GFO Part I Basic Principles
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8.1 Processes and Time, Process Boundaries, and Processual Roles

The category of processes captures those entities that develop over time or unfold in time. Accordingly, processes are tied to temporal entities in a special way, which we call the projection relation $\Gprt(p, c)$ (connecting a process $p$ with its chronoid $c$).

Sometimes, e.g. with a series of events considered as a whole, the time entity appears to be a non-connected aggregate of chronoids (i.e., a time-region). In this case, however, the process of the lecture series can be derived from the processes of the separate lectures. More precisely, we call these entities process aggregates or generalized processes. In many cases what is said about processes herein can be easily extended to process aggregates.

Just as parts of chronoids can be chronoids themselves, we assume that parts of processes are always processes themselves. Another temporally derived notion is the idea of meeting processes. Two processes meet if their corresponding chronoids temporally meet.

If a process is projected onto a chronoid in terms of $\Gprt(p, c)$, each time-boundary $b$ of $c$ refers to a presential $e$, which is called the boundary of the process, denoted by $\Gprb(p, b, e)$, which further implies $\Gat(e, b)$. Analogously to chronoids and time-boundaries, The boundaries of processes are not considered to be parts of processes, because parts of processes are themselves processes and cannot exist at a single time-point. Secondly, processes cannot be considered as mere aggregates of their boundaries.

In a general sense, a presential identified as a process boundary will be classified as a configuration, i.e., a conglomeration of material structures, qualities and relators (see sect. 11). Every constituent $s$ of that configuration $e$ is said to participate in $p$, a relation that is expressed as $\Gpartic(s,p)$.

Apart from participation based on time-boundaries, a notion of participation of persistants is required. Consider John drinking some water, $p$. This corresponds to a participation relation between the persistant $j_{pers}$ and $p$, because every presential instance of $j_{pers}$ is constrained to a single time boundary. On the other hand, the persistant gives rise to a part or a ``layer'' of the process, not cut along the temporal dimension, but regarding persistant participants. Such parts of a process are called processual roles, because they essentially capture the role of the participant in a process. In the given example, John plays the role of the drinker, while the water has the role of the ``drunken''. To a large extent, processual roles exhibit the character of processes, i.e., they are temporally extended entities. However, the processual roles of a process are mutually dependent, i.e., they cannot exist independently.

The notion of processual roles can be generalized as a structural layer of a process. A structural layer $q$ of some process $p$ is a ``portion'' of $p$ satisfying the following conditions:

  1. $q$ is a process, such that every boundary contains a material structure,
  2. $p$ and $q$ are projected onto the same chronoid, and
  3. Let $t_1$, $t_2$ be arbitrary time-boundaries of the framing chronoid of $p$, such that $t_1$ occurs before $t_2$, and let $\Gprb(q, t_1, e)$ and $\Gprb(p, t_2, f)$. Then: if $m$ is a material structure that is contained in the $q$-boundary $e$, and $n$ is a material structure that is contained in the $p$-boundary $f$, and $m$, $n$ are ontically connected, $\Gontic(m, n)$, then $n$ is contained in the corresponding $q$-boundary $g$, where $\Gprb(q, t_2, g)$.

Robert Hoehndorf 2006-10-18


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