Re: OWL semantics is monotonic?

Mayyam@is.pku.edu.cn wrote: 

> for example, it was said that 
> "if c \in CEXT(S(owl:SymmetricProperty)) iff  <x,y> \in EXT(c) implies
> <y,x> \in EXT(c)"
> in short, c is a SymmetricProperty iff c(x,y)->c(y,x).

Please note that the iff condition is actually: FOR ALL x, y: <x,y> \in
EXT(c) implies <y,x> \in EXT(c).

>  
> ok, now we turn to the RDF graph. 
> firstly, we only have two facts "c(x,y), c(y,x)" to be the set
> S={c(x,y), c(y,x)}. then, S entail E={c is a SymmetricProperty} (what
> is "if" tells us)
> secondly, we add a new fact "c(x,z)" to have the set S'={c(x,y),
> c(y,x), c(x,z)}. of course, c is not a SymmetricProperty any more, at
> least it is unknown now!  i.e., S' cannot entail E!

S' does not satisfy the iff condition.

-- 
Lei Zhang

Everything starts from a dream.
http://apex.sjtu.edu.cn/people/zhanglei