OWL semantics is monotonic?


as it was mentioned that RDF semantics is monotonic, i.e., Suppose S is a 
subgraph of S' and S entails E. Then S' entails E.

however, according to http://www.w3.org/TR/owl-absyn/rdfs.html (OWL Web 
Ontology Language Semantics and Abstract Syntax Section 5. RDF-Compatible 
Model-Theoretic Semantics), the  If-and-only-if conditions is too strong to 
destroy the monotonicity !!!

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).

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!

Sorry for bothering you all, however i wonder if i am right or just i have 
done some stupid mistakes?

Best wishes,
Sincerely your, Jing Mei

Received on Tuesday, 9 November 2004 09:10:44 UTC