GFO Part I Basic Principles
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8.2 Related Notions

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 $\Gchange(e_{1}, e_{2}, u_{1}, u_{2}, u)$, where $e_1$ and $e_2$ capture the pair of coincident process boundaries17, and $u_1$ and $u_2$ are disjoint sub-universals of u, such that $e_1$ and $e_2$ instantiate $u_1$ and $u_2$, respectively. Note that this implies instantiation of both $e_1$ and $e_2$ of $u$, 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 $\Delta $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 $\Gchange(e_{1},
e_{2}, u_{1}, u_{2}, u, \Delta c)$ 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.

8.2.2 Discrete vs. Continuous Processes and States

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.

8.2.3 Simple and Complex 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.

8.2.4 Histories

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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