The term of a “process” is used in Software Engineering (SE) theories and practices in many different ways, which cause confusion. In this paper we will firstly give a general overview how the term “process” is used in SE context. Secondly, we describe how ambiguous the way of using the term “process” in SE discipline is compared to practical SE management. Then, thirdly, we will consider a process ontology in which everything is in a process. Our overall view is that everything in the world is composed of processes. Lastly, we propose a topological model of process in SE context.
The term of a “process” is used in many widely known theories and essential practices of Software Engineering (SE). Earlier computers were used to solve mathematical problems. The same people who implemented the programs were customers of the process of a software development. Later on it was noticed that this “process in the small” was not well enough understood to deal with the emerging problems of producing a large and complex software system. Nowadays the scope of interest is widened to an engineering discipline, which concerns all aspects of software production including management and the improvement of processes. “Process thinking” has become one of the major efforts to make software engineering to an engineering, which has a qualitative value.
This paper is composed as follows. Firstly we give a general overview how the term “process” is used in SE context. Secondly, we describe how ambiguous the way of using the term of a “process” in SE discipline is compared to practical SE management. Then, thirdly, we will consider a process ontology in which everything is in a process. Our overall view is that everything in the world is composed of processes. Lastly, we propose a topological model of process in SE context. We will present four domain areas how the term “process” is used in SE context. These domain areas overlap and interact with each other.
The first domain area is a traditional software engineering, where a process is
considered a production process, which includes support and organizational processes.
For example a software life circle model and a process model are instances of these
domains
The second domain area is a software process engineering. It is considered as a
part of an enterprise level process engineering, which, according to
The third domain area is a SE knowledge model, e.g. a framework like SWEBOK,
In the four domain areas where the term “process” is used in SE context both the
intension and extension of the term “process” vary. Also, SWEBOK recognizes the
ambiguous role of the term “software engineering process”
The term “process” is used in a different way in a SE discipline community
compared to a practical SE management. SE management tends to make the process
straightforward and as simple as possible by using the viewpoint of a key process.
This approach has its roots in the definition of an organizational process and
enterprise process engineering.
Software engineering as a discipline has become to a phase, where a domain is
recognized as a set of complex processes, where their relations, interactions,
improvements, and implementations to reality are profoundly analyzed. This is due to the
young nature of the SE discipline.
The most famous work of process philosophy is Alfred North Whitehead’s Process and Reality, (1929). He believed that all events are related to one another and to the environments in which they occur. The world can best be understood as interrelated systems of larger and smaller events, some of which are relatively stable. Whitehead’s metaphysics was also a philosophy of process. Events are always changing. Change represents the actualization of certain potentialities and the disappearances of others. The world does not simply exist, it is always becoming.
According to Whitehead, the world is a process which is the becoming of actual entities (or actual occasions). They endure only a short time, and they are processes of their own self creation. There are also eternal objects to be understood as conceptual objects. They enter into the actual entity becoming concrete without being actualities themselves. Although novel actual entities are progressively added to the world, there are no new eternal objects. They are the same for all actual entities.
However, we will not make any detour into Whitehead’s “process philosophy”
here. Nor will we make any study of the Process of Reality, such a complex and a
difficult book as it is.1 Instead of that we will just adopt an idea that everything
consists of processes, and that these processes are divided into eternal processes
interpreted as concepts, and actual processes, which we will interpret to be events
occupying a finite amount of a four dimensional space-time. Thus, the world is constructed
out of events. Every event in space-time is overlapped by other events, i.e., events are
not impenetrable. A space-time order results from a relation between events. Also, in
terms of these events spatio-temporal point-instants, lines, surfaces, and regions can
be defined by using the Method of Extensive Abstraction as follows,
A fundamental relation in construction of point-instants in a four dimensional space-time is a five-term relation of co-punctuality, which holds between five events having a common area to all of them. A set of five or more events is called copunctual if every quintet chosen out of the set has the relation of co-punctuality. A point-instant is a co-punctual set which cannot be enlarged without ceasing to be a co-punctual. The existence of point-instant so defined is provided if all events can be well-ordered, i.e. if the Axiom of Choice is true, (cf. Russell 1927, 299)
Given two point-instants κ andλ , we denote by κλ their logical product, i.e., the events which are members of both. If κλ is non-empty, then κ and λ are said to be connected. A set of point-instants is defined to be collinear, if every pair of pointinstants are connected, and every triad of point-instantsα , β , γ are such that either αβ is contained in γ , or αγ is contained in β . A set of point-instants is defined to be a line, 1 For more recent study of process philosophy in this line of thought we refer to After Whitehead: Rescher on Process Metaphysics, 2004, edited by Michael Weber. if it is collinear, and it is not contained in any larger collinear set. The lines so defined are not supposed to be straight.
That definition of a line is analogous to that of a point-instant. It is possible to
extend this method to obtain surfaces and regions, as well,
A space-time order is constructed out of the relation between events as follows. Two events are said to be compresent when they overlap in space-time. With respect to a given event it is possible to divide events into zones as follows: In the first zone there are those events that are compresent with a given event. The, in the second zone, there are those events which are not compresent with a given event, but compresent with an event compresent with it, and so on. The nth zone will consist of events that can be reached in n steps, but not in n–1 steps, in which a step is taken to be as the passage from an event to another which is compresent with it. Assuming a minimum size of events, it is possible to pass from one event to another by a finite number of steps. Two point-instants are connected, if there is an event which is a member of both. Thus, point-instants can be collected into zones as well, and the passage from event to event by the relation of compresence can be replaced by the passage from point-instant to point-instant by the relation of connection. Accordingly, suppose there are n events, e1, e2, … , en, and suppose e1 is compresent only with e2, e2 is compresent with e1 and e3, e3 with e2 and e4, and so on. We can then construct the order e1, e2, … , en. The relation of connection is a causal relation between events, where the cause of an event occurs earlier than its effect.
We shall also distinguish events in a living brain from events elsewhere,
Accordingly, in our view, ontologically, everything consists of processes. Among processes, firstly, there are eternal processes and actual processes. Eternal processes are interpreted as concepts, whereas actual processes are interpreted as space-time events. Eternal processes are instantiated in actual processes. Secondly, among actual processes there are mental events and physical events. Mental events consist of bundles of compresent qualities which can be known without inferences, whereas physical events, if known, are known only by inference as regards to their space-time structure. 5
We shall give a topological model for a process, in which events are interpreted as open sets, i.e., events will have a one-one correspondence with open sets. To get an idea, a few topological concepts are defined as follows. Consider a set T. Let {Oi∈I} to be a set of open subsets of T satisfying the following axioms:
A1 A2 A3
The union of any number of open sets is an open set.
The intersection of two open sets is an open set.
T itself and the empty set ∅ are open sets.
A topology on a set T is then the specification of open subsets of T which satisfy these axioms, and this set T is called a topological space.
A set of open subsets {Oi∈I} of T is said to be an open covering of T, if the union of Oi∈I contains T. An open covering {Vj∈I} of a space T is said to be a refinement of an open covering {Oi∈I}, if for each element Vj of {Vj∈I} there is an element Oi of {Oi∈I} such that Vj ⊆ Oi. If {Oi∈I} is any open covering of T, and there is some finite subset {Oi1, Oi2, … , Oin} of {Oi∈I}, then a space T is called a compact.
A topological space T is separated, if it is the union of two disjoint, non-empty open sets. A space T is connected, if it is not separated. A space T is said to be pathconnected if for any two points x and y in T there exists a continuous function f from the unit interval [0, 1] to T with f(0) = x and f(1) = y. This function is called a path from x to y. A space T is simply connected if only if it is a path connected, and it has no “holes”.2 A space T, which is connected, but not simply connected, is called multiply connected.
Given two points a and b of a space T, a set {O1, O2, … , On} of open sets is a
simple chain from a to b provided that O1 (and only O1) contains a, On (and only On)
contains b, and Oi ∩ Oj is non-empty if and only if⎟i - j⎢≤ 1. That is, each link
intersects just the one before it and the one after it, and, of course, itself. It can be proved
that if a and b are two points of connected space T, and {Oi∈I} is a set of open sets
covering T, then there is a simple chain of elements of {Oi∈I} from a to b,
2 More formally, a path-connected space T is simply connected if given two points a and b in T and two paths p : [0,1] → T and q : [0,1] → T joining a and b, i.e., p(0) = q(0) = a and p(1) = q(1) = b, there exists a homotopy in T between p and q. Two maps p, q : X → Y are said to be homotopic if there is a map H : [0, 1] × X → Y such that for each point x in X, H(0, x) = p(x) and H(1, x) = q(x). The map H is called a homotopy between p and q. Intuitively, maps p and q are homotopic, if p can be continuously deformed to get q while keeping the endpoints fixed, and a path-connected space T is simply connected, if every closed path in T can be continuously deformed into a point. A topological model is used as follows: a process as a whole is interpreted as a topological space T, which, at least for empirical reasons, is compact and, depending on the number of parallel processes, is either a simply- or a multiply connected. The space T contains a start point a and an endpoint b of the process. The start point a is an event, which is included in the open set O1, and, similarly, the endpoint b is an event, which is included in the open set On. The simple chain from a to b consists of sequences of events interpreted as a set {O1, O2, … , On} of open sets. Moreover, it is possible to get as coarse or as fine a chain from a to b as necessary. In a case there are parallel processes, i.e., processes which we want to keep distinct in a certain moment, for example feedbacks, we just add “holes” to our space T. This prevents the parallel processes from deforming to each other. The space T will then be multiply connected.
We have given a general overview how the term “process” is used in SE context. We have also described how ambiguous the way of using the term of a “process” in SE discipline is compared to practical SE management. As there is ambiguity of the term of a “process” used both in a SE discipline community and in a practical SE management, we have introduced the theoretical backgrounds of a process-ontology and a topological model of the term of a “process” to be used in SE context where processes are understood as space-time events – either mental or physical.
As a result we think that a process-ontology and its topological model will provide an appropriate philosophical foundation to a SE discipline. They will give a common conceptual framework for the SE researches as well as for the SE practice; for example, it gives a possibility to compare their different SE process-models and concepts and to interpret the dependencies between two different SE models.