RDF Semantics: subinterpretations

RDF Semantics document,
last call version, 23 january 2003
This comment was mailed earlier to the WebOnt WG [1].

The definition of subinterpretation I << J in Appendix B
is not clear, as
it is not clear what a "projection mapping from IR into JR,
IS into JS, IL into JL and IEXT into JEXT" is.
IR and JR are sets, so the first part is clear: a function
from IR into JR. However, IS and JS are functions.
(What is meant by a mapping from a function to a function?)

It seems that the following definition suits the intended
use in the Herbrand lemma:

I is a subinterpretation of J, I << J, when there is a projection
mapping f : IR -> JR such that the following hold:
- f(IP) subsetof JP  [this is needed for the last condition]
- for each v in V, JS(v)=f(IS(v))
- for each typed literal l, JL(l)=f(IL(l))
- for each p in IP, 
{ <f(x),f(y)> : <x,y> in IEXT((I(p)) } subsetof JEXT(f(p))

Then, automatically, the property that is desired in the text
follows: any triple is true in J if it is true in I.

Herman ter Horst
Philips Research

[1] http://lists.w3.org/Archives/Public/www-webont-wg/2003Feb/0313.html

Received on Friday, 21 February 2003 11:04:20 UTC