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
**RDF ALLOWS MULTIPLE INTERPRETATIONS**!
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.
David
