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Re: rdfs:Graph ? comment on http://www.w3.org/TR/rdf11-concepts/#section-dataset and issue 35

From: David Booth <david@dbooth.org>
Date: Fri, 13 Sep 2013 12:07:09 -0400
Message-ID: <5233382D.50302@dbooth.org>
To: Pat Hayes <phayes@ihmc.us>
CC: Sandro Hawke <sandro@w3.org>, www-archive <www-archive@w3.org>
On 09/12/2013 03:18 AM, Pat Hayes wrote:
> On Sep 11, 2013, at 9:33 PM, David Booth wrote:
>> [Let's move this discussion to www-archive@w3.org
> Sure. I thought we were doing that, in fact. Sorry about the slip
> there.
>> please, as it isn't relevant to Jeremy's comment.  All follow-ups
>> there please.]
>> On 09/11/2013 10:32 PM, Pat Hayes wrote:
>>> On Sep 11, 2013, at 5:38 PM, David Booth wrote:
>>>> On 09/09/2013 02:51 AM, Pat Hayes wrote:
>>>>> The question though is, whether
>>>>> I(<http://my.graph.name.example.org/>) = the graph you want
>>>>> it to mean. The problem is that there are people who want to
>>>>> use an IRI to simultaneously denote a person (say) but also
>>>>> be the name of a graph (eg of information about that person).
>>>>> And they have deployed systems and much money vested in being
>>>>> able to do this.
>>>> Uh . . . this may be opening up a can of worms, but what
>>>> you're saying sounds a lot like the IRI resource identity
>>>> ambiguity issue that has been discussed quite a lot in the
>>>> past.  In short, there is no conflict if either: (a) the class
>>>> of persons has not been asserted to be disjoint with the class
>>>> of graphs
>>> Indeed. I am assuming throughout this discussion that graphs and
>>> persons are disjoint classes, and that this is known by all
>>> parties involved.
>> Okay, but not all software needs to make that distinction.  So
>> unless it has been explicitly stated in the graph (or implied as a
>> valid entailment)
>>>> ; or (b) the IRI denotes a person in one RDF interpretation
>>>> (e.g. in one system) but denotes a graph in a different RDF
>>>> interpretation (e.g. in a different system).
>>> That is nonsense, as I have explained to you many times in the
>>> past.
>> Baloney!  *Each* interpretation maps an IRI to one resource, but
> Of course. This is a little like getting excited about the fact that
> 2+2=4.

Well, when someone asserts that x+y is always 6, sometimes it's 
necessary to jump up and point out that 2+2=4.

>> And different interpretations can perfectly well map the same IRI
>> to different resources.
> Of course. That is what interpretations are for.
>> Please stop trying to look at RDF in terms of only one
>> interpretation!  That is *not* the only way -- or the only correct
>> way -- to think about RDF.
> I am not looking at it that way. And this discussion is not about
> RDF, by the way, it is about the basic ideas of model-theoretic
> semantics, which I regret to have to tell you, you apparently do not
> fully understand.

I'm sure I don't understand model theory as well as you, but unless you 
are suggesting that there is some hidden magic, I can certainly follow 
basic logic, and that's what I'm doing.

>>> Interpretations are not systems: they are alternative ways to
>>> construe what IRIs denote.
>> Yes, and different systems (or people) can and do construe them
>> differently.
>>> But each IRI denotes one thing, in all possible interpretations.
>> No, in *each* possible interpretation, not in *all* possible
>> interpretations.
> Yes. In every interpretation, it is the case that each IRI denotes
> one thing. Anything true in all possible interpretations is a
> logically necessary truth.

Not true!  That is only a logically necessary truth if one can only talk 
about one interpretation at a time -- the "single-interpretation 
assumption".  But as soon as we start talking about more than one 
interpretation at once, then it is no longer true (because the same IRI 
can map to different resources in different interpretations).  And that 
is exactly what we do when we talk about sets of satisfying 
interpretations, for example.

You seem to be assuming that interpretations have some kind of divine 
significance -- a "magic happens here" sort of assumption.  Imagine that 
we are talking instead about houses (instead of interpretations) and 
living room and dining room colors, and we prove that for any h in 
Houses, color(h, LR) = color(h, DR).  Does that mean that it is a 
"logically necessary truth" that every living room color matches every 
dining room color?  Of course not!  The color of the living room in one 
house may still be different from the color of the dining room in 
another house, even if the colors are constrained to be the same in 
every *individual* house.

Does it make sense to talk about more than one house at a time?  Sure! 
We can talk about the color of the living room in house h1 and the color 
of the dining room in house h2, and discuss whether they are the same or 
different, etc.  And yet you seem to be assuming that interpretations 
are somehow different -- magical -- and that for some reason we are not 
allowed to talk about what a URI denotes in two different 
interpretations, and I don't agree with that.  That assumption leads to 
overly broad (and therefore wrong) conclusions like the following:

> Therefore, that each IRI denotes one
> thing, is a logically necessary truth.

But that is a logically necessary truth only **in any one 
interpretation** -- not across interpretations.

> Here's a terse way to show it, using a more conventional logic than
> RDF. Suppose we have equality in our logic. Then
> a=a
> is logically true, true in all interpretations, necessarily true.
> Why? Because, in every interpretation, *both* occurrences of 'a'
> denote the *same thing*. The fact that in one interpretation, the
> first 'a' might denote me, and in another interpretation,. the second
> 'a' might denote you, does not make the equality false in any
> interpretation.

Quite true, but that does *not* imply that 'a' always denotes the same 
thing unless you are *also* making the single-interpretation assumption, 
i.e., that we are only ever able to talk about one interpretation at a 
time.  But it is quite reasonable to talk about what 'a' denotes in 
different interpretations, and it may not be the same thing.

>> I.e.,
>> For any interpretation I and URIs U1 and U2, (U1=U2) => (I(U1) =
>> I(U1))
>> NOT:
>> For any interpretations II and I2, and URIs U1 and U2, (U1=U2) =>
>> (I1(U1) = I2(U2))
>> I.e., the uniqueness does not hold *across* interpretations.  It
>> only holds within *each* interpretation individually.
> Of course. But since it holds in all of them, it is always true: in
> fact, necessarily true.

Again, it is only "always true" if you further assume that you are only 
ever talking about *one* interpretation at a time.  But I'm not.  I am 
specifically talking about multiple interpretations.

>>> (The current RDF 1.1 semantics socument makes thie very explicit,
>>> by the way.)
>> Yes, I noticed that, and the current wording is *incorrect*.
> No, it is exactly correct.
>> It needs to be fixed, as it wrongly implies that RDF may only be
>> viewed from the perspective of a single RDF interpretation, and
>> that is simply *wrong*.
> I have no idea what this 'perspective' language is siupposed to mean.

It isn't a language, it is a way of thinking.  I'm using the term in the 
conventional English sense.

> Each interpretation is a possible way that the universe  that RDF
> describes might be configured. That is what "interpretation" means.
> It is sometimes called a "possible world", though that term comes
> with lots of extra baggage which is best avoided, IMO.

Yes, I am aware of that.  That's a way of thinking about it, but AFAICT 
it has no bearing on the mathematics.  If you think it does, please tell 
me how.

>> I have not yet raised that issue, but I will.  I wanted to talk it
>> over with you first, before causing a long email thread.
> I suspect it will be quite short, in fact.
>>> If we want to allow different occurences of an IRI to denote
>>> different things, then we would need some kind of context
>>> mechanism in RDF, which it currently does not have, and providing
>>> which would have been beyond this WGs charter.
>> You are talking about something entirely different than what I am
>> talking about.  I am not and never have been talking about that
>> kind of notion of context.
> Actually you are, although you apparently do not realize it. That
> kind of notion of context is the only way to have different
> occurrences of the same name denoting differently. That, in fact, is
> often taken to be the *definition* of what makes a logic contextual.

No, again you seem to be making the single-interpretation assumption. We 
already established many times that an IRI may denote different things 
in different interpretations -- you referred to this observation rather 
derisively as equivalent to pointing out that 2+2=4 -- and if those 
different interpretations happen to be applied to different graphs, then 
different occurrences of that name *are* denoting differently in those 
graphs, i.e., 2+2=4.  If you want to talk about these different 
interpretations *within* the RDF semantics framework, then a contextual 
logic as you suggested would indeed be required.  But I am looking at 
the RDF semantics as a whole from the outside, and I can perfectly well 
talk about different interpretations without adding contextual logic to 
the RDF semantics.

>> I am talking about the *existing* RDF Semantics, BUT from the
>> perspective of looking at the set of satisfying interpretations for
>> an RDF graph -- not from the perspective of a single
>> interpretation.
> This entire idea of 'perspectives' arises from a confusion that you
> have about how model theory works. The whole point of interpretations
> is to provide an exact statement of entailment, which as I am sure
> you know, refers to *sets* of interpretations.

I have no beef with the way entailment works in the RDF semantics.

> Sorry, David, but this debate is pointless. Go read a book about
> semantics, or something. You are just plain confused.

I hope it isn't pointless.  I hope we can come to some common 
understanding on this.  But it sounds like you have not yet understood 
my points.

Received on Friday, 13 September 2013 16:07:57 UTC

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