Re: model-theoretic semantics for DAML-ONT

From: Jerome.Euzenat@inrialpes.fr (Je'ro^me Euzenat)
Subject: Re: model-theoretic semantics for DAML-ONT
Date: Thu, 16 Nov 2000 23:45:32 +0100

> Hello,
> 
> some comments on the first version :
> 
> In his message (model-theoretic semantics for DAML-ONT) of 16/11/00,
> Peter F. Patel-Schneider wrote:
> >The semantics uses a domain of discourse, DD, which is the collection of
> >all DAML-ONT individuals.  The semantics assigns a meaning to various
> >syntactic constructs by means of several interpretation functions, namely
> >	IC, which maps classes (nodes) into subsets of DD
> >	IO, which maps individuals (nodes) into elements of DD
> >	IR, which maps relationships (nodes) into subsets of DD x DD
> 
> I would drop the ", which is the collection of all DAML-ONT individuals,".
> For several reasons:
> - IO would be from DD to DD.
> - it would introduce (a sort of) closed-world assumption.
> - it is useless.
> No?

Sorry. I was unclear in my statement.  DD is the class of semantic
individuals.  The domain of IO is syntactic individuals (i.e., nodes).  I
could identify DD as all DAML-ONT semantic objects, perhaps.  I've modified
the wording of this section accordingly.

> >There currently is no unique name assumption nor is there a means of
> >asserting equality or inequality between individuals.  One or the other is
> >needed.
> 
> The second one seems more realistic to me.

It may be that the intended meaning of equivalentTo allows the assertion of
equality of individuals.  (However, there needs to be a way of stating
inequality of individuals.)

> >If <cardinality,?R,?n> is in KB
> >and x is in IC(?C) for each ?C such that <domain,?R,?C> is in KB
> >then there are n distinct y in DD such that <x,y> is in IR(?R)
> 
> What if <domain,?R,?C> is missing? (I am not very knowledgeable in 
> RDF(S) but it seems that range can be missing, what about domain?). 
> Since RDF provides disjunctive domains, the absence of a domain close 
> should be interpreted by the empty set: that seems to be OK.
> If we no consider that the absence of range denotes the set of all 
> resources (here DD), then you can replace the occurence of DD in the 
> last line by the range of ?R. But this is useless. OK.

I think that RDF uses the absence of a domain statement to mean that the
domain is the entire universe.  (Yes, this is not in keeping with the
disjunctive reading of multiple domain statements.)  If there is no domain
statement then a cardinality statement means that all elements of the
universe must have n R fillers.  This is yet another reason to dislike
cardinality statements.

> >If <type,?R,UniqueProperty> is in KB then if <x,y> and <x,z> are in IR(?R)
> >then y=z
> 
> I'd suggest to put it out of the semantics and back to axiomatics:
> <type,?R,UniqueProperty> <==> <cardinality,?R,1>

This could be done, but I tried to produce direct meaning for all
constructs and not use any translation.

Thanks for the comments.

peter

Received on Thursday, 16 November 2000 19:38:06 UTC