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Re: RDF Semantics review: RDFS interpretations

From: Dan Connolly <connolly@w3.org>
Date: Wed, 12 Feb 2003 08:55:37 -0600
To: herman.ter.horst@philips.com
Cc: Pat Hayes <phayes@ai.uwf.edu>, www-webont-wg@w3.org
Message-id: <1045061736.7839.11.camel@dirk.dm93.org>

On Thu, 2003-02-06 at 13:05, herman.ter.horst@philips.com wrote:
> RDF Semantics, version of 23 January 2003

Could you please summarize your review with one bit,
i.e. RDF semantics is acceptable or unacceptable
as is for use by WebOnt?

Also, I can't tell if these are editorial suggestions
or substantive issues.

If they're substantive, I'd very much appreciate
example/test case(s) where the outcome is
wrong as written and would be correct if the
document were changed as you/we are requesting.


Details below...

> There is confusion about the definitions of IC / ICEXT
> in the WebOnt Working Group (see the discussion
> on RDFS-compatible OWL semantics pointed to in [1]).
> 
> In order to eliminate this confusion, this is a somewhat 
> extensive request for clarification of Section 3.3, 
> RDFS interpretations.


This seems like a matter of editorial preference.
(That doesn't mean the comment isn't in order...)

> In an earlier email to www-rdf-comments [2]
> I noted that there seemed to be a circularity
> between the definitions of IC and ICEXT.
> Subsequently the text was slightly extended, and made
> clear to me that IC is defined before ICEXT.
> 
> For convenience I include below rather concrete suggestions
> for extending the text further, in order to clarify the intent that 
> seems to be already expressed.
> (I do not claim that what I describe below would be sufficient
> editorial work, of course.)
> 
> A central point is that the distinction between definitions 
> and semantic conditions should be made more clear.
> 
> Another central point is that there is much analogy between
> IP/IEXT and IC/ICEXT.  IP/IEXT is already defined as part
> of a simple interpretation, while the definition of IC/ICEXT
> is given for each rdf-interpretation.
> 
> > Although not strictly necessary, it is convenient to state the 
> > RDFS semantics in terms of a new semantic construct, a 'class', 
> > i.e. a resource which represents a set of things in the universe
> which 
> > all have that class as the value of their rdf:type property. 
> > Classes are defined to be things of type rdfs:Class. 
> It seems to be desirable to introduce the symbol IC here, 
> for example in the following way:
> For an rdf-interpretation I of a vocabulary that includes
> rdfV as well as rdfsV, the set IC (of classes) is defined to be
>    IC = {x in IR: <x,IS(rdfs:Class)> in IEXT(IS(rdf:type))}.
> > We will assume that there is a mapping ICEXT (for the Class
> Extension 
> > in I) from classes to their extensions; the first semantic condition
> > in the table below amounts to the following definition of this
> mapping 
> > in terms of the relational extension of rdf:type:
> >   ICEXT(x) = {y | <y,x> is in IEXT(I(rdf:type)) }
> It seems that clarity is improved if the reference
> to semantic conditions is deleted here, and if it is said that,
> for the same rdf-interpretation I as I just described,
> the function 
>    ICEXT from IC into the powerset of IR
> is defined by 
>    ICEXT(x) = {y in IR | <y,x> is in IEXT(I(rdf:type)) } 
> (for x in IC).
> 
> [...]
> 
> (Note that similarly, the definition of simple interpretation
> speaks of the function "IEXT from IP into the power set of IRxIR")
> 
> 
> > The first condition can be understood as a definition of ICEXT 
> > and hence of IC, the set of classes.
> > Since I is an rdf-interpretation, this means that 
> > IP = ICEXT(I(rdf:Property))
> 
> > [table:]
> 
> > x is in ICEXT(y) iff <x,y> is in IEXT(I(rdf:type))
> > IC = ICEXT(I(rdfs:Class))
> 
> The last condition here, IC = ICEXT(I(rdfs:Class)), follows from 
> the definition of IC and the assumption that I(rdfs:Class)
> is in IC.  So this is not really a condition, and can be
> stated before the table, in conjunction with the already
> noted conclusion that
>   IP = ICEXT(I(rdf:Property)).
> In other words, IC = ICEXT(I(rdfs:Class)) is a true characterization
> of the set IC, but not the original definition of the set IC.

Again, editorial, yes?

> Most of the next to last condition here,
> x is in ICEXT(y) iff <x,y> is in IEXT(I(rdf:type)),
> is implied by the definition of ICEXT.
> One point that is not implied is the following:
>   if <x,y> is in IEXT(I(rdf:type)), then y is in IC.
> However, this is implied by two later conditions
> listed in the table:
> 
> > rdf:type rdfs:range rdfs:Class
> 
> > If <x,y> is in IEXT(I(rdfs:range)) 
> > [then x is in IP and y is in IC] and 
> > [if, in addition,] <u,v> is in IEXT(x) then 
> > v is in ICEXT(y)
> (Between brackets [] I have made some additions which
> seem to be implied here.  See separate remark below.)
> 
> Therefore, the condition
> x is in ICEXT(y) iff <x,y> is in IEXT(I(rdf:type))
> could be dropped from the table.
> For clarity, I would add that the statement
>   if <x,y> is in IEXT(I(rdf:type)), then y is in IC.
> is implied by the table, in the way noted above.
> 
> ==
> 
> A consequence of the new setup of the RDF model theory
> is that for each occurrence of IEXT(x) or ICEXT(x), it
> should be clear that x is in IP or that x is in IC,
> respectively.  For example, the semantic conditions
> on subClassOf and subPropertyOf take care of this
> explicitly.
> 
> In this connection, I would move the semantic conditions
> > IC contains ...[many items]
> > IP contains ...[many items]
> to become the first conditions, as each of the other
> conditions actually uses one or more of these 
> conditions.
> 
> Note that IP is listed to contain I(rdfs:label) twice.
> 
> Note that IC is not listed to contain I(rdf:XMLLiteral).
> This seems to be an error.
> 
> The semantic conditions on rdfs:range and rdfs:domain
> do not yet incorporate an explicit domain assumption as just
> discussed.  It seems that additions such as the following need 
> to be made:
> 
> If <x,y> is in IEXT(I(rdfs:range)) 
> [then x is in IP and y is in IC] and 
> [if, in addition,] <u,v> is in IEXT(x) then 
> v is in ICEXT(y)
> 
> If <x,y> is in IEXT(I(rdfs:range)) 
> [then x is in IP and y is in IC] and 
> [if, in addition,] <u,v> is in IEXT(x) then 
> u is in ICEXT(y)

That seems substantive, but I'm not sure I understand
the problem. Could you state it as an entailment test,
please?

> ==
> 
> Finally, not related to these IC/IP domain issues,
> note that the rdfs:ContainerMembershipProperty condition
> speaks of rdfs:Property instead of rdf:Property.
> 
> Herman ter Horst
> 
> [1]
> http://lists.w3.org/Archives/Public/www-webont-wg/2003Jan/0426.html
> [2]
> http://lists.w3.org/Archives/Public/www-rdf-comments/2002OctDec/0096.html
-- 
Dan Connolly, W3C http://www.w3.org/People/Connolly/
Received on Wednesday, 12 February 2003 09:56:03 GMT

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