2013).
31. Zinder, E.Z. and Yunatova, I.G.: Digital economy and knowledge barriers: their origin and
dealing with them. In: Proceedings of the Digital Transformation and Global Society:
Second International Conference (DTGS 2017). St. Petersburg, pp. 445-463 (2017).
32. Zinder, E.: Data, information, and knowledge: concepts in standards, changes and conjoint
applications. In: Selected Papers of the XXII International Conference "Enterprise
Engineering and Knowledge Management (EEKM 2019), Moscow, CEUR-WS.org, Vol-2413,
pp. 198-209 (2019).
33. Zinder, E.Z.: Modeling and formation of the common as a condition for managing the
development of large-scale network systems with heterogeneous participants (in Russian).
Materials of the XII Int. conf. IPU RAS "Management of the development of large-scale
systems" (MLSD’2019), pp. 217-220 (2019).
34. Zinder, E.Z.: Values-directed enterprise engineering. Business Informatics, No. 3 (45), pp.</p>
      <p>7-19 (2018).
35. Open agile architecture. A standard of the Open Group. Document number: C208. The
Open Group (2020).</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          1.
          <string-name>
            <surname>Lapalme</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          (et al.)
          <article-title>: Exploring the future of enterprise architecture: A Zachman perspective</article-title>
          .
          <source>Computers in Industry. No. 70</source>
          . pp.
          <fpage>103</fpage>
          -
          <lpage>113</lpage>
          (
          <year>2016</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          2.
          <string-name>
            <surname>Zinder</surname>
            ,
            <given-names>E.Z.</given-names>
          </string-name>
          :
          <article-title>Expanding enterprise engineering paradigm</article-title>
          .
          <source>Business Informatics</source>
          <volume>4</volume>
          (
          <issue>38</issue>
          ), pp.
          <fpage>7</fpage>
          -
          <lpage>18</lpage>
          (
          <year>2016</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          3.
          <string-name>
            <surname>Sowa</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Zachman</surname>
          </string-name>
          , J.:
          <article-title>Extending and formalizing the framework for information systems Architecture</article-title>
          .
          <source>IBM Systems Journal, 31/3</source>
          , pp.
          <fpage>590</fpage>
          -
          <lpage>616</lpage>
          (
          <year>1992</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          4.
          <string-name>
            <surname>Wetering</surname>
          </string-name>
          , R.:
          <article-title>Dynamic enterprise architecture capabilities: conceptualization and validation</article-title>
          .
          <source>In: Proceedings of the 22nd International Conference on Business Information Systems. Seville</source>
          ,
          <volume>12</volume>
          p. (
          <year>2019</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          5.
          <string-name>
            <surname>Jusuf</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Kurnia</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          :
          <article-title>Understanding the benefits and success factors of enterprise architecture</article-title>
          .
          <source>In: Proceedings of the 50th Hawaii International Conference on System Sciences, Hawaii</source>
          , pp.
          <fpage>4887</fpage>
          -
          <lpage>4896</lpage>
          (
          <year>2017</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          6.
          <string-name>
            <surname>Wetering</surname>
          </string-name>
          , R.:
          <article-title>Dynamic enterprise architecture capabilities and organizational benefits: an empirical mediation study</article-title>
          .
          <source>In: Proceedings of the Twenty-Eigth European Conference on Information Systems (ECIS2020)</source>
          , Marrakesh,
          <year>2020</year>
          . 18 p. (
          <year>2020</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          7.
          <string-name>
            <surname>Koffi</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          :
          <article-title>Enterprise architecture dynamic alignment model</article-title>
          .
          <source>Journal of Enterprise Architecture. Association of Enterprise Architects, No. 2</source>
          ,
          <year>October 2017</year>
          , pp.
          <fpage>1</fpage>
          -
          <lpage>13</lpage>
          (
          <year>2017</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          8.
          <string-name>
            <surname>Gerber</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Roux</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Merve</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          :
          <article-title>Enterprise architecture as explanatory information systems theory for understanding small- and medium-sized enterprise growth</article-title>
          .
          <source>Sustainability</source>
          , vol.
          <volume>12</volume>
          , Issue
          <volume>20</volume>
          ,
          <issue>15</issue>
          <year>October 2020</year>
          .
          <volume>31</volume>
          pages.
          <source>DOI:10.3390/su12208517</source>
          (
          <year>2020</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          9.
          <string-name>
            <surname>Mangayarkarasi</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          and
          <string-name>
            <surname>Selvarani</surname>
          </string-name>
          , R.:
          <article-title>Dynamic enterprises architecture for one or more clouds</article-title>
          . In: Meghanathan,
          <string-name>
            <surname>N.</surname>
          </string-name>
          et al. (Eds.):
          <source>CCSIT</source>
          <year>2012</year>
          ,
          <string-name>
            <surname>Part</surname>
            <given-names>II</given-names>
          </string-name>
          , LNICST, vol.
          <volume>85</volume>
          , pp.
          <fpage>109</fpage>
          -
          <lpage>114</lpage>
          (
          <year>2012</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          10.
          <string-name>
            <surname>Kotusev</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          :
          <article-title>What is agile enterprise architecture?</article-title>
          <source>British Computer Society</source>
          , pp.
          <fpage>1</fpage>
          -
          <lpage>6</lpage>
          (
          <year>2020</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          11.
          <string-name>
            <surname>Filet</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Wetering</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          and
          <string-name>
            <surname>Joosten</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          :
          <article-title>Enterprise architecture alignment</article-title>
          . Chapter in: Enterprise Architecture and
          <string-name>
            <surname>Service-Oriented</surname>
            <given-names>Architecture</given-names>
          </string-name>
          ,
          <volume>32</volume>
          p. (
          <year>2020</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          12.
          <string-name>
            <surname>Maniam</surname>
            ,
            <given-names>N.:</given-names>
          </string-name>
          <article-title>An overview of challenges in enterprise architecture</article-title>
          .
          <source>Universiti Kebangsaan</source>
          , Individual assignment,
          <source>Malaysia</source>
          , 8 p. (
          <year>2019</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          13.
          <string-name>
            <surname>Zimmermann</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ;
          <string-name>
            <surname>Schmidt</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          and
          <string-name>
            <surname>Sandkuhl</surname>
            ,
            <given-names>K.</given-names>
          </string-name>
          :
          <article-title>Multiple perspectives of digital enterprise architecture</article-title>
          .
          <source>In: Proceedings of the 14th International Conference on Evaluation of Novel Approaches to Software Engineering</source>
          , Volume
          <volume>1</volume>
          : ENASE, pp.
          <fpage>547</fpage>
          -
          <lpage>554</lpage>
          (
          <year>2019</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          14.
          <string-name>
            <surname>Korhonen</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          and
          <string-name>
            <surname>Halén</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          :
          <article-title>Enterprise architecture for digital transformation</article-title>
          .
          <source>In: Proceedings of the IEEE 19th Conference on Business Informatics. IEEE</source>
          , pp.
          <fpage>349</fpage>
          -
          <lpage>358</lpage>
          (
          <year>2017</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          15.
          <article-title>Enterprise modelling and architecture - Requirements for enterprise-referencing architectures and methodologies</article-title>
          .
          <source>ISO</source>
          <volume>15704</volume>
          :
          <year>2019</year>
          (
          <year>2019</year>
          ).
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>