Comparative logical analysis of substantive and processual ontologies

Abstract

In the works of Aristotle, we find an example of a thoroughly constructed substantial ontology, which has played the role of the philosophical foundations of logic and all of Western European science. Historically, there was another -- a processual view of the structure of the surrounding world, the most prominent representative of which was Heraclitus.

In the paper, we analyze the substantial ontology and propose an approach to the construction of the ontology of processes. We introduce the relation $\textit{$\textbf{D}$pxy }$ of dividing by the duration of the process $ p $ into two successively connected subprocesses $ x $ and $ y $ and then formulate a series of intuitively obvious postulates that describe this relation. Using this relationship, we define the notion of local process time, which has the properties of a dense linear order without the first and last elements.

Objects in process ontology are understood as “bundles” of subprocesses. To characterize them, we introduce the relation $ x\leq y $, which means that process x is a subprocess of process y. This is a partial order relation with the largest element$ \textit{$\textbf{W}$}$, which is understood as a global process that is a representative of the world as a whole. Using this relation, one can define syllogistic constants for reasoning about subprocesses.

Since both relations describe two sides of the same ontology, two additional postulates of the connection between them are accepted. This allowed us to define the concept of global time, and the concept of parallel processes.

At the end of the paper, we show how in a process ontology it is possible to define concepts that correspond to the concepts of individuals and properties of a process and substantial ontology.