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:
[ . . . ]
Read the spec: http://www.w3.org/TR/rdf-mt/
Indeed. Section 1.2, first paragraph: "... the semantics simply
assumes that ... a single URI reference can be taken to have the
same meaning wherever it occurs. Similarly, the semantics has no
special provision for tracking temporal changes. It assumes,
implicitly, that URI references have the same meaning whenever
they occur."
[ . . .]
But presumably that passage from Section 1.2 means ". . . whenever
they occur _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. But as you
clearly admit below, "there can be many of these interpretations", and
each interpretation could map the URI to a *different* resource.
Thus, to be very clear, under the existing RDF Semantics specification,
a given URI does *not* necessarily map to only one resource.
So, returning to my point made many messages ago, the idea that a URI
denotes only one resource is a good architectural goal, but it is *not*
required under existing RDF Semantics.
It is important that we avoid slipping into the trap of assuming that
there is only one interpretation.
[The rest of my response is mostly nitpicking, so readers who only want
to read the main point may safely stop reading here.]
since the spec would be meaningless if it were predicated on the
assumption that a URI always has the same meaning everywhere:
It had better not be, as it is predicated upon that assumption :-)
1. If a URI always denoted the same resource then there would be no
need in the RDF Semantics for multiple interpretations that map URI
references to different resources, because every interpretation
would necessarily map a URI to the exact same resource.
No. Lets make sure we are speaking very carefully here. An
interpretation is a mapping from names (URIrefs - now called IRIs -
and literals) to things in a universe. Each such mapping is from the
names to what they are being interpreted, in this interpretation, to
name. (In the RDF 1.1 spec just being written, by the way, every
interpretation mapping is a mapping on *all* names, not just a
'vocabulary V' of names.) So each interpretaton is a decision about
what the names mean.
But of course there can be many of these interpretations.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Exactly.
One of them
might map "ex:PatHayes" to me, considered as a continuant, and
another might map it to the number 37.5, and yet another to my cat's
right front paw. But each of the many (maybe uncountably many)
interpretation mappings maps each *name* to some thing, and it
applies to *all occurrences* of that name. There is no such thing as
an RDF interpretation which maps an URI in one graph to one thing and
the same URI in a different graph to something else.
The RDF Semantics would need only one, unique global mapping! But
as we know (and Section 1.3 states): "there is no such thing as
'the' unique interpretation of an RDF graph". Presumably these
non-unique interpretations can and do map the same URI to different
resources, do they not?
DIfferent interpretations map the same URI to different resources,
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Ah-ha! The smoking gun! :)
yes. But each interpretation fixes that resource for each URI, and it
applies to every occurrence of the URI.
Yes, exactly.
2. As we know, a false assumption entails everything. If I were a
drug dealer, I could one week declare to my co-conspirators that
this week, http://dbooth.org/x means heroin, and next week it means
morphine.
True, but you and your evil henchmen would then be using RDF in a
noncompliant way which does not fit with the normative specs. (People
do do such things, of course; but specifications do not cease to be
normative when people fail to conform to them.)
In which case, that URI clearly would *not* have the same meaning
whenever it occurs. So if the RDF Semantics were predicated on the
false assumption that it does, the RDF Semantics would be
meaningless.
No, it would have the consequence that if someone were to follow the
RDF specs in this case, they would get into trouble. That often
happens to people who believe the specs and try to act on them, when
other people don't follow the specs. Still, that distasteful fact
about the dirty real world does not make normative specifications
meaningless.
In short, I can only see how the RDF Semantics could possibly make
sense if the idea that "URI references have the same meaning
whenever they occur" is talking about a *single* interpretation.
Yes, it is talking about a single **interpretation**. See above.
Whatever each URI means - we might not know what it means, hence the
need to consider alternative interpretations, but whatever it
actually means - every occurrence of it means that. It means what it
means globally.
Have I completely misunderstood something fundamental here?
Possibly. I'm not sure. Do my answers make sense to you?
They do make sense. You have confirmed my previous understanding of
the RDF Semantics.
The RDF semantics is only defined for a *given* RDF graph. It
does not constrain a URI's resource identity across *different*
graphs.
No, it does so constrain what URIs mean. It presumes that a
given URI denotes some single thing, wherever it occurs. The
interpretation mappings are defined as mappings upon URIs. not
upon occurences of a URI token in a particular graph; and the
semantics does not mention contexts or any other mechanism which
would allow a URI in one place to denote differently from the
same URI in another place (or at another time, cf the above
quote.)
The RDF Semantics spec defines a procedure
Well, not actually a *procedure*. It is not required to be
computable. But OK, leave that aside for now...
that is *parameterized* by a given interpretation (called "I"), and
a given RDF graph or piece thereof (called "E").
No, it defines an interpretation mapping and explains how to *apply*
that mapping to a graph E.
It certainly does *not* define interpretation I. "I" can be *any*
interpretation. It is universally quantified.
If I say "For any dog D, if D is black then D is a poodle", that does
*not* define D.
E is an argument, not a parameter.
Uh . . . no. Perhaps we have a clash of terminology here, between
mathematicians and computer scientists, but please look up the
difference between "parameter" and "argument":
http://en.wikipedia.org/wiki/Parameter_%28computer_programming%29#Parameters_and_arguments
The two terms are often used interchangeably, but (at least in computer
science) if a distinction is made, E would be called a *parameter* --
not an argument. Perhaps it's different in mathematics? Clearer terms
are "formal parameter" and "actual parameter", in which case "E" is the
formal parameter. An actual parameter would be a piece of RDF syntax,
such as a URI, triple or graph.
The spec is riddled with references to those parameters, and
semantic rules are written in terms of them. A typical example
from Section 1.4 reads:
"if E is a ground RDF graph then I(E) = false if I(E') = false for
some triple E' in E, otherwise I(E) =true."
How could this procedure possibly define the semantics of a graph
that it has not been given -- i.e., a graph that is not E?
E can be *any* ground graph. The symbol "E" in this text is not the
name of a particular graph, it is a universally quantified varaible
ranging over all ground graphs. ALL of them.
Of course one may choose any graph to consider, so any graph *may*
be considered E, in which case the procedure tells you the
semantics *of* *that* *graph*.
Yes, exactly.
But AFAICT, there is no way around *first* deciding what RDF graph
and interpretation you wish to consider, and *then* the procedure
defined in the RDF Semantics will tell you the truth value of
*that* graph relative to *that* interpretation.
This is mathematics, not an algorithm. There is no first/then
involved.
AFAICT, it says nothing about any other RDF graph that is not under
consideration.
It says something about all (ground) graphs, and it does not mention
being "under consideration", whatever that means.
I see no requirement in the RDF Semantics that interpretation "I"
be the *same* interpretation for every graph "E" to which this
procedure is applied.
There is none, of course. The semantic definitions you are citing
here apply to all interpretations and all graphs. (I really don't
understand what point you are making here, to be honest.)
The point that I attempted to make was that a URI *can* and often *does*
denote different resources, in full conformance with the current RDF
Semantics specification. As we have now so laboriously agreed, the RDF
Semantics only requires that a URI always map to the same resource
within a *single* interpretation. But it permits many interpretations.
Ergo my point.
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. ;)
But we are not in doubt that they do actually, or
are intended to actually, refer to something, and that **what they
refer to is not dependent on where they occur**: a given URI in one
graph refers to the same thing as it does in another graph, which is
why we can glean RDF from many sources and mash it together to draw
inferences.
Except that we can't. Because in reality, what those URIs refer to
*does* sometimes depend on where they occur, since people with different
perspectives *do* make different assumptions in different graphs. Thus,
to correctly interpret those graphs, different interpretations sometimes
*should* be used. And the existing RDF Semantics works just fine for
this, until you try to merge those graphs, at which point the semantics
would have to be extended to handle contexts.
David
The RDF semantics is predicated on this assumption. And a
context version of RDF would not assume this: it would allow a single
URI to mean one thing in one graph and a different thing in another
graph, consistently, in a *single* interpretation.
Am I right, or have I completely misunderstood something
fundamental?
Entailment, for example, is defined upon *sets* of RDF graphs,
and the definition of merging makes sense only if the URIs in
these various graphs all denote in the same way.
[Side note: As discussed above, surely you mean that "merging makes
sense only if the URIs in these various graphs all denote in the
same way" *in* a given interpretation. Right?
In *all* interpretations, but yes, OK.
]
Of course, but again, merging is defined on a *given* set S of RDF
graphs.
It is defined on sets of graphs. Being "given" is not a meaningful
mathematical term, AFAIK.
Once the user of the RDF Semantics spec has *chosen* S, the spec
defines entailment upon *that* S -- not on some other, unspecified
set. Is that correct
No. Entailment is a relation between sets of graphs, and graphs. No
choosing involved.
, or have I completely misunderstood the spec?
And here is a trivial existence proof that demonstrates that a
URI does *not* necessarily denote the same resource in
different graphs.
Graph 1 (assuming standard owl: prefix):
<http://example/h> a <http://example/WhiteHorse> .
<http://example/WhiteHorse> owl:disjointWith
<http://example/BlackHorse> .
Graph 2:
<http://example/h> a <http://example/BlackHorse> .
<http://example/WhiteHorse> owl:disjointWith
<http://example/BlackHorse> .
Each graph (by itself) has satisfying interpretations per
standard RDF (and OWL) semantics. And <http://example/h>
denotes a resource in each graph. But clearly it denotes a
*different* resource in each graph.
The conclusion you should draw here is that these graphs cannot
both be true. And indeed, if you merge those graphs into one,
then that merged graph is owl-inconsistent. But that does not
mean that the URIs denote differently in the two graphs. What it
does reflect is the fact that no interpretation of names will
make a contradiction true.
Of course both graph 1 and graph 2 can both be true! They are just
true under different interpretations!
There is no interpretation that makes them both true. That is the
precise way to say that they cannot both be true.
And in this case, those interpretations will necessarily map
http://example/h to different resources.
Well, they might interpret http://example/WhiteHorse and
http://example/BlackHorse differently. But I expect this is
nit-picking.
On the other hand, the merge of graphs 1 and 2 is necessarily false
under any interpretation.
Right.
Unless I am terribly mistaken, the RDF Semantics spec does not
mandate the use of a single, a unique interpretation that must be
applied to every RDF graph.
It does not mandate a single interpretation, of course, But it does
presume that each interpretation determines the truthvalue of every
graph.
Indeed, to my mind the main value of the RDF Semantics is that,
given an RDF graph, it allows one to determine the range of
possible interpretations under which that graph is true.
Yes. And it does that for *every* graph :-)
that does not concur with either the web specifications
Correct. As I pointed out, the AWWW's statement that "a URI
identifies one resource" is a good goal, but it does not
concur with standard RDF semantics.
It is quite consistent with, indeed presupposed by, RDF
semantics. As to whether it is really the case, that is a whole
more complicated question. But note that when AWWW says
"identify", it apparently does not always mean what RDF semantics
means by "denote". There is no assumption in RDF theory or
practice that a URI must denote what it 'dereferences' to using
http.
Right, that's a different question.
It might well be the case that
awww-identification is unique even while denotation is not.
nor the goals they were built to satisfy. Caveat emptor.
Not true! As I said before, I *agree* with the goal stated in
the AWWW, that a URI should denote one resource! But that does
not change the reality: that a URI does *not* necessarily
denote only one resource.
You are probably right, but to the extent that they do not, then
meaningful communication fails. So communication usually
presumes that they do, until circumstances force this assumption
to be revisited.
I think that is overly pessimistic. I think useful communication
can still be achieved, provided that the ambiguity is bounded.
Ah, we in fact agree here, but your way of phrasing it led me astray.
OK.
Pat
And when URI definitions are shared, the RDF Semantics (and its
semantic extensions) provide a very neat way to bound that
ambiguity.
David
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