Okay, finally zeroing in on the crux of the matter . . .
On 03/23/2013 12:49 AM, Pat Hayes wrote:
On Mar 22, 2013, at 10:30 PM, David Booth wrote:
On 03/21/2013 01:02 PM, Pat Hayes wrote:
On Mar 20, 2013, at 9:58 PM, David Booth wrote:
On 03/20/2013 12:04 AM, Pat Hayes wrote:
On Mar 18, 2013, at 4:04 PM, David Booth wrote:
On 03/17/2013 10:02 PM, Pat Hayes wrote:
On Mar 16, 2013, at 11:26 PM, David Booth wrote:
[ . . . ] But presumably that passage from Section 1.2
means ". . . [the semantics simply assumes that ... a
single URI reference can be taken to have the same meaning
whenever it occurs] _in the *given* graph, i.e., the graph
whose semantics are being determined_",
No, it means wherever they occur, period. If they occur in
several graphs, they all refer in the same way in all of
them.
Absolutely not. That is only true for *one* interpretation.
Absolutely yes. It is true for all interpretations. There is no
interpretation which allows a single URI to refer in different
ways when it occurs in different graphs.
Uh-oh, there's that single-interpretation assumption creeping in
again!
No assumption is creeping anywhere in that statement. I said, for ALL
interpretations.
The "single-interpretation assumption" that you keep making is to assume
that one can only talk about **one interpretation at a time** when
talking about whether a URI can "refer in different ways when it occurs
in different graphs". But as I pointed out below -- and you agreed --
in different interpretations the same URI *can* refer to different
resources.
While it is true that there exists no *single* interpretation that
allows a single URI to refer in different ways when it occurs in
different graphs
There exists no interpretation which ... No need to say or emphasise
"single".
The emphasis was added to point out that you were making the
single-interpretation assumption. While it is true that "There exists
no [single] interpretation which ...", it is NOT true that "There exist
no *two* interpretations which ...". And the example that I gave
(directly below) demonstrates this.
, surely you would agree that under standard RDF Semantics:
There exist interpretations I1 and I2, RDF graphs G1 and G2, URI U
and resources R1 and R2, such that I1 maps U to R1, I2 maps U to
R2, and R1 != R2.
Of course.
Therefore, under standard RDF Semantics:
1. A URI can map to *different* resources in *different* graphs.
(Proof sketch: Use I1 for one graph and I2 for the other.)
No, and your proof is faulty. You don't get to use an interpretation
for one graph and a different interpretation for the other.
Sure I do. I just did, above, and you agreed with it! Notice that the
sentence "A URI can map to *different* resources in *different* graphs"
does not mention or constrain the number of interpretations that may be
used. You (wrongly) assumed that I meant "under any *single*
interpretation". But I am specifically raising the point that it is
useful to consider multiple interpretations.
Each
interpretation is a mapping *on names*, not on graphs. GIven such an
mapping on names, the truth or falsity of all graphs is determined.
Yes, for all graphs relative to *that* interpretation. But it does
*not* determine the truth-value of a graph relative to some other
interpretation. I'm being picky about this because you keep slipping
into the single-interpretation assumption, and I'm trying to point out
that it is useful to be able to talk about more than one interpretation
at a time, and to apply *different* interpretations to different graphs.
What does it mean to "use" I1 on G1 and "use" I2 on G2?
It means to apply I1 to G1 and apply I2 to G2, i.e., to determine the
truth-value of I1(G1) and I2(G2), per RDF Semantics.
Each of I1
and I2 apply to all the names in both G1 and G2. The "combination"
you have sketched is not an interpretation mapping, so (a) what is
it? and (b) what relevance does it have to what we are talking about,
which is interpreting RDF graphs?
What "combination" do you mean? I did not talk about combining either
I1 and I2 nor combining G1 and G2. I talked about considering the
semantics of G1 and G2 *separately*.
Here's the corrected version:
1. Lemma. A URI maps to the same thing, no matter what graph it
occurs in. (Proof: Let I be an interpretation mapping and U a URI.
Then I maps U to I(U). The previous sentence did not mention graphs,
so it applies regardless of what graphs contain U. But I was
arbitrary, so this is true of any interpretation. QED.)
Of course that is true of any *one* interpretation -- i.e., when you
make the single-interpretation assumption. But that isn't the point.
The point is that the RDF Semantics specifically permits multiple
interpretations. The spec defines a standard way to determine the
truth-value of *any* <interpretation, graph> pair. It is explicitly
agnostic about the interpretations (and the graphs) that may be used.
You are of course free to limit *your* use of the RDF Semantics to the
single-interpretation assumption. That is your prerogative. But it is
*not* a requirement of the RDF Semantics specification. Given n
interpretations and n graphs, it is perfectly valid to use the RDF
Semantics to determine the truth-values of each of those n graphs
relative to those n interpretations, without in any way violating the spec.
2. A URI can map to *different* resources. (Proof sketch: Use
different interpretations, I1 and I2.)
In different interpretations, yes, of course.
Some may claim that this
What is "this" ?
This way of using the RDF Semantics spec.
is a misuse of the RDF Semantics -- that there really is only one
"correct" interpretation, even though we may not know which one it
is. (This is the single-interpretation assumption.) But the RDF
Semantics makes no such requirement, and to my mind that is part of
its genius, because the allowance of multiple interpretations is
valuable! It lets us better account for the real world use of RDF
-- **under standard RDF Semantics** -- because in the real world,
RDF authors *do* make different assumptions in their
interpretations of URIs, and different RDF consumers *do* apply
different interpretations to the URIs they encounter.
I have separately tried to point out how the existing RDF Semantics
spec already supports a poor person's notion of context *because*
of its allowance of multiple interpretations:
http://lists.w3.org/Archives/Public/public-semweb-lifesci/2013Mar/0099.html
But your argument there is faulty, because the presence of multiple
interpretations does not, by itself, provide any notion of context,
poor or otherwise.
It does provide a very simple notion of context, as explained below --
not a fully featured notion of context that one would normally expect
when one talks about having a notion of context. That's why I called it
a "poor person's" notion of context.
The purpose of a context is to enable the same RDF graph to have
different truth-values in different contexts.
Actually, more basically, it is to enable a single URi to refer to
different things in different contexts. Which then has the graph
consequence that you mention.
Fine, use that definition instead. The consequence is the same.
But this is exactly what an interpretation does!
No, that is not what an interpretation does.
Surely you would agree that interpretations enable a single URI to refer
to different things in different interpretations. Therefore, if a
context *is* an interpretation, then a context would enable a single URI
to refer to different things in different interpretations. And that is
exactly how you described the purpose of a context.
An RDF interpretation
maps each URI into a single referent (and each graph to a single
truth-value.). It does not provide for one URi to have different
meanings in different contexts, because it does not provide any
contexts to pur URIs into. To do that, it would have to be a mapping
from (URIs x contexts) to referents.
Correct. A *single* interpretation does not provide for one URI to have
different meanings in different contexts. But if a context *is* an
interpretation, and multiple interpretations are considered, then those
interpretations *do* provide a way to map one URI to different meanings
in different contexts/interpretations.
So if you think of an RDF interpretation as a context -- which IMO
is quite a natural way to think of it
I am afraid that if this seems natural to you, then you really have
not understood the basic idea of model-theoretic semantics. (Ask
yourself: if interpretations are contexts, how does one provide a
semantics for an actual context logic, such as ICL or Cycl, which has
names for contexts in the syntax of the language?
As I said below, the RDF Semantics would have to be extended to do
things like that.
And if
interpretations are contexts, then all logics ever invented have been
context logics, so why did context logicians feel that they had any
need to invent them again? And what did Guha get his doctorate for,
if all the work he did was already somehow inside the standard Tarski
model theory?)
Because people often want to do more things with contexts than merely
considering the semantics of n graphs separately. They want to be able
to consider the semantics of the *merge* of two graphs, for example, and
that indeed does require more than just interpretations.
-- then different RDF graphs can *already* be interpreted in
different contexts (i.e., according to different RDF
interpretations) under the *existing* RDF Semantics, because as we
have laboriously agreed, **the existing RDF Semantics allows
different interpretations to be applied to different RDF graphs**.
I hope I did not agree to that as stated. The semantics allows for
different interpretations, and it defines the truth of a graph in an
interpretation. Each interpretation determines the truth-value of
*all* graphs. The semantics does not mention, and does not provide
any way to make sense of the idea of, applying one interpretation to
one graph and a different interpretation to another graph. That idea
is a pure figment of your imagination.
The semantics does not have to mention how to do that. If I define a
function f from two integers, f(x,y) = x+y, I do not have to "provide a
way" for you to apply it to multiple <integer, integer> pairs. You are
perfectly free to do so!
Similarly, in essence the RDF Semantics specification defines a function
-- call it RS -- that, given any interpretation I and any RDF graph G,
determines the truth-value of I(G). The definition of RS does not have
to give anyone permission or "provide a way" to apply that function to
multiple <interpretation, graph> pairs. RS may be applied to *any*
number of interpretation-graph pairs, in full conformance with its
definition.
[Actually, to be slightly more technical, in this approach to
contexts it would be better to view a context as a *set* of
interpretations, rather than a single interpretation, because it is
still useful to talk about the set of satisfying interpretations
for an RDF graph, subject to a particular context. But that's an
unimportant detail at the moment.]
Indeed, people *already* use RDF graphs in this way: intentionally
keeping graphs separate if they come from different perspectives,
sources, provenance, etc., *because* the graphs may cause
inconsistencies or lead to incorrect conclusions if merged
injudiciously.
That is true, but...
Knowingly or not, different interpretations are being used for
different graphs.
...that does not follow. Consider: if the URIs referred differently
in the various graphs, then these graphs would *not* cause
inconsistencies if taken together. The inconsistencies arise
precisely *because* we all assume that a given URI denotes the same
thing in every graph in which it occurs, and that interpretations
apply across graphs.
When the graphs are merged then the assumption is made that a given URI
denotes the same thing in all of the graphs that are being merged, yes.
But different interpretations can and often are used for different
graphs when those graphs are *not* merged.
A simple example is Ian Davis's famous toucan-versus-its-web-page
example,
http://blog.iandavis.com/2010/11/04/is-303-really-necessary/ in
which the same URI "ambiguously" denotes both a toucan and the web
page describing that toucan. One RDF graph, Gt, may be written
under the assumption that the URI denotes the toucan. Another
graph, Gp, may be written under the assumption that the URI denotes
the toucan's web page. Gt may work perfectly well in an
application that merely categorizes different animal species --
*unambiguously* interpreting the URI as denoting the toucan. And
Gp may work perfectly well in an application that merely lists web
page authors -- *unambiguously* interpreting the URI as denoting
the toucan's web page. In fact, even the merge of Gt and Gp may
work perfectly well in both applications, provided the RDF authors
have not asserted that toucans are disjoint from web pages!
This is called punning, AKA overloading.
Well, no, that isn't what I meant. But it isn't worth pursuing. I
think I've made my points enough above.
David
As you point out, it works
up to a point. But this is not context reasoning. In fact, it is
might be described as un-context reasoning: it is what happens when
you mush what should be distinct contexts into a language which does
not have a context mechanism to distinguish them. If this were
written in a real context logic, then you would have explicit
contexts for the two distinct meanings.
Applications that consume RDF and faithfully follow the RDF
Semantics are free to choose their own interpretations, and this is
A Good Thing.
On the other hand, an application that needs to distinguish between
web pages and animal species will find this toucan/webpage URI
hopelessly ambiguous, and will not be at all happy with the merge
of Gt and Gp. This is why I have been pointing out (in other
conversations) that ambiguity is *relative* to the application: a
URI may be unambiguous to some applications, but ambiguous to
others.
But although the existing RDF Semantics does support this simple
"poor person's" notion of context-as-interpretation (or
context-as-set-of-interpretations), it does not support other basic
features that one would expect in a context-aware semantics. Most
notably, it does not support the ability to retain contextual
differences when RDF graphs are merged. To account for that and a
few other basic operations, the RDF Semantics would indeed have to
be extended, as you and a few others have proposed.
[ . . . ]
The semantic rules simply specify when a graph (any graph)
is true in an interpretation (any interpretation). But
interpretations are not defined "on" graphs: they are
mappings from *names* to things. That does not mention graphs
at all. So to then start talking about one graph in one
interpretation and another graph in another interpretation
simply misses the point. The fact that there are many
possible interpretations is a reflection of the fact that we
typically are in a state of doubt about what the names (URIs)
actually refer to.
That sounds dangerously close to falling into the trap of
assuming that there really is only one, global, correct
interpretation. And it is *my* interpretation, of course. ;)
It is not anyone's interpretation: it is the fact of the matter.
Of course, we don't have access to the facts, only our
representations of them, which allow many interpretations.
I don't see how this "fact of the matter" has any relevance
I probably shouldn't have mentioned it, as it seems to have been more
confusing than enlightening. (It is the standard way to understand
model theory when discussing mathematics, eg people talk about
"standard arithmetic", meaning the single "correct" way to interpret
formal arithmetics.)
Pat
, since: (a) the RDF Semantics says nothing about it; and (b) it is
an application's own business what interpretations it chooses to
use. If that application causes some harm by applying the wrong
interpretation, then the owner may be liable, but that is an
entirely separate issue from the question of compliance with the
RDF Semantics.
David
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