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Re: summary of current position with respect to semantics proposals (was Re: WOWG: agenda Aug 15 telecon)

From: Dan Connolly <connolly@w3.org>
Date: 14 Aug 2002 14:29:29 -0500
To: "Peter F. "Patel-Schneider <pfps@research.bell-labs.com>
Cc: Guus Schreiber <schreiber@swi.psy.uva.nl>, www-webont-wg@w3.org
Message-Id: <1029353370.17704.1253.camel@dirk>

On Wed, 2002-08-14 at 13:17, Peter F. Patel-Schneider wrote:
> 
> 
> We would like to summarise (our understanding of) the current situation
> with respect to OWL semantics ahead of tomorrow's discussion.

This is nearly a fair summary, but the use of 'syntax' to
characterize things such as inverseOf is
a part of proposal [2], and shouldn't be used in
the summary.

>  There are
> two proto-proposals [1] [2] currently available for the semantics of OWL.
> These proposals differ in a number of areas, but we feel that the most
> significant difference is how certain entailments come out.  In proposal
> [1] there are entailments like
> 
> Entailment 1:
> 	John in the intersection of Student and Employee
> 	entails
> 	John in the intersection of Employee and Student
> 
> This is the standard way of treating syntactic constructs like
> intersection, union, conjunction, and disjunction.  Proposal [2]
> necessarily has weaker entailment, with the result that the above is no
> longer an entailment.
> 
> Extending the approaches in the two proposals to the logic layer would
> result in Proposal [1] supporting and Proposal [2] not supporting
> 
> Entailment 2:
> 	`it is raining'  or  `today is Tuesday'
> 	entails
> 	`today is Tuesday'  or  `it is raining'

I think this discussion of extension to the logic layer is
something of a red herring, but in fact, that entailment
*does* follow if you look at log:or as a property that
relates two (quoted) formulas. It can be axiomatized
without resorting to existentials in the conclusion of any rules,
so it works fine:

From
  { :it :is :raining } log:or { :today :is :Tuesday }.
  log:or a ont:SymmetricProperty.
along with the usual rules for SymmetricProperty, we deduce
    { :today     :is :Tuesday . } log:or {:it  :is :raining .} .


In more traditional first-order logic syntax, that would
look more like:

	(PropertyValue log:or '(is it raining) '(is today Tuesday))
        (PropertyValue rdf:type log:or ont:SymmetricProperty)

==>

	(PropertyValue log:or '(is today Tuesday) '(is it raining))

and yes, quantifying into quoted formulas is messy.

I don't claim that this log:or design is the way to go;
new syntax is necessary for universal quantification,
and quite likely cost-effective for negation and
maybe even disjunction.

But at the 'ontology building' level, i.e the level of
inverseOf and SymmetricProperty, it's pretty clear to me that normal
RDF properties are the most cost-effective way to go.

In fact, that's what I thought this working group was all
about: figure out the sort of modelling gizmos that
fit neatly as RDF properties, ala rdfs:subClassOf
and rdfs:subPropertyOf.

> We feel that any formalism that does not support entailments like 1
> and 2 would manifestly fail to promote interoperability and to support
> the development of "applications that depend on an understanding of
> logical content" [3].

Folks should keep in mind that while entailment 1 doesn't work,
this analog does:

 	John in the intersection of Student and Employee
 	C is the intersection of Employee and Student
 	entails
	John is in C.

and this analog is what you acutally need to deal with the
case where one ontology gives the intersection in one
order and the other does it the other way.


> The two proposals differ on these entailments because Proposal [2] includes
> syntax in its domain of discourse.

That is: proposal [2] treats notions such as
inverseOf, SymmetricProperty, as RDF properties, i.e.
resources one can talk about, rather than as new syntax.

>  When syntax is in the domain of
> discourse the above entailments require comprehension principles which lead
> to paradoxes when the formalism has sufficient expressive power.

So it seems.

>  OWL has
> sufficient expressive power for this purpose, e.g., see [4].

That argument asserts the conclusion. I suggest that OWL should not
have sufficient expressive power for this purpose.

> There are other differences between the two proposals, which are summarized
> below:
> 
> Proposal [2]:
>  
>   - start with RDF
>     - all RDF graphs are OWL KBs
>   - OWL model theory is an augmentation of RDF model theory
>     - everything is in the uniform domain of discourse
>       - including syntax, so entailment is weak to avoid paradoxes

i.e. including terms such as inverseOf, SymmetricProperty.

>       - including classes, so classes are also instances

as well as properties.

> Proposal [1]:
> 
>   - start with abstract syntax
>     - only RDF graphs that correspond to the abstract syntax are OWL KBs
>   - provide model theory for abstract syntax
>     - entailment is standard
>   - translate abstract syntax to RDF graphs
>     - only RDF graphs that are the result of this translation are OWL KBs
> 
>   - Pat Hayes is providing an RDF-like model theory for those RDF graphs
>       that correspond to the abstract syntax
>     - translating the model theory into one based on triples
>     - adding necessary syntactic constraints and "darkening"

It's hard to see why Pat's work is more related to one of the
proposal than the other until we see it.


> Ian Horrocks
> Peter F. Patel-Schneider
> 
> 
> 
> [1] http://lists.w3.org/Archives/Public/www-webont-wg/2002Jun/att-0082/01-semantics.html
> [2] http://lists.w3.org/Archives/Public/www-webont-wg/2002Jun/0208.html
> [3] http://www.w3.org/2001/sw/WebOnt/charter
> [4] http://lists.w3.org/Archives/Public/www-webont-wg/2002Jan/0099.html
-- 
Dan Connolly, W3C http://www.w3.org/People/Connolly/
Received on Wednesday, 14 August 2002 15:28:40 GMT

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