Re: model-theoretic semantics for DAML-ONT


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.

>There currently is no unique name assumption nor is there a means of
>asserting equality or inequality between individuals.  One or the other is

The second one seems more realistic to me.

>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.

>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>

>If <type,?R,UnambiguousProperty> is in KB then if <x,y> and <z,y> 
>are in IR(?R)
>then x=z

Same thing:
<type,?R,UnambiguousProperty> <==> <inverseOf,?R,?S> & <cardinality,?S,1>

In his message (Re: model-theoretic semantics for DAML-ONT) of 16/11/00,
Dan Connolly wrote:
>"Peter F. Patel-Schneider" wrote:
>  > If <equivalentTo,?C,?D> is in KB then IC(?C) = IC(?D)
>Isn't "IC(?C) = IC(?D)" asserting the equality of individuals?

No because the codomain of IC is subsets of the domain. So no 
individuals involved here, just sets.

Also note that this semantics considers that some things are elements 
of the domain and some others are subsets of the domain (like in DL 
and thus in OIL). This is a difference from the Fikes-McGuiness 
approach (and RDFS) as far as I know.

  Jérôme Euzenat                  __
                                  /      /\
  INRIA Rhône-Alpes,            _/  _   _   _ _    _
                               /_) | ` / ) | \ \  /_)
  655, avenue de l'Europe,    (___/___(_/_/  / /_(_________________
  Montbonnot St Martin,       /
  38334 Saint-Ismier cedex,  /

Received on Thursday, 16 November 2000 17:47:16 UTC