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a theory of rdf:Bags

From: Dan Connolly <connolly@w3.org>
Date: 17 Feb 2002 09:38:21 -0600
To: w3c-rdfcore-wg@w3.org
Message-Id: <1013960302.19851.65.camel@dirk>
The traditional meaning of 'bag' is:

If
	Bag(?x) and Bag(?y)
and
	forall ?z, count(?x, ?z) = count(?y, ?z)
then
	?x = ?y.

We can't apply this directly to memebers
of class rdf:Bag, because we would end up with
the corrollary:

	rdf:_1(?x) = rdf:_1(?y)
	rdf:_2(?x) = rdf:_2(?y)
	rdf:_3(?x) = rdf:_3(?y)

and so on; this doesn't work out; for example,
consider
	?x = <Fred, Fred, Bob>
	?y = <Bob, Fred, Fred>

we'd end up with Fred = Bob, which isn't
what we want.

But consider an asRealBag property that relates
rdf:Bag's to RealBag's; we start with an
axiom that says there's exactly one for every
rdf:Bag:

	for all ?b, if type(?b, rdf:Bag)
	then there exists ?b' where
	asRealBag(?b, ?b') and type(?b', RealBag) and
	forall ?x, if asRealBag(?b, ?x) then ?x = ?b'.

in DAML+OIL terms, asRealBag has cardinality
1 on class rdf:Bag.

Then we define the membership of the real bag
straightforwardly:

	if bagMember(?b, ?b') then
	forall ?x,
	bagMember(?b', ?x) iff
	exists ?cmp with
	type(?cmp, rdfs:ContainterMembershipProperty)
	and ?cmp(?b, ?x)

Hmm... this is of limited utility, due
to the "and that's all!" problem with
rdf container syntax (i.e.
rdfms-seq-representation). There's no
way to tell that something is *not*
in a bag. But maybe we'll fix that someday.


Anyway... then we'd say that for RealBags,

If
	RealBag(?x) and RealBag(?y)
and
	forall ?z, count(?x, ?z) = count(?y, ?z)
then
	?x = ?y.

Now the RealBags can be in the universe
of discourse (my preference), or they can
just be artifacts
in the model theory (replace
the asRealBag property with
a BagEXT ala IEXT and CEXT).

Anyway... that's my idea. I meant to write
it down in RDF/n3, but I haven't gotten
around to it. Maybe Jos will beat me to it. ;-)

Is there code out there that behaves this
way, does anybody know? would it be useful
to specify it sorta like this? Or should
we leave rdf:Bag as just a hint,
ala rdf:Alt?

-- 
Dan Connolly, W3C http://www.w3.org/People/Connolly/
Received on Sunday, 17 February 2002 10:37:51 EST

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