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Onto-Med >> Theories >> GFO Part I Basic Principles

 
   

3.2 Abstract Top Level

The abstract top level (ATO) of GFO contains mainly two meta-categories: set and item. Above the abstract top level there is a (non-formal) level, which might be called philosophical level. On this level, several distinct, philosophically basic assumptions are presented, mainly around the notion of existence.

The abstract top level is used to express and model the lower levels of GFO by set-theoretical expressions. To the abstract top level two basic relations are associated: membership ($\in$) and identity ($=$). The abstract top level of GFO is represented by a weak fragment of set theory, and some weak axioms connecting sets with items. Among the axioms concerning sets belong the following:


$\exists x (\GSet (x)) \wedge \neg \exists x (\GSet(x) \wedge \GItem(x))$

$\GSet(x) \wedge \GSet(y) \rightarrow (x = y
\leftrightarrow \forall u ( u \in x \leftrightarrow u \in y))$

$ \forall x y (\GItem(x) \wedge \GItem(y) \rightarrow \exists z (\GSet(z)
\wedge z = \{ x,y \})$

$ \exists x (\GSet(x) \wedge \forall u (u \in x \leftrightarrow
\GItem(u))$


We may constrain the expressive power of the abstract top level by stipulating that $\in$, $=$ are the only binary relations that are admitted in the formulas of the ontology.



Robert Hoehndorf 2006-10-18
 
       
     
     
     

   
     
     
       
 

deutsch   imise uni-leipzig ifi dep-of-formal-concepts