GFO Part I Basic Principles
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3.4 Basic Level

The basic level of GFO contains all relevant top-level distinctions and categories. One should distinguish between primitive categories (whose instances are individuals), and higher order categories. In the present document we consider primitive categories and the category of persistants (which is a special category of second order). These categories will be be extended in the future using a number of non-primitive categories. Primitive categories and persistants of the basic level will be discussed further in the following sections and are the main content of the current report. All basic relations and categories are presented as set-theoretical relations and set-theoretical predicates. The ontology of the basic level is expressed in a formal language with restricted expressive power. We use a common (first-order) language througout all levels, but constrain the expressive power at every level, mainly by restricting the scope of the quantifiers. At the basic level, an unrestricted quantification over categories is not allowed. The basic predicates as $\GProc(x)$, $\GInd(x)$, $\GPres(x)$, $\GPerst(x)$, and others, are considered (understood) to be meta-categories over the object level (domain) ontologies. $\GPerst(x)$ is a predicate whose elements contain those categories, which are persistants. The notion of a persistant is the result of an ontological analysis of notions as continuant, or endurant. One may extent the vocabulary of the basic level by adding further predicates, whose elements are categories. Examples of such predicates are stratum-predicates, $\GCatMat(x)$ is a predicate that contains all categories of the material stratum, $\GCat_{tp} (x)$ is a predicate that contains all categories of a certain structural type tp.

Categories which are not contained within the basic level we call domain categories. Domain categories are related to a certain part $D$ of the real world, and on the domain level they are not presented (and considered) as sets, but as entities of its own. Formally, the vocabulary at the basic level of GFO is extended by additional constants denoting proper categories or individuals. If, for example, $C$ denotes a domain category we write $x \Ginst C$ instead of $C(x)$, indicating that $x$ is an instance of $C$. For the purpose of abbreviation we write sometimes $C[x]$ instead of $x \Ginst C$.

Domain categories may be linked in a simple way to the basic level predicates of GFO, using domain-upper linking axioms. For example, if we want to say that a certain domain category $C$ is a process category (i.e., all its instances are processes) we write the following linking axiom: $\forall x (x \Ginst C \rightarrow \GProc(x))$, or, by using the abbreviation $\forall x (C[x] \rightarrow \GProc(x))$. Domain-Upper-Linking axioms exhibit an ontological embedding of a domain ontology into a foundational ontology.

We introduce particular notations for treating the persistants. If $C$ is a persistant then $C[t]$ denotes the instance of $C$ at the time-point $t$, and the relation $C[x,t]$ is defined by $x \Ginst C \wedge at(x,t)$.

Robert Hoehndorf 2006-10-18


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