Work Systemswork-systems 30-01-06

Beter vooruitlopen op ons doel. Laat vast een ORM voorbeeld zien en ontleed
die in elementen, etc.

In this chapter, we discuss our fundamental view on work-system, organization
and information-system. We will provide a definition of terms, which is based
on a system theoretic 2001-Bertalanffy-GST foundation.

Discuss the idea that we are using DM approach to understanding OASs, and
ultimately IIO and/or IS. Repeat this (or move) discussion to next chapter.

Exploring systems Even though the notion of system is, in an IT context, often
equated to ‘software system’, the original sense of the word is much broader.
The notion of system††The term ‘system’ is derived from the Greek phrase ‘Syn
histanai’ ($\sigma\upsilon\nu$ $\acute{\i}\sigma\tau\eta\nu\alpha\iota$): ‘to
put together’. is also not uniquely defined in the literature, but typically,
it can be found explained as: “A collection of interrelated parts
characterized by a boundary with respect to its environment” 1983-Iivari-
Systemeering or just as: “A set of objects with a set of link” 1971-Langefors-
InformationSystemsTheory. In general, humans refer to all sorts of things as
‘system’. The broadness of our understanding of the concept of ‘system’ comes,
for example, to the fore in the definition as found in 2003-Webster-
Dictionary:

> A regularly interacting or interdependent group of items forming a unified
> whole, as:
>
>   1. 1.
>
> a group of interacting bodies under the influence of related forces,
>
>   2. 2.
>
> an assemblage of substances that is in or tends to equilibrium,
>
>   3. 3.
>
> a group of body organs that together perform one or more vital functions,
>
>   4. 4.
>
> the body considered as a functional unit,
>
>   5. 5.
>
> a group of related natural objects or forces,
>
>   6. 6.
>
> a group of devices or artificial objects or an organization forming a
> network especially for distributing something or serving a common purpose,
>
>   7. 7.
>
> a major division of rocks usually larger than a series and including all
> formed during a period or era,
>
>   8. 8.
>
> a form of social, economic, or political organization or practice.
>
>

The IEEE Recommended Practice for Architectural Description of Software-
Intensive Systems [1999-IEEE-Architecture] provides a functionality-oriented
perspective on systems:

> A collection of component organized to accomplish a specific function or a
> set of functions.

In practice, most people intuitively agree on such simple definitions of
system. Apparently these definitions are broad enough to cover the meaning of
usual linguistic constructs where ‘system’ is used. But system is a much more
difficult concept. If we look at what in practice are considered system, and
if we really think about it, it becomes obvious that some very important
aspects of the system concepts are missing in the traditional definitions. In
[1998-Lindgreen-FRISCO] some examples are given of what we would, and would
not, observe to be system in our daily life: One can regard an organization or
a bicycle as system. Also a Hitchcock film recorded on a video cassette, which
is inserted in a video cassette player, which again is connected to a TV-set,
could easily be interpreted as a system. Nothing is unusual with such system
views, and they are well covered by the definitions. But if you buy some eggs
from a farmer and use two of them for breakfast, then the domain of obviously
interrelated phenomena: You, the farmer, the farmers hen that laid the eggs,
the frying pan you used to prepare the eggs, and the two eggs now in your
stomach (and thereby in some transformed form a part of yourself) – this
domain might probably not be regarded as a system, because it might be
difficult to see a purpose for that. But it fits the definitions. Or consider
a single raindrop in an April shower: It consists of a vast number of water
molecules, kept together by surface tension and constantly moving around among
each other in a complicated manner controlled by a set of (thermo-) dynamic
forces. Again according to the simple definitions above, the drop qualifies as
a system. But that is strange, because when you on your way back from the
farmer, happen to get soaked in the shower, you might feel it is caused by
raindrops – not by system. On the other hand, a meteorologist studying
possible weather situations that could cause rain, may see a purpose in
regarding a raindrop as a system in interaction with the surrounding
atmosphere, but in most other situations a raindrop is just a raindrop.
However, when looking at what is regarded as a system in practice, it becomes
apparent that some very important aspects of the system concept are missing
from the traditional definitions. In [1999-Ropohl-SocioTech] it is argued
that, strictly speaking, there exist three different interpretations of
system:

[Structural] The structural interpretation is known best. According to this
interpretation, a system includes a set of element and a set of link between
these element. This interpretation complies with the ancient definition of the
_holon_ by Aristotle. [Functional] The functional interpretation views a
system as an entity, sometimes called black box, which transforms inputs into
outputs. Depending on specific internal states; the kind of transformation is
called a function (in the descriptive meaning of the word). [Hierarchical] The
structural interpretation turns into the hierarchical interpretation, if (some
of) the constituting element are regarded as subsystems. Concluding by
analogy, the original system may be considered as a subsystem of a more
extensive supersystem.

##  1 Observing systems

The aim of this section is to more precisely define the concept of system,
also giving more foundation to our earlier definitions of work-system,
organizational-system, and information-system.

###  Subjectivity

When two people discuss a system, do they really mean the same system? One
serious cause for confusion in our professional domain is, that people,
usually, think about a system as something that can be objectively determined,
for example by a specification of its parts and their relationships, as the
above quoted definitions may indicate. But even then, the problem remains. Are
both people indeed discussing the same system? As an example take the simple
domain of a car and its driver in the traffic of a city. One person may see it
as a useful transport system in action, which is able to move large objects
from one location to another in a convenient way. The driver alone cannot, nor
can the car, but in combination they can. However, a policeman on his job will
regard the same domain differently – as a controllable system which behavior
can be directed by road regulations, traffic lights, arm signals and by
certain traffic rules. Again, an environmental activist would probably regard
the car as a dangerous polluting system, which is a potential cause of injury
or death to persons in the traffic. Here we have three views of the same
domain, but with quite different sets of properties. All three persons could
in fact be the same viewer of the same system, e.g. a transport conscious
public servant caring about the conditions for people in the city, who just
conceives different properties by regarding the same system from different
points of view. Let us elaborate this car example a little further in order to
illustrate the difficulties we face when we regard something as a system.
Consider for example the question about which parts and which activities are
involved in the possible system view: Are the driver and the car two
interacting sub-system – one with the property of being able to observe the
traffic and to control the car, and the other with the property of being able
to transform chemical energy into movement in a controlled manner. Or is the
car to be regarded as a single system with the driver, motor, gear, and
steering devices as sub-system each with their own properties? Is the motor
the active part and the chassis a passive component, or is it the other way
around – the car as a device transporting among other things the motor. Quite
another view – but still one from the same domain – could be to regard the car
as a moving cage of Faraday protecting the driver from certain kinds of
dangerous electrical fields. There are many possible system views, and still
the domain is extremely simple compared with the organizational domains
usually considered as system. If we regard a business enterprise, an
institution or any other kind of organization as a system – an organizational
system – we have a domain which is much more complicated than a car and
driver. Furthermore, the number of possible views of an organization is most
often enormous. Key to understanding the system concept, and ultimately
organization is therefore to realize that a system is a subjective phenomenon.
In other words, it is not an absolute or objective thing. system are not a
priori given. As Checkland [1981-Checkland-SystemThinking] expresses it, there
must be a describer/observer who conceives or thinks about a part of the world
as a system. In other words, it is important, that there is a _viewer_ who can
see a purpose in regarding some ‘ _set of element_ ’ as a system. viewer may
also be regarded at an aggregated level. For example, a _single_ business
manager, observing an organization, is indeed a viewer, but the _collective_
business management can be seen as a viewer of the organization as well. The
purpose in regarding some _set of element_ as a system should be expressed in
terms of at least one meaningful link between the _set of element_ and its
_environment_. Such a link is called a _systemic-property_. It is a property
the viewer associates with the _set of element_ they experience as a system.
One viewer may regard the _set of element_ as a system having one set of
systemic-property, while another viewer may see other systemic-property
concerning the same set of element. Most often, the systemic-property of a
system cannot be attributed exclusively to any of its constituent component.
For example, none of the constituent parts of a train has the exclusive ‘train
property’. A separate carriage is not a train. A locomotive on its own is
(from the perspective of a passenger) also not a train. Together, however, the
parts do have the ‘train property’. In other words, the whole is more than
just the collection of its parts. The farmer-you-frying-pan-eggs-hen situation
as discussed in the above example, is a situation which may not constitute a
‘whole’ with any sensible systemic-property. In which case we will not
consider it to be a system. In the case of the train, we have an interesting
situation if the train consists of two connected train-sets. In this case,
each of the individual train-sets still has the ‘train property’. In order for
us to gain a fundamental understanding of system, and ultimately the kind of
systems we refer to as organization, we first need to introduce some core
concepts, most of which are based on the ones found in [1998-Lindgreen-
FRISCO].

###  Observing the universe

Let us start by considering what happens if some viewer observes ‘the
universe’. It is our assumption, based on the work of C.S. Peirce
[1969-Peirce-Collection1, 1969-Peirce-Collection2, 1969-Peirce-Collection3,
1969-Peirce-Collection4], that _viewer_ perceive a _universe_ , leading to a
_perception_ of this universe and then produce a _conception_ of that part
they deem relevant. Peirce argues that both the perception and conception of a
viewer are strongly influenced by their interest in the observed universe.
This leads to the following (necessarily cyclic, yet irreflexive) set of
definitions: universe viewer perception conception In general, people tend to
think of the universe as consisting of element. In [1998-Lindgreen-FRISCO]
this approach is indeed taken. In our view, presuming that the universe
consists of a set of element constitutes a subjective choice, which
essentially depends on the viewer observing the universe. Nevertheless, taking
this assumption has proven to be a sensible assumption, in particular in the
context of system. However, we do _not_ presume the _universe_ itself to
consist of elements, but _rather_ the _conception_ of a universe. This makes
the identification of element relative to a viewer. The conception harbored by
a viewer are impossible to communicate and discuss with other viewer unless
they are articulated somehow. In other words, a conception needs to be
_described_ somehow in terms of a description:111In [1998-Lindgreen-FRISCO]
the term _representation_ is used rather than the term _description_ as it is
used here. We have chosen to favor the term _description_ , as it is the term
of choice of [1999-IEEE-Architecture]. description The resulting situation is
illustrated in description. 13cm A viewer, having a conception of the
universe, and describing this in terms of a description. description
description may be:

  * •

Formal or informal

  * •

Complete or incomplete

  * •

More refined/less refined

A system description may have a formal semantics, in mathematical terms, and
will also have an intensional (pragmatics!) semantics. Formal semantics is
needed when approaching design. The latter is likely to be of more use when
communicating with different stakeholders. The underlying relationships
between viewer, universe, conception and description can be expressed in terms
of the so-called FRISCO tetrahedron [1998-Lindgreen-FRISCO], as depicted in
tetrahedron222The original FRISCO tetrahedron uses ‘domain’ where we use
‘universe’. This difference is due to the above, more refined, discussion on
the subjectivity of viewing the universe as a set of element.. 8cmThe
(revised) FRISCO tetrahedron.tetrahedron

###  Conceptions

To express the above discussions more formally, let Universes333The reader is
advised that appendix LABEL:ch:Math provides an overview of the mathematical
notations/conventions used in this textbook. be the set of universe that may
be observed, and let Viewers444One should actually regard this set as the set
of _states_ a viewer may have. A viewer may for example have, in differing
states, different interest with which they conceive the universe. The elements
from $\Viewers$ should really be regarded as the states of these viewer. be
the set of all possible viewer. Let furthermore, Elements be the set of
element that may be part of conception. These basic sets should be disjoint: S
$\Viewers$, $\Universes$ and $\Elements$ are mutually disjoint. Let Conception
be the link expressing which conception is held by which viewer. The fact that
a viewer $v\in\Viewers$ harbors a conception $C\subseteq\Powerset(\Elements)$
for universe $U\in\Universes$ can be expressed as $\Conception{U}{v}{C}$. This
situation is depicted more graphically in painting1. A viewer, when observing
a domain, draws a picture of the observed universe (their conception). In
painting this picture of the world, they will use certain ‘constructs’. At the
moment the only constructs we presume to exist are _element_. Note: the fact
that viewer can change their conception over time is ignored for the moment.
6cmPainting a picture of the universepainting1

####  Domains and their environments

A viewer may zoom in on a particular part of the universe they observe, or to
state it more precisely, they may zoom in on a particular part of their
conception of the universe. domain When reasoning about system, which we will
regard as a particular class of domain, it is commonplace to also identify
their environment [2001-Bertalanffy-GST]. Even more, the very definition of a
system depends on our ability to distinguish it from its environment. This is
illustrated in painting2. 6cmIdentifying a domain and its environmentpainting2
To be able to define the environment of a domain in general and a system in
particular, however, we must first be able to define the direct environment of
a domain. Formally, a domain $D$ can be regarded as a subset of a conception
$C$, in other words a sub-conception $D\subseteq C$. If $\Conception{U}{v}{C}$
and $D\subset C$ is some domain within $C$, then the environment of $D$ will
not generally be $C\SetMinus D$ as a whole, but rather a subset $E\subseteq
C\SetMinus D$. For $E$ to be a sensible environment of domain $D$, the element
in $E$ must have some link to the element in $D$. In order to more precisely
define the notion of environment, we should therefore first refine our notion
of element of a conception. There are really two types of element: concept and
link connecting the concept. We will define these notions as follows: element
concept link The distinction between a link and an concept for the element of
a given conception, may not always be that clear, as the distinction is rather
_subjective_. It all depends, to no surprise, on the viewer of a domain. Let
Concepts be the set of concept and let Links be the set of link. These sets
should form a partition of $\Elements$: S
$\Concepts\intersect\Links=\emptyset$ and $\Elements=\Concepts\union\Links$.
In terms of painting2, our viewer can now select from two classes of element:
concept and link. This is depicted in painting3. In the next chapter, we will
provide an even more refined view on the classes of element we identify.
6cmPainting a more refined picture of the observed domainpainting3 If
$X\subseteq\Elements$, then we will use the following abbreviations:

$\SymbolDefinition{ConceptsSubset}\mbox{~{}and~{}}\SymbolDefinition{LinksSubset}$

link run between concept. We furthermore presume functions From and To to
exist, providing the source and destination of these link respectively. As an
abbreviation we will use:

$\SymbolDefinition{Involved}$

to select the concept involved in a link, and:

$\SymbolDefinition{LinkedTo}$

to represent the fact that a concept $e$ is connected to concept $f$. A
conception $C$ is considered to be closed iff:

$\Al{r\in\LinksSub{C}}{\Involved(r)\subseteq C}$

conception of viewer should indeed be closed: Sclosed-conception If
$\Conception{U}{v}{C}$, then $C$ is closed. ontology1 provides a model, our
ontology, of the classes of elements which a conception may consist of and
their mutual relationships. The notation we have used there is the ORM
(Object-Role Modeling) [2001-Halpin-ORM]555We have used the extension
introduced in [1995-Halpin-ORMPoly] to signify that Concept and Link are
really self-defining subtypes, i.e. not requiring a dedicated subtype defining
rule. notation, which is the same notation as used in the _Domain Modeling_
course. 8cmThe ontology of a viewer’s conceptionontology1 A conception $C$
which is closed under $\Links$ can essentially be regarded as a graph:

$\tuple{\ConceptsSub{C},\LinksSub{C},\From,\To}$

A conception $C$ is called connected iff the associated graph is connected. A
conception is required to be a connected graph: Sconnected-conception If
$\Conception{U}{v}{C}$, then $C$ is connected. Note: if a conception would not
be a connected graph, it would be a conception of multiple universes. We
generalise $\From$ and $\To$ to sets of link as follows: (L) (l)l ∈L
(L) (l)l ∈L We are now in a position to properly define the environment of a
domain: environment Formally, we view a domain $D$ and an environment $E$ as
being a subset of a conception $C$, in other words a sub-conception
$D,E\subseteq C$. Let DomainInEnvironment now be the relation expressing which
domain and environment a viewer conceives. The fact that a viewer $v$ harbors
a conception of domain $D$ and environment $E$ for universe $U$ can be
expressed as $\DomainInEnvironment{U}{v}{C}{E}{D}$. This link should limit
itself to the conception held by viewer $v$: S If
$\DomainInEnvironment{U}{v}{C}{E}{D}$, then $\Conception{U}{v}{C}$ and
$E,D\subseteq C$. A domain and its environment should not overlap: Snon-
overlapping-domain-environment If $\DomainInEnvironment{U}{v}{C}{E}{D}$, then
$E\intersect D=\emptyset$. The domain and environment should be closed:
Sclosed-domain If $\DomainInEnvironment{U}{v}{C}{E}{D}$, then $D$ is closed.
Sclosed-domain-environment If $\DomainInEnvironment{U}{v}{C}{E}{D}$, then
$E\union D$ is closed. A domain should be connected: S If
$\DomainInEnvironment{U}{v}{C}{E}{D}$, then $D$ is connected. The combination
of a domain and its environment is connected as well: Sconnected-domain-and-
environment If $\DomainInEnvironment{U}{v}{C}{E}{D}$, then $D\union E$ is
connected. Note that an environment does not have to be connected! concept in
the environment are related somehow to concept in the domain: related-
environment Let $\DomainInEnvironment{U}{v}{C}{E}{D}$ with a non-empty
environment $E$. If $P$ is a _maximum_ 666In other words, there is no
$P^{\prime}$ such that $P\subset P^{\prime}\subseteq E$ while $P^{\prime}$ is
still connected. subset of $E$ such that it is connected, then:

$\Ex{e\in\ConceptsSub{P},r\in\LinksSub{E},d\in\ConceptsSub{D}}{\setje{e,d}=\Involved(r)}$

The authors of [1998-Lindgreen-FRISCO] also define the notions of domain and
environment. However, they do not take the subjectivity with regards to
viewing the universe as a set of element into consideration. As a result, they
define domain and environment as being parts of the _universe_ as opposed to
being parts of a viewer’s conception of the universe. In the remainder of this
book, we will use the phrase: _a viewer $v$ observing a domain (of interest)
$D$ (with environment $E$)_ as an abbreviation for: _a viewer $v$ having a
conception of the universe, zooming in on domain $D$ (with environment $E$)_.

####  Decomposition of conceptions

When a viewer conceives a domain, we presume there to be an concept in their
conception representing the _whole_ of the domain as well as one representing
the _whole_ of the environment. The same applies to the universe. In other
words, the concept in the domain and the environment can be regarded as
decompositions of entities representing the whole of the domain and
environment, while these latter concept are decompositions of another concept
representing the universe as a whole. This is illustrated in figure
LABEL:decomposition1. 4cmDecomposition of the universedecomposition1 This
‘decomposition game’ can be played repeatedly. When viewing a domain a viewer
may decide to zoom in further into a specific part of this domain. For
example, when observing an insurance claim-handling process, involving amongst
other things an evaluation of the claim, one may decide to zoom in closer into
the actual evaluation process. This has been illustrated in figure
LABEL:decomposition2. 4cmDecomposition of a part of a domaindecomposition2 The
fact that one concept is in the ‘decomposition’ of another concept really
means that there is a link between them in the viewer’s conception. This has
been illustrated in figure LABEL:decomposition3. This really implies we need
to identify a specific class of link called decomposer. Let us therefore
presume we have a set: Decomposers of link. 4cmDecomposer
relationshipsdecomposition3 To more easily reason about decompositions within
a conception, we will introduce the derived relationship
$\SymbolDefinition{DecomposedInto}$. If $\DecomposedInto{x}{C}{y}$, the
concept $x$ in conception $C$ is decomposed into (possibly amongst others)
concept $y$. This relationship is defined (precisely) by the two following
(recursive) derivation rules:

$\begin{array}[]{llll}1:&\Ex{d\in\DecomposersSub{C}}{x=\From(d)\land
y=\To(d)}&\vdash&\DecomposedInto{x}{C}{y}\Eol
2:&\DecomposedInto{x}{C}{y}\land\DecomposedInto{y}{C}{z}&\vdash&\DecomposedInto{x}{C}{z}\end{array}$

The decompositions should be acyclic: Sacyclic-decompositions
$\DecomposedInto{x}{C}{y}\implies x\neq y$ As an abbreviation we introduce:
DecomposedIntoEq. To enforce the fact that a viewer’s conception of a universe
consists of one ‘top’ concept representing the universe as a whole, we
require: Sconception-has-top If $\Conception{U}{v}{C}$, then:
$\ExAl{u\in\ConceptsSub{C}}{x\in\ConceptsSub{C}}{\DecomposedIntoEq{u}{C}{x}}$
Even more, the $u\in C$ is unique: unique-top If $\Conception{U}{v}{C}$, then:
$\EuAl{u\in\ConceptsSub{C}}{x\in\ConceptsSub{C}}{\DecomposedIntoEq{u}{C}{x}}$
Similarly, for domain and environment we have: Sdomain-has-top If
$\DomainInEnvironment{U}{v}{C}{E}{D}$, then: $\ExAl{d\in
D}{x\in\ConceptsSub{D}}{\DecomposedIntoEq{d}{D}{x}}$ Senvironment-has-top If
$\DomainInEnvironment{U}{v}{C}{E}{D}$, then: $\ExAl{e\in
E}{x\in\ConceptsSub{E}}{\DecomposedIntoEq{e}{E}{x}}$ unique-top applies to
each of these as well. So for $C$, $D$ and $E$ there are unique tops in the
hierarchies. This unique _top_ element will be referred to as $\Top(C)$,
$\Top(D)$ and $\Top(E)$ respectively. For these tops, we should have: S If
$\DomainInEnvironment{U}{v}{C}{E}{D}$, then:
$\Eu{d\in\DecomposersSub{C}}{\Top(C)=\From(d)\land\Top(E)=\To(d)}$ S If
$\DomainInEnvironment{U}{v}{C}{E}{D}$, then:
$\Eu{d\in\DecomposersSub{C}}{\Top(C)=\From(d)\land\Top(D)=\To(d)}$ S If
$\DomainInEnvironment{U}{v}{C}{E}{D}$, then:
$\Eu{r\in\LinksSub{C}\SetMinus\DecomposersSub{C}}{\Top(D)=\From(d)\land\Top(E)=\To(d)}$
These three axioms require the top part of a conception to have the structure
as depicted in decomposition3. By adding the set of decomposer, we have now
enriched our ontology to the situation as depicted in figure LABEL:ontology2.
Note that the asterisk (*) attached to the is decomposed into relationship
signifies this to be a derived relationship. 8cmOntology refined with
decomposersontology2

###  Model

In the context of organization, we are not interested in all types of
conception. Our interest is limited to those conception, that may be referred
to as a _model_ : model As a model is a conception, it also consists of
element, which can be specialized further into concept and link: model-element
model-concept model-link We are now also in a position to define more
precisely what we mean by _modeling_ : modeling For practical reasons, we will
understand the act of _modeling_ to also include the activities involved in
the _description_ of the model by means of some language and medium. To
represent the fact that some viewer produces a model in an environment when
they observe some part of the universe, we introduce the relation:

$\SymbolDefinition{ModelInEnvironment}$

Formally, the fact that a viewer $v$ views the universe $U$ and in doing so
has a conception $C$ including a model $M$ with environment $E$ is represented
by: $\ModelInEnvironment{U}{v}{C}{E}{M}$. Every model is a conception. We
should therefore have: Smodel-as-domain If
$\ModelInEnvironment{U}{v}{C}{E}{M}$, then
$\DomainInEnvironment{U}{v}{C}{E}{M}$. If
$\DomainInEnvironment{U}{v}{C}{E}{M}$, then $\Conception{U}{v}{C}$. Note that
not all conception of a domain produce model. So the reverse of the above
axiom does _not_ hold! As an abbreviation we also introduce:

$\SymbolDefinition{ModelConception}$

###  System

Using the above general definitions, we can, in line with [1998-Lindgreen-
FRISCO], more precisely define the way we view system: system-domain systemic-
property system-viewer system system-description The element, concept and link
concepts can be further specialized to system: system-element system-concept
system-link As identified in [1998-Lindgreen-FRISCO], there is a potential
objection against our subjectivity-based definition of system. In daily life,
it is quite sensible to talk about “designing, constructing and implementing a
system” or “to interact with a system”. The use of the terms ‘system’ gives
associations to this term as denoting something that can be interacted with in
a rather concrete way and not just as a conception. These associations,
however, do not lead to any inconsistencies. These example phrases are simply
convenient abbreviations for more elaborate expressions. For instance, “to
interact with a system” really means:

> to interact with phenomena in the system-domain that is conceived as a
> system (because of its systemic-property).

To “design, construct and implement” a system really means:

> to bring together and structure phenomena in a particular part of the world
> (which then becomes the system-domain) with the purpose of constructing them
> such that they together have certain systemic-property.

To represent the fact that some viewer ‘sees’ a system in an environment when
they observe some part of the universe, we introduce the relation:

$\SymbolDefinition{SystemInEnvironment}$

Formally, the fact that a viewer $v$ views the universe $U$ and in doing so
has a conception $C$ including a system $S$ with environment $E$ is
represented by: $\SystemInEnvironment{U}{v}{C}{E}{S}$. Every system is a
model. We should therefore have: Ssystem-as-model If
$\SystemInEnvironment{U}{v}{C}{E}{M}$, then $E\neq\emptyset$ and
$\ModelInEnvironment{U}{v}{C}{E}{M}$. Note that not all conception of a domain
produce model. So the reverse of the above axiom does _not_ hold! As an
abbreviation we also introduce:

$\SymbolDefinition{SystemConception}$

In our informal exploration of the concept of system, we already discussed
that there are three major ways of viewing system [1999-Ropohl-SocioTech]:
_structural_ , _functional_ and _hierarchical_ (as a specific class of
structural). A major difference between a structural and a functional
perspective is the distinction between the white-box and black-box approach
when regarding system. In other words, is one looking _inside_ the system
(white-box) or is one only looking at the _outside_ of the system. This does
seem to raise the question whether, when viewing a system as a black-box, one
can still argue that the system consists of element? The answer to this
question is a resounding _yes_. When a viewer, for some reason, views a domain
as a system, and does so using a black-box approach, that what they conceive
of as being a system is still a conception consisting of element. The
difference between a white-box and a black-box approach when viewing a system,
however, is in the concept and link one will see. When taking a black-box
approach, one will only see the external behavior of the system, while when
taking the white-box approach one will see the internal structure/behavior of
the system as well.

##  2 Studying systems

In order to really to understand the concept system it is necessary to be
aware of a number of important aspects:

  * •

that the system domain always comprises several elements,

  * •

that all elements are related to each other such that it constitutes a
transitively coherent whole,

  * •

that the whole is conceived to have at least one systemic property,

  * •

that it is only relevant to incorporate a thing as an element of the
particular system domain if in the system view it somehow contributes to the
systemic property,

  * •

that when viewing a thing as an element of a system domain then only those
aspects of the thing that directly or indirectly contributes to the systemic
properties are relevant for the system view.

###  Sub-systems

To gain a better understanding of complex system it has proven to be useful to
identify smaller-scale system within a larger system, leading to sub-system. A
detailed discussion on dealing with complexity by system in general, and the
role played by hierarchical decomposition, may be found in e.g. [1962-Simon-
ComplexArch]. In this textbook, for example, information-system will be
positioned as sub-system of organizational-system. However, when it comes to
the point of being less intuitive and more explicit about the concept, there
is little consensus about what really characterizes a sub-system – or rather
what should characterize it, if the concept is to be a useful one. The
influence from the absoluteness of the ‘classical’ system concept together
with some apparent preference to associate the understanding of sub-system
with the subset concept seem to be the main cause of the confusion. The ‘old’,
simple interpretation of the concept system as being just ‘a set of
interrelated parts’, made it rather obvious to think of sub-system as: A
subset of the parts together with an appropriate subset of their mutual
relationships. However, with the introduction of the notion that in order for
something to be a system, it must have at least one systemic-property, the
matters became more difficult: Should the definition of sub-system then also
involve the specification of a subset of the systemic-property? Intuitively
this notion could be reasonable, and it may even work in some cases, but the
problem is that this is not always so. Consider, for example, a well-
functioning mechanical watch. It can be conceived to have the systemic-
property that under certain conditions it ‘shows the time’. A possible sub-
system of such a watch is the energy supplying device for the clockwork
consisting of the spring, the winding knob, the exchange and click mechanism
for tightening the spring, and a part of the frame to support these mechanical
parts. The only sensible systemic-property of such a sub-system is that it
serves as a storage of mechanical energy. But then we have a serious problem
with the subset notion applied on the systemic-property, because being an
energy storage is in no way a subset of the systemic-property of showing the
time. The problem of defining a sensible sub-system concept by means of subset
relationships becomes even more difficult with the notion of a system as a
subjective issue. Apart from the systemic-property not being absolute, but
rather depending of the viewer, one element in the system-domain may now also
potentially be viewed as several different component in the system. Consider,
for example, an organization that is viewed as an and a person from that
organization: Here the person may appear as an actor of the type salesman that
is the agent of various sales activities. But independent hereof, the same
person may also be conceived as having the type employee relevant in
connection with calculations of salaries and the planning of sales campaigns.
The person may even be regarded as being of type transportable object in the
context of an activity transport by car during sales trips. This causes the
following question: Should a possible subset relationship applied in attempts
to define a sub-system concept then refer to the domain alone, or to the
system alone, or to both? It is certainly difficult to find logical or
pragmatic arguments that universally justify any of these choices. (For
further aspects of the problems encountered when one is aiming at defining
sub-system by means of subsets, see the more comprehensive discussion in
[1998-Lindgreen-FRISCO].) It is necessary to consider the sub-system concept
differently – in fact, in a way that very well is in accordance with the way
people intuitively apply it in practice. The ‘solution’ is to realize that
when viewing something as a system then only one system should be considered
at a time. Applied here, either one must consider that which is regarded as
the system or that which is regarded as the sub-system. The advantage of this
sub-system interpretation is exactly what appears to be the main positive
feature of the intuitively applied concept: Depending on which level of detail
as regard potential component you want to consider, you can use the concept to
encapsulate unnecessary details on a chosen level of abstraction. Applied to
organization one obvious way to consider the relationship between an
organization and a sub-system of it, is to conceive the sub-system equivalent
with what an actor in the organization does (or a part of that). Typically a
whole department (a possible system candidate in itself) may be considered a
single actor in the organization, and (part of) what is done in that
department in respect to other departments (i.e. possible systemic-property of
the “department system”) may be conceived as a single action at the
organizational-level. A data-processing system may be conceived as a single
(artificial) actor carrying out data-processing actions in the organization,
even if we know that it, in fact, is composed of a lot of component. A sub-
system may, in line with [1998-Lindgreen-FRISCO], defined as: sub-system
Formally, this can be expressed as:

$\SymbolDefinition{SubSystem}$

sub-sys-top If $\SubSystem{U}{v}{S^{\prime}}{S}$, then: $\ExAl{s\in
S^{\prime}}{x\in\ConceptsSub{S^{\prime}}}{\DecomposedIntoEq{s}{S^{\prime}}{x}}$
Two common dimensions along which to define sub-system are: component-system
and aspect-system. component-system Formally:

$\SymbolDefinition{ComponentSystem}$

aspect-system Formally:

$\SymbolDefinition{AspectSystem}$

Note that some authors, for example [1992-In'tVeld-SystemenProcessen,
1998-Bemelmans-BISA], use the term sub-system to refer to the above defined
concept of component-system. However, we prefer to use the term sub-system as
defined above (following the definition in [1998-Lindgreen-FRISCO]), as it
allows us to view it as a generalization of the concepts component-system and
aspect-system. Different viewer may disagree on the fact whether some sub-
system is an aspect-system or a component-system (or a combination thereof).
This can be traced back to the subjectivity involved in distinguishing between
link and concept. Whenever there is a ‘clear’ analogy to physical structures,
it will be easier to identify the difference. Consider a freight-train as an
example system. Typical component-system of such a system are: the locomotive,
the engine-driver, several types of box-cars, etc. An aspect-system of a
freight-train would be the hydraulic braking system of the train as a whole. A
sub-system is indeed a system. As such, a sub-system $S^{\prime}$ of a system
$S$ will also have its own systemic-property. However, these properties are
most likely no subset of the systemic-property of $S$. For example, the
engine-driver’s systemic-property are by no-means a clear subset of the
systemic-property of a freight-train.

###  Describing systems

When a system developer in a system viewing or modeling process gradually
realizes what (currently) ‘is the system’, i.e. becomes conscious of all
relevant aspects of the involved element and of each of the systemic-property,
it is very useful to be aware of the type of system in question and to produce
a system-exposition in accordance with the system-type. system-type system-
exposition A system-type can be regarded as a viewing template to be used by a
system developer, analyst or modeler in order to decide which kinds of things
(and thereby which aspects of the things) to consider relevant in realizing
what actually ‘is the system’. A system type comprises:

  * •

Properties determining ‘the nature’ of the systemic properties, for example
for open active systems that the system is seen as something that changes
things in the domain of the environment and that the environment is seen as
changing things in the system domain. This set of properties may be called the
_system characteristic_.

  * •

Properties determining the kinds of things which are relevant to incorporate
in the exposition of the system domain, and for each kind the kinds of roles
they may play in respect to the potential kinds of systemic properties.
Examples of such kinds of things are for dynamic systems: states, transitions
and transition occurrences, and for open active systems (among other things):
actions, subjects, agents, transitions in the domain of the environment caused
by actions in the system, etc. This set of properties may be called the
_exposition characteristic_.

A more detailed elaboration of concepts related with the system viewing
process can be found in [1998-Lindgreen-FRISCO]. A semi-formal description of
it based on an example is presented in [1992-Lindgreen-SemanticStructures]. In
conceiving a domain as an organization, several classes of element may be
relevant to include in a system-exposition of that domain. As part of the
domain it may also be relevant to incorporate a number of concepts generally
relevant in an organizational context, for example public services, laws or
other kinds of constraints imposed by society, or aspects of the particular
professional field of the organization. However, for an organization it is
generally relevant to consider the following kinds of things as candidates to
(at least) be included in a system-exposition: [Actors] human actors as well
as artificial actors and all kinds of symbiotic compositions of these two
kinds. [Actions] (together with the associated goals) such that a (not
exclusive) distinction is made between those influenced by impressions from
the environment and those either directly constituting expressions of the
system or only contributing to (or in some cases even explicitly
counteracting) the expressions. Actions that are irrelevant for the expression
of the system should be ignored in the exposition. [Co-actions] i.e. co-
ordinated actions performed by several actors together. [Knowledge] that is
necessary for the actors to know the relevant pre-states of their actions and
the respective goals. A goal may be situation dependent. [Triggers] involving
internal and/or external dynamic criteria for the initiation of actions
(temporal, impressive and actor- or action-caused transitions).
[Communication] between actors to ensure that they have the information
necessary to perform their actions. [Representation] of the
information/knowledge relevant to the organization’s activities, in order to
enable the preservation or communication of it. That includes all relevant
aspects of the use of data technology and/or data-technical sub-systems to
accomplish the preservation or communication. In practice, aspects of
organizational culture, social norms, empation (i.e. knowledge that cannot be
properly represented), resources in general (energy, skills, intellect, etc.),
ecology, economy, etc., may be added to this list.

###  Classes of systems

A work-system, a organization, as well as an information-system belong to a
system type that primarily is characterized as being open and active (where
the latter implies also that it is dynamic). We can define these specific
types of system as: active-system dynamic-system open-system Note that a
system may be active and yet be non-dynamic. For example, the mere presence of
a dummy speeding camera, i.e. one that is not able to capture speeding
vehicles on film, may lead drivers to drive more slowly. The dummy speeding
camera may thus be seen as an active-systemactive, yet non-dynamic, system.
Note that the sub-system of an open-active-system does not have to be an open-
active-system. In other words, even though our main interest lies with open-
active-system, we may quite well need to consider non-open or non-active sub-
system of these system. For open-active-system – therefore for organization
too – it is relevant to consider the following. The behavior of an open-
active-system is generally reflected as:

[Internal function] conception of changes in the system domain caused by
processes in the domain itself. [External function] Here the following two
kinds are distinguished:

[Impression] conception of changes in the system as caused by the environment.
[Expression] conception of changes in the environment as caused by the system.

The very fact that something is regarded as a system often serve the purpose
of hiding the internal function and focus on the external function. (Like the
phrase “a black-box system”). The internal function of an open-active-system
is referred to as “the function _in_ the system”, while the external function
is “the function _of_ the system”. The latter is equivalent with the systemic-
property of an open-active-system. One can classify open-active-system in
several ways according to their behavior (for details see [1971-Ackoff-
SystemConcepts]). Here we shall only distinguish between three kinds of open-
active-system based on the following distinctions. A reaction of an open-
active-system is an expression that is seen as unconditionally caused by an
impression. An action of an open-active-system is an expression that is seen
as being completely independent on any kind of impression. Thereby we can
define the three additional types of open-active-system: reactive-system
responsive-system autonomous-system As mentioned before, in [1999-Alter-
WorkSystems, 2002-Alter-WorkSystems] Alter defines a work system as:

> A work system is a system in which human participants and/or machines
> perform business processes using information, technologies, and other
> resources to produce products and/or services for internal or external
> customers.

where _information systems_ are to be regarded as special classes of work
systems. We will therefore operate under the assumption that we have the
following hierarchy of systems:

  1. 1.

Systems in general.

  2. 2.

Open active systems: Subclass of systems

  3. 3.

Work systems: Subclass of open active systems.

  4. 4.

Organizational systems: Subclass of work systems.

  5. 5.

Information systems: Subclass of work systems and a sub-system of
organisational systems.

  6. 6.

Computerised information systems: Subclass of work systems and a sub-system of
information systems.

Based on [1998-Lindgreen-FRISCO] and [1999-Alter-WorkSystems], we can provide
the following stacked set of definitions: work-system organizational-system
computerized-information-system information-system

##  3 Dealing with evolution of conceptions

Before concluding this chapter, there is one final issue to deal with. An
organizational-system is an . This specifically means that it is a system
which changes over time. Thus far we have taken the assumption that the
conception of a viewer is a static notion. If we write $\Conception{U}{v}{C}$
it really means that viewer $v$ has _at some point in time_ the conception $C$
when observing (a part of) universe $U$. However, in the course of time this
conception will evolve, which raises the question: _How to deal with evolution
of conception?_. 6cmModeling evolution by snapshotssnapshots Several
strategies exist to deal with evolution [1994-Proper-EvolvConcModels]. One
strategy to deal with this evolution is to take snapshots, like photographs,
of a viewer’s conception. This leads to the situation depicted in figure
LABEL:snapshots. This approach, however, does have as drawback that one cannot
‘trace’ the evolution of a specific element in a viewer’s conception. The
approach we take, therefore, is illustrated in figure LABEL:evolution1.
6cmModeling evolution by functions in timeevolution1 Based on the approach
taken in [1994-Proper-EvolvConcModels], the evolution of the element in a
viewer’s conception is treated as a set of (partial777For a discussion on the
difference between total and partial functions, see appendix LABEL:ch:Math.)
functions over time. At each point in time, a specific element (a version) may
be associated to such a function. This means (as also illustrated in figure
LABEL:evolution2), the situation depicted in figure LABEL:snapshots can still
be derived. When we know the entire evolution of a nation, we can also provide
a detailed descriptions of the state-of-affairs as it holds at any arbitrary
point in time. 6cmDeriving snapshotsevolution2 In order to introduce the
notion of evolution formally, we first need to define a time axes. We presume
all viewers to agree that the time axes (at least) consists of:

  * •

A set of points in time TimePoints.

  * •

A complete and total order Later.

We also define: $t_{1}\LaterEq t_{2}\EQ t_{1}\Later t_{2}\lor t_{1}=t_{2}$.
Since we have a complete order on the points in time, we can define the
relation $\Next\subseteq\TimePoints\times\TimePoints$ with intended intuition:
if $t_{1}\Next t_{2}$, then $t_{2}$ is the next point in time immediately
after $t_{1}$. Formally, this relation is defined as:

$\SymbolDefinition{Next}$

As, $\Later$ provides a _complete_ and _total_ order, for a given $t_{1}$
there is always at most one $t_{2}$ such that $t_{1}\Next t_{2}$: single-next
$t_{1}\Next t_{2}\land t_{1}\Next t_{3}\implies t_{2}=t_{3}$ As a result, we
can actually view $\Next$ as a function: $\Next:\TimePoints\Func\TimePoints$
and write $\Next t$ as an abbreviation for: the unique $t^{\prime}$ such that
$t\Next t^{\prime}$. The evolution over time of an element from a conception,
can now indeed be modelled formally as a function:
$h:\TimePoints\PartFunc\Elements$. By means of $h(t)$ we obtain the “version”
of the element’s evolution as described by $h$ at point of time $t$, while
$h(\Next t)$ would yield the version at the next point in time. These
functions, which represent an element’s evolution, will be referred to as
_element-evolution_. This also requires us to think of the element in
$\Elements$ as the possible _versions_ an element-evolution may take on.
Whenever we need to emphasize this, we shall therefore use the term _element-
version_. element-evolution are _partial_ functions, which means that they are
not required to be defined for all points in time. In other words, at some
point in time an element-evolution may not have an element-version associated,
which really means that the element-evolution does not exist yet at that point
in time (it has not been born yet), or that it has ceased to exist (it died).
In other words, element-evolution are allowed to be re-born. We could, for
example, have a situation where: $h$ is an element-evolution, $t_{1}\Later
t_{2}\Later t_{3}$ are points in time, while:
$\DefinedAt{h}{t_{t}}\land\lnot\DefinedAt{h}{t_{2}}\land\DefinedAt{h}{t_{3}}$888Please
refer to appendix LABEL:ch:Math for an explanation of the notion used.. The
set of all element-evolution is defined as: ElementEvolutions, in other words
the set of partial functions from the time axes to the possible element-
version. The evolution of an entire conception can then be represented
formally as a set of element-evolution. In other words: ConceptionEvolutions.
To formally express the fact that $H\in\CEvolutions$ is a conception of viewer
$v$ for universe $U$, we will write $\Conception{U}{v}{H}$. 6cmAn element
evolution migrating from the environment to the domainelement-migration If
$H\in\CEvolutions$, then we will use as abbreviation: $H(t)\EQ\Set{h(t)}{h\in
H}$, yielding the entire “state” of $H$ at time $t$. If $H$ is a conception of
some viewer, then each of the states should be a valid conception: S If
$\Conception{U}{v}{H}$, then: $\Al{t\in\TimePoints}{\Conception{U}{v}{H(t)}}$.
Similarly, to $\Conception{\\_}{\\_}{\\_}$ we want to extend
$\DomainInEnvironment{\\_}{\\_}{\\_}{\\_}{\\_}$,
$\ModelInEnvironment{\\_}{\\_}{\\_}{\\_}{\\_}$ and
$\SystemInEnvironment{\\_}{\\_}{\\_}{\\_}{\\_}$ to deal with evolution as
well. We might, for example, view
$\DomainInEnvironment{U}{v}{H_{C}}{H_{E}}{H_{D}}$ to means: viewer $v$ has a
conception-evolution $H_{C}$, environment-evolution $H_{E}$ and domain-
evolution $H_{D}$ of universe $U$, where $H_{D},H_{E}\subseteq H_{C}$. The
difficulty with this is that an element-evolution might start out as being in
the environment, but might evolve _into_ the domain, or vice versa. This is
illustrated in element-migration. To properly deal with such evolution, we
will need to regard $H_{E}$ and $H_{D}$ as a classification of the element-
evolution from $H_{C}$ at each point in time. In other words as functions:

$H_{E},H_{D}:\TimePoints\Func\Powerset(H_{C})$

yielding the set of conception-evolution from $H_{C}$ that are part of the
environment/domain respectively at a given point in time. This means that
$H_{E}(t),H_{D}(t)\subseteq H_{C}$ are sets of element-evolution, while
$H_{E}(t)(t)$ and $H_{D}(t)(t)$ yield the actual environment and domain as it
holds at $t$. For this we have: bound-environment-domain If
$\DomainInEnvironment{U}{v}{H_{C}}{H_{E}}{H_{D}}$, then:
$\Al{t\in\TimePoints}{H_{E}(t)(t)\subseteq H_{C}(t)}$ and
$\Al{t\in\TimePoints}{H_{D}(t)(t)\subseteq H_{C}(t)}$. Note: the same would
hold for $\ModelInEnvironment{U}{v}{H_{C}}{H_{E}}{H_{D}}$ and
$\SystemInEnvironment{U}{v}{H_{C}}{H_{E}}{H_{D}}$. In each case, the states of
the evolutions should be valid conception/environment/domain as well:
Scorrect-snapshots If $\DomainInEnvironment{U}{v}{H_{C}}{H_{E}}{H_{D}}$, then
$\Al{t\in\TimePoints}{\DomainInEnvironment{U}{v}{H_{C}(t)}{H_{E}(t)(t)}{H_{D}(t)(t)}}$
S If $\ModelInEnvironment{U}{v}{H_{C}}{H_{E}}{H_{D}}$, then
$\Al{t\in\TimePoints}{\ModelInEnvironment{U}{v}{H_{C}(t)}{H_{E}(t)(t)}{H_{D}(t)(t)}}$
S If $\SystemInEnvironment{U}{v}{H_{C}}{H_{E}}{H_{D}}$, then
$\Al{t\in\TimePoints}{\SystemInEnvironment{U}{v}{H_{C}(t)}{H_{E}(t)(t)}{H_{D}(t)(t)}}$
Adding evolution of conception to our ontology from figure LABEL:ontology2,
leads to the refinement of our ontology to the situation as depicted in figure
LABEL:ontology3. 13cmOntology with evolution addedontology3 Mainly due to non-
overlapping-domain-environment, we have: non-overlapping-evolution If
$\DomainInEnvironment{U}{v}{H_{C}}{H_{E}}{H_{D}}$, then:
$\Al{t\in\TimePoints}{H_{E}(t)(t)\intersect H_{D}(t)(t)=\emptyset}$ Even more
specifically, we have: non-overlapping-evolutionsets If
$\DomainInEnvironment{U}{v}{H_{C}}{H_{E}}{H_{D}}$, then:
$\Al{t\in\TimePoints}{H_{E}(t)\intersect H_{D}(t)=\emptyset}$

##  4 Conclusion

In this chapter we have taken a highly fundamental and formal outlook on
information systems, organizations and work systems, and the way they are
modeled, including their decompositions and evolutions.