RE: SEM Solipsistic answers to Peter's entailments and Paradox

I'll reply to Mike's message in a different order.

> Normally we would expect collections to be relatively straightforward to
> formalize.  After all, they have been many times. But, RDF is at heart a
> scopeless set of arcs (triples) defining a graph. It seems that a set
> theoretic interpretation of a collection doesn't graft onto that in a
> completely obvious way.

I agree wholeheartedly. I tend to believe that doing RDF collections again
is probably not our job, and if we can make do with some of what's been done
before then I think we should; even if that is a choice between a couple of
far from perfect solutions.

> This particular example seems to be confusing surface syntax with
> semantics.

I agree, with all this too.

Peter's original examples were about the confusion of surface syntax and
Person union Student = Student union Person.
And Peter made the worthwhile point that unfortunately the most obvious
extension of RDF semantics to his SWOL proposal did leave syntax and
semantics confused.

Peter seems to be looking for a fix, in which the surface syntax had ; my
posting, in contrast, is to say that it is possible to accept that

> A tool, when asked to return an answer, will not be required to list all
> possible equivalent surface syntactic forms.  More to the point,
> what a tool
> does and what the semantics entitle it to do are two different things.

Discussing entailment is trying to clarify meaning. I believe that the
entailments licensed by my position do achieve that objective. What is
required, IMO, is that:
- the meaning of OWL is clear and agreed
- the meaning of OWL does not contradict standard set theory (I think
Peter's paradox is a problem that needs addressing).

This does not mean that we need to have an entailment (at all); nor that we
need an entailment that captures set theoretic entailments.

However, semantic entailment and the operation of query subsystems are
related and it is important to give some account of that relationship.

OWL does embed a substantial chunk of set theory. In particular, it embeds
enough so that most sets will have multiple representations possible.

> Having used some variant of set theory to formalize parts of the model we
> get all of a set's desirable properties.  The infinite possible
> expressions
> of this set in our surface syntax are by definition identical in
> the model.

How to deal with this infinite set of possible expressions is a significant
practical matter which, as an implementor, has caused me some concern.

An answer is ...

Michael K Smith:
> And tools that reason about such things will do their best to canonicalize
> expressions so that repetition and ordering don't matter.

A different answer is that (a core set of) tools will only refer to sets by
constructs that have already been used by users (and more peripheral, helper

I suspect that given an appropriate ontology some very different intensional
definitions may have the same extension ....

e.g. a oneOf over the members, a unionof a number of named classes, or a
restriction of some intersection to members with a certain value for a
certain property.

Given the desire to manipulate intensional descriptions of sets we need to
say where we stop. One answer is that we try to systematically avoid
manipulating such intentionsal descriptions and use model theory to convert
syntactic intensional descriptions into sets that have their normal
mathematical (ZF?) meaning.


Received on Monday, 18 March 2002 05:41:08 UTC