Saturday, 23 May 2020

The Fundamental Concepts of Modelling Langauges

Abstract

This report looks to understand the fundamental concepts of modelling and how it can then be used in a business. This was done with a series of rational arguments from a set of definitions and axioms through a set of propositions and finally a conclusion. It finds that a model must necessarily be created from information, processes, systems and relationships. That none of those concepts could be removed from a model and each of them must be made specific in order to deliver in an environment with finite resources. The opening argument looks at if a model can be developed using process alone. This is invalidated by the necessary join between process and information within physics and linguistics. A second proposition looking at only information to model a business is invalidated for the same reasons. Next a view of creating a model with only information & process is proposed but this cannot work as it creates models with no concept of agency. The concept of a system is added alongside information and process but there is no means of joining those concepts together and therefore a model that offers completeness in its description of something cannot be created. Finally, a proposition that says a model must contain information, process, systems and relationships is proposed and no compelling counterarguments to this proposition have been found. Building upon that there is the view that because each of those concepts necessarily has relationships that there are interfaces. Those interfaces have the potential to be affected by noise and therefore must be controlled. As each modelling language has to make each of these concepts specific in order for efficient delivery it will necessarily bias itself towards certain technological architectures. Practitioners and managers alike should be aware of each of the true propositions when assessing an existing modelling capability or when looking to develop a modelling capability.

Introduction

We all live in a world where we must work and communicate with a vast array of people and an ever-increasing number of electronic systems. Each one of those people and systems have their own way of understanding the world which when grouped together are forced to develop common forms of communication often termed languages. Beyond the natural languages such as English, Russian and Chinese to name but a few there are also languages developed artificially to support the world of business and technology. These languages used by professionals such as business analysts, enterprise architects, software developers and managers, describe the world in the past present and future. They do not however all speak the same language and as such, there is the potential for miscommunication.

This report looks to understand the fundamental concepts underpinning the languages of each of those professions use to work. To be able to convey that understanding to give each of them a more sophisticated means of communicating, as well as offering guidance on how managers can understand their businesses modelling capabilities and conduct the necessary analysis to improve their business’s performance.

The report covers basic background research done into how different models try to describe the world as well as efforts to draw together meta-models of those as well as the steps taken to prepare this report. It uses three specific modelling languages used by different professions to ensure the concepts exist in multiple languages each with a different purpose. The selected languages are ArchiMate which is used by enterprise architects, Business Process Modelling Notation which is used by managers & business analysts and Uniform Modelling Language is used primarily by software engineers.

The core structure of the report is based on Ethics by Spinoza. This looks to give the definitions of each of the fundamental concepts that are unique and independent. Then a set of axioms, accepted truths, that all models must adhere to. Then a set of propositions that look to link the concepts together and align them with the axioms put forth.

An evaluation into the limitations of the work will then be performed. Followed by a conclusion wraps up each of the propositions caveat it against any noted issues from evaluation.

Preparation

In order to devise the fundamental concepts of modelling an approach was taken to understand a few different business domains. To select a modelling language from each of the domains, with the chosen domains being process modelling, architecture and software engineering.

Then to draw out the concepts conveyed in each and to generalise them. Those general concepts would then need to be validated and defined using knowledge beyond each of the original modelling languages. To do this each concept will be looked at from a colloquial, philosophical, and scientific viewpoint. In order to gain a viewpoint within the time available, high-level summary articles will be sought, viewpoints could be refined in the future with more detailed research.

The structure of the report was selected before the key concepts were gathered. That structure is mentioned in the introduction taken from a philosophical work that aims to understand fundamental concepts of the universe which parallels the arguments made within this report but at a different level of abstraction. With the structure already selected and based around a logical series of propositions, the debate behind each of those propositions is what guided the next stage of research.

Any questions raised about the definition during the investigation into each proposition would mean going back to the start, reworking the definition and then revisiting each of the propositions. This process was repeated until none of the propositions were invalidated.

Selected Model Descriptions

A description of the selected modelling languages and their purpose.

ArchiMate

ArchiMate is a modelling technique ("language") for describing enterprise architectures. It presents a clear set of concepts within and relationships between architecture domains and offers a simple and uniform structure for describing the contents of these domains. [1]

ArchiMate is primarily used by an enterprise, business and solutions architects trained within the open group’s framework and has tools that support its use alongside TOGAF (an architectural framework).

Business Process Modelling Notation

“The Business Process Modelling Notation (BPMN) is a graphical notation that depicts the steps in a business process. BPMN depicts the end to end flow of a business process. The notation has been specifically designed to coordinate the sequence of processes and the messages that flow between different process participants in a related set of activities.

BPMN is targeted at a high level for business users and at a lower level for process implementers. The business users should be able to easily read and understand a BPMN business process diagram. The process implementer should be able to adorn a business process diagram with further detail in order to represent the process in a physical implementation. BPMN is targeted at users, vendors and service providers that need to communicate business processes in a standard manner.” [2]

Uniform Modelling Language

“The OMG's Unified Modelling Language™ (UML®) helps you specify, visualize, and document models of software systems, including their structure and design, in a way that meets all of these requirements. (You can use UML for business modelling and modelling of other non-software systems too.)” [4]

The Uniform Modelling Language is primarily designed for the development of software as stated above in an object-orientated fashion. This means it focuses on how it describes objects, called classes, that are capable of executing functions and storing data. This will be primarily used by software engineers in developing coded applications although UML can be repurposed as a business modelling language. It does not prescribe to any particular methodology to develop the models, those have to be developed separately.

Definitions

Definition: A statement of the exact meaning of a word.

Each of the definitions below are aiming are for unique and independent concepts found in current business modelling languages and validated with colloquial, philosophical and scientific viewpoints. The detail for each definition is aimed at lending understanding to the reader as well as some general properties about the concepts. Those described properties will then be used to understand how each of those independent concepts interrelate in a model.

Def1: Information

There is great difficulty in understanding what information is because of the plethora of definitions and the fact a lot of them are bound in specific contexts for example Data being defined as ‘quantities, characters or symbols on which operations are performed by a computer’. The first section is fine however ‘performed by a computer’ adds a constraint that is plainly wrong. It is perfectly possible for a human to perform the same operations on data that a computer does.

Data: facts and statistics collected together for reference or analysis or the quantities, characters or symbols in which operations are performed by a computer, which may be stored and transmitted in the form of electronic signals and recorded on magnetic, optical, or mechanical recording media [2]

This gets more confusing when the Definition of information is thrown in as a synonym of data and thus allows the two to be used interchangeably.

Information: facts provided or learned about something or someone or data is processed, stored, or transmitted by a computer [3]

What each definition agrees upon is that information is a thing, a noun in language terminology. That information has the ability to describe something and that description can be made up of a variety of characters, symbols or numbers. Those descriptions fit into one of five categories: natural language, optimal codes, numbers, physics and logic. [4]

Each of those types of information have their own areas of research and understanding however they generalise into two types, Information that has semantic meaning and information without semantic meaning. Information without semantic meaning can be measured in bits. Where a bit has a state that is either true or false. Each of the five categories of information can be written using a collection of bits. [5]

semantic information cannot be measured however in order to be represented and communicated it has to be put into a form that is communicable. That communicable form is always one of the non-semantic information types.

This leaves us with information as a thing of the fixed state that can convey a description. That there may be many interpretations of a set of information but in that information has to be represented by a fixed number of bits, structured using a natural language, optimal codes, numbers, physics or logic.

There remains a final and complex point. Information being something that can describe means that the description of information is itself information. Although non-semantic information can break down to the fundamental level of bits, it is possible for us to describe what bits are using bits, meaning we can continue within that particular loop forever. Understanding how exactly this can happen is unimportant but understanding that information is capable of self-reference is.

Information: a thing of state that can describe, often represented using symbols, numbers and code in a language and measured in bits.

ArchiMate

“Structure elements are the strategic element resource, and structural elements, which can be subdivided into active structure elements and passive structure elements” [7]

Information within ArchiMate that relates closest to our description of Information is the noun based elements within the ArchiMate model. There are two types of structure active and passive as you’ve seen in our investigation into information so far it is prescribed no agency of its own therefore it is the passive structure element that aligns with our view of information.

“A passive structure element is a structural element that cannot perform behaviour. Active structure elements can perform behaviour on passive structure elements. Passive structure elements are often information or data objects, but they can also represent physical objects.”

ArchiMate may differentiate between physical, logical or conceptual objects within its model but the general definition lines up with our view that information is the stateful concept of description, and has no agency of its own.

Business Process Modelling Notation

“Data Objects provide information about what activities require to be performed and/or what they produce, data objects can represent a singular object or a collection of objects.” [8]

BPMN suffers from the information/data confusion mentioned earlier though at this point it places information as a component of data. This does not invalidate our views as we have already pointed out that is possible for information to describe information especially when the information has a semantic meaning which is not attached to the limitations of the physical world.

Uniform Modelling Language

“A classifier describes a set of objects. An object is an individual state and relationship to other objects. The state of an object identifies the values for that object of properties of the classifier of the object.” [9]

In UML classifiers are a describable thing. As UML was created to allow the models to create software, a classifier acts as a description of a possible set of objects. Classes can contain functions, our view of information within UML would be for classes without functions. Within a model, these would usually be represented by an entity-relationship diagram. This would then hold to the view looked at earlier and seen in the other modelling languages that information is that which can be described and remains in a fixed state unless acted upon. There is also inbuilt in the definition the self-referencing required the concept of information. In this case, a classifier describes an object and an object is a group of properties/attributes which could be represented within a computer by bits.

Def2: Process

Process suffers from a similar fate to data and information as it can be expressed with a multitude of words. Such as procedure, activity, task and operation which are but a few of the other possible words that fit within the same definition.

Process: series of actions steps taken in order to achieve a particular end [10]

Each of these words are verbs that convey the concept of change, each one breaks down into a subset of instructions that take one state of the world and turn it into another. We can, therefore, take two things, one process is something that changes the state of things, two it can be broken up into a series of smaller changes which are often seen as instructions or action steps or tasks. That breakup should be seen as self-reference, the same concept of change can be decomposed. This avoids defining change as a hierarchy of different words that all have the same meaning.

Process unlike information has less exact philosophical or mathematical constructs or at least vaguer more rational approaches. Process is often given different names usually the names of the discipline themselves which are often seen as the process or undertaking of discovering something or expanding our knowledge about the world. For example, business is the process making exchanging goods and services for money. [11]

Within science, General Relativity, and Quantum theories both contain the concept of change, generally measured using time, of course, change within those mathematical models is not related to just time but time is the process of change that we experience and can most easily relate to.

Within each of the models, the concept of change was looked for and separated where possible from the thing it changes or the thing that performs the change. Each of these definitions should ideally be able to be decomposed into smaller concepts of change.

The colloquial, scientific and modelling languages use of process all align fairly closely as a change to something that can be broken down or compounded into larger or smaller chunks of change. Where change is something done to a state to move it to another state.

Process: Means of changing a state.

ArchiMate

“This generic metamodel fragment consists of two main types of elements: structure (‘nouns’) and behaviour elements (‘verbs’)” [7]

The highest level concept of change within ArchiMate is what it terms behaviour elements. These like our analysis align with verb like concepts that are considered to bring about change.

“Behaviour Element: element that represent a dynamic aspect of an enterprise.” [13]

This is expanded further detailing behaviour elements as the dynamic aspect of an enterprise, the piece of the business that is capable of changing. How that change is broken up is not mentioned.

“Process: a series of behaviours that achieve a specific outcome.” [14]

The lowest level definition of change is process, which aligns with our view of change including self-reference. This is shown by the fact the process is broken up into a series of behaviours that achieve a specific outcome. Which aligns almost exactly to our view of the concept change from one state to another that can be broken down into smaller concepts of change.

Business Process Model Notation

“A process depicts the interactions between two or more business entities. These interactions are defined as a sequence of activities.” [15]

Once again, we can see a concept of change performed to a stateful thing and that this change can be broken down into smaller concepts of change.

“An activity is a generic term for work that a company performs.” [16]

“A Task is an atomic activity that is included within a process. A task is used when the work in the process is not broken down to a finer level.” [16]

The same effect can be seen to go down another two levels from the definition of process through activity all the way to task, that considered to be atomic although tasks are defined as a set of steps. The fact that any business model has to avoid trying to describe things infinitely is an unnecessarily confusing part of many models.

Uniform Modelling Language

“Behaviours. A behaviour describes a set of possible executions. An execution is a performance of a set of actions (potentially over some period of time) that may generate and respond to occurrences of events, including accessing and changing the state of objects” [9]

The highest level within UML ‘s behaviours is the concept of change that acts upon a state, in this case objects, and can be broken down into smaller units of change described as executions. Multiple levels of change is shown further in the way that executions can be broken down into actions.

Def3: System

System, as a concept, unlike process and information doesn’t suffer from a multitude of terms but it does suffer from a general vagueness. There are a huge number of fields that happily use the word system but very few define exactly what they mean by it. Generally, the meaning of system within any particular piece of work is considered to be implicit.

System: a set of things working together as parts of a mechanism or an interconnecting network; a complex whole [16]

Given that no scientific or philosophical consensus exists regarding what a system is. One of the many fields that define systems is Cybernetics, which builds on the general theory of communication and looks to understand interaction and control within animals and machines. The view in cybernetics on systems links to the colloquial understanding, a set of things that form a complex whole. As a multidisciplinary field Cybernetics looks to see if issues in both machines and animals can be compared. The central idea is that both animals and machines are the same thing and that the actions or mechanics of both things are therefore comparable.

“Computing machines are essentially machines for recording numbers, operating with numbers, and giving the results in numerical form.” [17]

The quote above places machines as things that operate on information that is given to them and that can provide a response back out again. if we take animals and machines as the same and say that they are capable of taking in information, changing information, storing information and outputting information. All of these actions on information also indicate that systems are capable of change and therefore of performing or being a part of processes. Systems are characterised as black and white boxes.

”Blackbox and white box are convenient and figurative expressions not very well determined usage. To understand by black box a piece of apparatus which performs a definite operation on the present and past of the input potential, for which we do not necessarily have any information of the structure by which this operation is performed. On the other hand, white box will be a similar network in which we built in the relation between input and output potentials in accordance with a definite structural plan for securing a previously determined input-output relation.” [17]

The explanation above again gives the view of a thing that can take in information perform processes and output information. This makes it a grouping of both, in the white box the internal processes and information can be understood and in the black box they remain a mystery but the interfaces can be understood. This can align with the colloquial definition of system a collection of things that we can refer to as a complete whole that perform actions or at least take part in processes.

System: a group of descriptive states capable of internal and external change that can be prescribed with agency

ArchiMate

“Active structure elements are the subjects that can perform behaviour. These can be subdivided into internal active structure elements; i.e., the business actors, application components, nodes, etc., that realize this behaviour, and external active structure elements expose this behaviour to the environment. An interface provides an external view on the service provider and hides its internal structure.” [18]

ArchiMate describes a system in terms of active structure elements that are capable of performing behaviour, they also can act as an interface a point of transferring information from one place to another. It differentiates between active structure elements that are considered to be inside the model and those that exist beyond the model or indeed the business.

Business Process Modelling Notation

“Participant: A business entity (e.g., a company, company division, or a customer) or a business role (e.g., a buyer or a seller) that controls or is responsible for a business process. If Pools are used, then a Participant would be associated with one Pool. In a Collaboration, Participants are informally known as “Pools”.” [19]

The concept system within business process modelling notation realised by a participant. Participants always interact with one another or information via process or messages.

Uniform Modelling Language

“A model is always a model of something. The thing being modelled can generally be considered a system within some domain of discourse. The model then makes some statements of the interest about that system, abstracting from all the details of the system that could possibly be described, from a certain point of view and for a certain purpose. For an existing system, the model may represent an analysis of the properties and behaviour of the system. For a planned system, the model may represent a specification of how the system being modelled is to be constructed and behave.” [9]

As seen previously classifier is within UML are capable not only of storing information but also performing functions. This lines up with our definition of a system being able to store information also be an agent of change. There is also an alignment with UML’s definition of a model as something that store state and is capable of internal and external change.

Def4: Relationship

Each view of relationships including the colloquial generally looks at how a collection of similar or different concepts join our link together.

“Relationship: the way in which two or more people or things are connected, or the state of being connected” [20]

A very formal definition of relationships is to use logic, that makes statements about the relationships between concepts. The mechanics of logic form the underpinnings that allow us to understand the grammars of natural languages, mathematics and physics.

“At their most basic, logic is the study of consequence, and information is a commodity. Given this, the interrelationship between logic and information will centre on the informational consequences of logical actions or operations conceived broadly” [20]

Now unlike process, logical action is not one of state change but one that asserts a link between two pieces of information to be true or not. For example, we could have a relationship logic of ‘A is in B’ which when filled out could be the ‘page is in the book’. Stating that a piece of information links to another piece of information and not at any change or process has been performed on either piece of information.

 

Relationship: A connection or link between concepts

ArchiMate

“relationships, each of which can connect a predefined set of source and target concepts (in most cases elements, but in a few cases also other relationships). Many of these relationships are ‘overloaded’; i.e., their exact meaning differs depending on the source and destination concepts that they connect.” [19]

ArchiMate uses a wide range of relationships which as defined above created using a source and target for any type relationship. When compared to a definition we see both align as a link between concepts.

Business Process Modelling Notation

BPMN again makes use of relationships and has different types depending on the relationship between information and flow objects or flow objects with other flow objects. Flow objects, in this case, being a process, activity or task.


Figure 1 Example Process flow with Associations, Sequence flows and Message Flows. [22]

Primarily sequence flows, the solid black lines with arrows on the end go-between each activity boxes and convey the order in which those activities should take place. Associations, the dotted lines between each activity. The data objects are visualised as letters. [22]

Uniform Modelling Language

“Association is a relationship between classifiers which is used to show that instances of classifiers could be either linked to each other or combined logically or physically into some aggregation.” [9]

The same is seen in UML where associations are used to link classifiers to one another.

Def5: Model

A model will be a collection of concepts where the rules by which those concepts relate to one another are defined by a language. This can be seen across topics mentioned before such as logic, mathematics, physics and natural languages.

“Model: A simplified description, especially a mathematical one, of a system or process, to assist calculations and predictions.” [20]

The specific science of philosophical view of models generally align directly with the colloquial definition from the dictionary given above. Model will serve as a simplified description of something. Within this particular piece of work those somethings will be concepts as is looked at within the definitions chapter.

Model: a group of concepts that form a description of something as defined by a language.

ArchiMate

“A collection of concepts in the context of the ArchiMate language structure.” [20]

This definition is similar to the one given in ArchiMate, where we can see that a collection of concepts grouped together using the rules of the language can describe a particular context.

Business Process Modelling Notation

There is no specific definition of a model is given within the BPMN specifications.

Uniform Modelling Language

“A model is always a model of something. The thing being modelled can generally be considered a system within some domain of discourse. The model then makes some statements of the interest about that system, abstracting from all the details of the system that could possibly be described, from a certain point of view and for a certain purpose. For an existing system, the model may represent an analysis of the properties and behaviour of the system. For a planned system, the model may represent a specification of how the system being modelled is to be constructed and behave.” [9]

Less concise than the ArchiMate definition but it speaks along similar lines. That a model is describing something. That something is detailed in a collection of concepts that have a particular purpose or viewpoint. It should be noted that the particular purpose or viewpoint has not been added to our own definition. This point is considered as an additional property that may or may not be necessary. The answer to which is looked at later in this document.

 Axioms

Axiom: A statement that is taken to be true, to serve as a premise or starting point.

As the definition states above each of these are to give a starting point to the propositions. They said the high-level limits by which each of the conclusions of the propositions must have dealt with.

Ax1: Models must reflect and move with the Zeitgeist

This axiom is hopefully the easiest to argue for. Views and understanding within philosophy and science and business should move with one another. An extreme example of this is the following: Currently, it is not compelling to build into any business case a means of persuading Poseidon for less storms and a larger yield on fish. More recently as the rise of technology perform roles used to be work by people, in a competitive world it does not pay to stick to tradition.

“The despotism of custom is everywhere the standing hindrance to human advancement, being in unceasing antagonism to that disposition to aim at something better than the customary” [22]

As per above by John Stuart Mill if we no longer have reasons for holding of you in that view has become custom, we should do everything we can to understand the views we have and if we no longer have reasons to understand those views then we should look to replace them. Or as put by philosopher Bob Dylan “The times they are a changin“.

Ax2: Concepts are infinite

The definitions given for information, process, systems and relationships have all been done to be independent of one another and based on philosophical, scientific and colloquial knowledge. As concepts , within our imagination, they are able to continuously break down and compound with no limit. Just like the scene with the information that can describe information and the process that can be broken down into processes there also seems no reason why our model cannot contain each of the concepts discussed breaking down infinitely and interacting infinitely between themselves.

This does not mean that this is not a problem or at least something to consider when looking through and arguing all is fundamental to a model but it seems like something that is necessary to point out in order to propose means of solving it.

Ax3: Money, Time & Resource are finite

Businesses are constrained by the amount of money, people and resources available to them. This means that any endeavour to model businesses will be subject to the same limitations.

Any pragmatic view on developing a model must necessarily take heed of the fact that there is not an infinite amount of time people money and resource to perform that endeavour. Modelling languages and practitioners are therefore looking at the balance between the infinity of concepts that encompass the best possible understanding of the world for the least amount of money time and resource.

Propositions

Proposition: A statement or assertion that expresses a judgement or opinion.

Each of the propositions below is targeted at leading the reader to a conclusion via a series of propositions about the fundamental components of a model. Each proposition is an argument that may reference others in order to build upon a growing theme.

Prop1: Process alone can model a business (FALSE)

Could a model of a business be constructed from process alone? As we have seen our definition process is “Means of changing a state.”. A cursory glance at physics will point out to us that change alone is not possible.

“General relativity tells us that what we call space is just another feature of the gravitational field of the universe, so space and space-time can and do not exist apart from the matter and energy that creates the gravitational field.” [22]

As we noted with our first axiom models should align and take understanding from the best view we have of the world at the time. It would seem that not only can our latest models of the universe from physics that process does not exist alone furthermore it is intertwined with physical substance in the form of space-time.

Should this example not be compelling or considered too high-level an example closer to how we operate on a daily basis comes from natural language as documented by linguistics. Within linguistics, our natural languages are categorised according to their basic word order which is constructed from (subjects, verbs and objects).[22]

Within the field of linguistic typology, there have been searches for asymmetric languages that do not follow or miss a particular part of the SVO construct, this however has only ever been seen with certain types of object/subject missing but not every kind of object/subject. [23] It would seem that the concepts of change cannot exist independently from concepts of state.

The model most likely to exist on change alone is BPMN which despite having a limited ability to model data objects, messages and participants it still keeps these constructs within its model. Both ArchiMate and UML have concepts other than just process within their language. All this invalidates the initial proposition, process alone cannot model a business.

Process alone cannot model a business.

Prop2: Information alone can model a business (FALSE)

Given the model could not be constructed from process alone. Is it impossible to construct a model from information alone where information is “concept of a thing of state that can describe, often represented using symbols, numbers and code in a language and measured in bits”?

The same arguments can be applied as shown above, because as it was pointed out that the concept of change in time is inextricably linked to space. Given that space is physical and information is used to describe physics then the fact that within those models of physics, state and change cannot be separated the same would apply to information’s ability to separate itself from process. [25]

The view of linguistics is similar, there are examples of languages without certain types of verb but they do not lack every type of verb. This time pointing out that information or things of state are also stuck with process. [27]

Only one of the modelling languages allows for a model to be constructed of only information, that model being UML. An example of which can be seen below.


Figure 2 Boxes = Entity, Lines = Relationships, Colours = Domain

There are two major issues presented to a proposition within the diagram above. The first is that despite this being a collection of entities we still require another concept to explain it. In this case, the concept being a relationship, although as we have already said information can be self-referencing the modelling language itself requires a relationship to demonstrate how each of these objects relate. The second issue is that these diagrams are used most commonly to structure information within a database for example SQL Server. Within SQL Server that data model is interacted with using a query language that allows you to create, read, update and delete from each of those entities.

From a technical point of view then it is important to understand the processes that interact with the information modelled above are still required and from a business point of view it would also be important to know who or what owns and manages the information modelled. Therefore, information alone cannot model of business and proposition once again is incorrect.

Information alone cannot model a business.

Prop3: Process & Information can Model a business (FALSE)

Given that Prop1 (Process alone cannot model of business) and Prop2 (Information alone cannot Model a Business) then perhaps the two together can. Leading to propose that process and information can model a business.

Within Cybernetics based on the general theory of communication, there are objects that perform processes but also objects that process & store information. This encapsulates the description given before of Black boxes and white boxes. Now although process and information can describe each of those boxes thus far we have no concept of grouping the two together. Furthermore, our definitions of processing information do not allow for agency or the idea that a thing is capable of acting of its own volition. Process does not cover this because it is merely the concept change and going from state A state B does not require any understanding of what performs a process. Information does not cover this because it is a fixed state unless acted upon and therefore necessarily cannot act upon other states via processes. [16]

In Linguistic, verbs are analogous to process and objects are analogous to information then there remains subject. Although generally, it is possible for the subject to be a verb or object. In the case of the subject playing a semantic role it is considered that the subject has agency which is a property beyond process and information. [28]

ArchiMate has a concept of active structure which is considered to be things that perform processes but also store information. They generally considered as interfaces which do not fit the definition of either a process or information that are the combination of both. In addition, there are also concepts of behaviour which are not merely just process, these include services and functions which are capable of performing processes and are also capable of storing and changing information. [17]

UML’s class is not a process or information even at a potential level, its capable of capturing both

The primary concept within UML is the classifier which does not symbolise process or information it constitutes both of them. This means that the proposition of information and process alone being enough to create a model is false. [8]

The other examples in order then BPNM has within it participants which are neither data objects or processes but are capable of performing processes bus prescribing them agency which again is not covered by process or information. Therefore, process and information alone cannot model of business.

Process & Information alone cannot model a business

Prop4: Processes, Information and Systems can model a Business (FALSE)

Given proposition three (Process & Information alone cannot model a business) the next proposition should support the additional concerns raised. The concept required is that of a system which we defined earlier as “a group of descriptive states capable of internal and external change that can be prescribed with agency”. The addition of system then means that we can say what is using information, what is performing processes. Where those systems could be as stated by Norbert Weiner animal or machine. [16]

There is however an issue with what we’ve just described we have process, we have information, we have systems, we said that somehow it is possible for information to be changed by process, we said it is possible to group information and processes into systems, and finally, it is possible for systems not only be composed of processes and information but to beyond their boundary play a part in processes and interact with external information.

Each of our definitions shown thus far are a concept of change, of state and of a group. None of which allows us to say anything about how particular instances of change, state and group could relate to one another. In our example so far both physics, Cybernetics and linguistics have not only the concepts we discussed but a means of joining them together. In the case of physics and Cybernetics the means of joining those concepts together is played by a series of logical and mathematical statements. Linguistics, on the other hand, has a grammar that denotes the possible relationships between each of the subject-verb-object concepts. [16] [28]

What a model would require in order to join together each of those concepts is a concept of togetherness, a link if you will. This was also covered as one of our definitions, our concept of relationship.

Every single one of three modelling languages, Archimate, BPMN & UML make use of relationships to join process, information and systems. An example from automate shown below which shows how an event leads to a series of processes being started how those processes at least some of them interact with information. There are other examples within every single one of the modelling languages could be sought out the point should be evident enough by now.


Figure 3 Access path example from ArchiMate. How could this be done without relationships? [29]

Concluding this particular proposition we can now say that a business cannot be modelled with processes, information and systems alone.

A Business cannot be modelled with Processes, Information & Systems alone.

Prop5: Processes, Information, Systems & Relationships can model a Business (TRUE)

Propositions 1 to 4 showed how each one of these unique and independent concepts cannot alone describe everything about the model and that they must necessarily all exist for a model to give a complete view of a business.

The first axiom covered that any model must move with the knowledge of the times, this been covered in our initial definitions supported with colloquial, philosophical and scientific examples where each of these concepts exist. Not only that in each of the propositions the falsification of each was achieved with examples from philosophy or science.

This will give us an overall model of models something like the diagram below.

Figure 4 Processes, Information, Systems & Relationships can model a Business.

ArchiMate, BPMN & UML can each have their concepts translated into either process, information, systems or relationships with no exceptions. They will, however, break apart their model as noted when each of them was introduced for specific purposes and to ensure they can offer value rather than being purely an exercise in reasoning.

The second axiom (Concepts are infinite) we noted that concepts without the bounds of reality would be infinite and that any reasonable model should be able to encapsulate infinity. The above diagram indicates how each of the concepts can exist and how they relate to one another and that because each can relate to one another and themselves then there is infinity for each concept and the model in general. For a business, however, this represents a problem as noted in axiom three (Money, Time & Resource are finite) we have finite money time and resource with which we can model. So the proposition that a business can be modelled process, information, systems and relationships are logically correct there is still some further investigation as to how to deal with the infinities presented by the proposition.

Processes, Information, Systems & Relationships can model a Business

Prop6: Models must set Context & Boundaries (TRUE)

In order to take our conclusion from proposition five (Processes, Information, Systems & Relationships can model a Business) and ensure that the conceptual infinity noted in axiom two (Concepts are infinite) can be dealt with in such a way so that it can coexist with axiom three (Money, Time & Resource are finite)) it will be necessary for us to understand the bounds of any particular piece of modelling work and if necessary create a more detailed modelling language from the abstraction from prop5 to ensure that the efforts of modelling provide value to a business.

This can be seen in your examples where specific key trends can be seen to limit the amount of time required to model and also to place complexity into defined boxes. Active structures as noted before used in ArchiMate act as interfaces between the business being modelled and the external world. This forms the first key boundary that each model covers which is between what is being modelled and what is beyond that model. However, depending on the scope of a modelling project it is also possible for internal interfaces between sections of any model to exist. This is particularly prescient when looking at the image below.

Figure 5 Aspects and layers as defined in ArchiMate [30]

The way in which each of the concepts is made more specific or applied to a particular area of the business will depend on the purpose of modelling taking place. The aspects and layers of ArchiMate enable the development of an enterprise, business, application and technology architecture. In doing so the purpose of the model to give a high-level view of each of the areas as well as a means of linking all those areas back together into a single picture is achieved. There are other ways of cutting up the concepts for specific purposes which can be seen in the image below.

Figure 6 UML Semantic Area. [31]

The purpose of our UML models to looking at a predefined area then offers a series of likely models that will be helpful in capturing or showing a particular view of the business based on the purpose that the exercise has initially been given. It would be possible to use each of these UML semantic areas to model each of the aspects and layers of an ArchiMate model rather than the language ArchiMate prescribes.

This offers the ability to understand a set of predefined deliverables they set purpose that is achievable within the finite money, time and resources available to a business and avoid the potentially infinite amount required if a complete model is asked for. It should however not be forgotten that there are core concepts behind a model that should always be considered and known even when those contexts and boundaries are set.

Models must set Context & Boundaries

Prop7: Relationships are affected by noise (TRUE)

The first axiom points out that any business modelling and pay heed to the knowledge and understanding we have of the world at the time. Given that as stated in proposition five (Processes, Information, Systems & Relationships can model a Business) the need for process, information, systems to relate then there are going to-be interfaces. Each of these interfaces will be affected by a concept called noise as defined by Claud E Shannon in the general theory of communication. The model proposed within that theory is shown below.

Figure 7 general schematic of communication [25]

We translate some of the sections figure 7 entire conceptual language we can say that the information source and destination something capable of storing information i.e. system. That the means of moving the information from that source to the target is going to be a process or something capable of realising a process such as a system. Finally, each of the lines on this diagram represents what we would term a relationship and wherever there is a relationship between information and process there is noise. When noise seen as the possibility of information systems suffer from interference or corruption. Interference is an issue with the transfer medium causing loss of information and corruption as an issue with the copying mechanism causing a loss of information.

Within a business context of this means is that once a model is used to change the reality that each of the interfaces on it a be relationships where information, process or systems interact there is the possibility for the information travelling between each of those concepts to be interfered with or corrupted. This means that anyone looking to ensure the best possible model of the business should consider the controls required over certain key interactions in order to mitigate the risks associated with miscommunication.

 

Proposition six (Models must set Context & Boundaries) stated that any modelling language would have to be placed within context boundaries and the boundaries created should also be considered as areas for possible miscommunication. That is, in the modern world, where we have process and data architects acknowledged that those two professions are focussed on an individual concept each. This means anyone looking to split apart the fundamental concepts in a single modelling language or employ multiple modelling languages which would split the overall model between professions should consider the likely impacts that will have and ensure the necessary controls are in place. In summary, silos within businesses whether they be technological, or business solutions cannot be destroyed only reformed and their interfaces understood and controlled.

Relationships are affected by noise

Prop8: A Modelling Language may determine a Business’s technology (TRUE)

Not only does our view of the world change as accepted by axiom one (Models must reflect and move with the Zeitgeist) but language also determines how we see and think about the world. Given that in proposition six (Models must set Context & Boundaries) it was deemed necessary that are fundamental concepts have to be given context boundaries thusly follows that any people using that language will have their worldview altered by it. This is a view espoused by Ludwig Wittgenstein in his philosophical investigations where he defines language games. Within the investigations, he pushes the view that our language is our reality and each of our languages can be broken up to a series of games. [32]

Where this becomes prescient as it points out as briefly spoken about the end of proposition seven (Relationships are affected by noise) is in creating interfaces whether they be between people or technology there lies the possibility of miscommunication. Moreover, models generally used to describe the past present and future which means that in those models are considered to be a language broken up into games and that language constitutes our reality then the models we choose will determine the solutions we go for.

This can be seen when looking through Microsoft as the guide to architecture. What it specifies our particular styles of architecture or technology that can be used when determining what products to buy from their platform. When looking at each of the styles it quickly becomes a close relationship between each of the models chosen in this particular investigation and the architectural styles that will lead you to purchase particular products. [26]

As noted in the original description of ArchiMate, it is a modelling language focused around services and that each of the models it draws over its layers and aspects of broken up into services that represent a grouping of information and process akin to a definition of a system. Now one of the styles Microsoft talks about is microservices which can be seen in the diagram below.

Figure 8 microservice architecture from Microsoft Azure architecture guide [34]

What we can see is that there is a direct corollary between the output of ArchiMate and a particular set of technologies readily available from the cloud platform that uses the same type of language and modelling structure. Thereby without further thought making it the most compelling technology architecture to go for. [34]

This can be seen again when looking at BPMN the breaks the world up into participants the activities they perform and then the messages they share between one another. Looking below at the N-Tier Architectural style in and then again season corollaries.

Figure 9 Microsoft Azure architecture guide N-Tier view [35]

Each of the layers performs a set of activities for the lower level tasks which associate with one another either through a sequence of events or using a message to relay information. Each component within this architecture aligns again neatly with BPMN and may mean that people inadvertently are driven towards technological choices that align with the outputs of BPMN.

Our language determines our reality in the modelling language we use to describe a business may result in its technology.

A Modelling Language may determine a Business’s technology

Evaluation

There was not time to give an in-depth investigation into each individual concept and the different ways in which the concept could be split up and categorised. It may be that within each concept there are also crucial types of each which cannot be removed.

There are far more than just the three models used to determine each of the fundamental concepts within this report. An extended report or research looking at additional models and if they adhere to the fundamental concepts devised will add any missing concepts further support the existing concepts.

There is the possibility that process and systems could be considered a relationship between states of information. This would limit the number of fundamental concepts to two but might have the knock-on effect of vastly complicating the creation of a particular context and boundary for a model that could be used by a business.

The investigation into philosophical and scientific examples for each of the concepts did not exhaust all the possible knowledge available in a further investigation into more in-depth answers from each would either support or potentially invalidate the definitions and propositions.

Conclusion

In conclusion the fundamental concepts of modelling that must exist in an environment where we continuously update our knowledge that only has finite resource to deal with infinite concepts which are information, processes, systems and relationships. Where each of these can be grouped together to describe something within a model. Where that model must be governed by a set of rules that would make up a modelling language. Where those rules are created to add context boundaries to that model. Interfaces within that model are subject to noise and must be considered for control depending on their importance. Those interfaces exist not only within the business & technical solution but the practitioners who create the models. That any modelling language will necessarily affect the likely outcome of technology used to realise the models created with that language.

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