Subsections
8.2.1 Changes
In contrast to a general understanding of ``change'' as an effect, a change
in the technical sense we define here refers to a pair of process
boundaries. These pairs occur either at coinciding boundries, like ``instnataneous
event'' or ``punctual'', or at boundaries situated at opposite ends of a
process of arbitrary extension.
The enrollment of a student is a good example for the first kind
of changes, called extrinsic. It
comprises two coinciding process boundaries, one terminating the
process of the matriculation, one beginning the process of
studying.
An example of intrinsic change is
illustrated by the placement
of two process boundaries in the middle of a continuous inflammation's
decline in the course of a rhinitis. If these boundaries
coincide, one may not be able to assign a difference to the severity
of inflammation, but if one considers boundaries that belong to an extended
part of the inflammation process, there will be a difference: the
intrinsic change.
Both notions of intrinsic and extrinsic change are relative to contradictory
conditions
between which a transition takes place. Frequently, these contradictions refer to
pairs of categories that cannot be instantiated by the same individual.
Relying on those universals, we finally arrive at the following
relations: Extrinsic changes are represented
by
 , where  and 
capture the pair of
coincident process boundaries17, and  and  are disjoint
sub-universals of u, such that and instantiate and
, respectively. Note that this implies instantiation of both
and of  , which prevents expressing artificial changes,
e.g. a change of a weight of 20kg to a color of red. For the purpose of
formalizing intrinsic changes, a minimal chronoid universal  c
is employed in order to embody the idea of observable differences
during certain chronoids, while the change itself does not allow the
observation of a difference. The predicate
 is intended to formalize
this approach.
Changes can only be realized in terms of ontical
connectedness and persistants (cf. sect. 6.1), in
order to know which
entities must be compared with each other to detect a
change.
Based on the notions of extrinsic and intrinsic change, processes can
be subdivided according to the nature of changes occurring within a
process. First, there are processes in which all (non-coinciding)
internal boundaries are intrinsic changes. These are purely
continuous processes, described e.g.
in physics by differential equations.
Secondly, there are
processes that exhibit extrinsic changes at coinciding boundaries.
However, a process only consisting of extrinsic changes does not
appear to be very reasonable, because it would be better
to employ other universals in order to arrive at a comprehensive
understanding of the process.
But extrinsic changes may alternate with periods without
changes (based on the same universals). Those parts of a process
without changes may be called a
state,
which constitutes its own type of process. States, however, are a
notion as relative as changes.
In summary, three common kinds of
processes can be identified: continuous processes based on intrinsic
changes, states, and discrete processes made up of alternating sequences
of extrinsic changes and states or continuous processes.
Another dissection of the category of processes is geared toward the
complexity of the process boundaries in their nature as presentials.
Consider a person walking compared to a clinical trial. In the first case, the process of walking focusses on the
person only (and its position in space), whereas the clinical trial is
a process with numerous participants and an enormous degree of
complexity and interlacement. It is clear that every process is
embedded in reality, so the walking is not separated from the world
and could be considered with more complexity18 However, processes often
refer to specific aspects of their participants, so that dividing
simple and complex processes appears to be
useful.
A process is called simple if its
process boundaries are simple presentials or even mere qualities of
presentials.
In contrast to simple processes,
complex processes involve more than a single presential at their boundaries.
A finer classification of simple processes (according to the nature of
its presentials) could be
quality-process and
material-structure-processes.
Another process-related notion of modelling relevance is that of
a history, which consists of a number of process
boundaries. Think of a series of blood-pressure measurements, for
example, that are taken in order to grasp the underlying
process of blood-pressure progression. Or any other field with
periodic measurements of certain properties or periodic determinations
of facts.
We assume that any history can be embedded into a process, which then
forms a foundation of the history. If there were no foundation,
one would face the problem of singling out the right boundaries in
order to obtain a ``natural'' history: It is not sensible to measure the
temperature of a patient first, then determine his weight, followed by
measuring his blood pressure and then to consider these arbitrary
process boundaries as a history of the patient's body data.
Robert Hoehndorf
2006-10-18
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