Hi Pat,
On 10/10/2013 02:05 AM, Pat Hayes wrote:
[ . . . ]
But, as I say, I now think that this idea, of trying to connect the
formal notions to an intuition, was probably a mistake in this
document and went against the spirit of a WG decision.
I don't know what was the WG decision, but formal specifications of any
significant size almost always benefit from helpful informal guidance
that gives insight about how they are intended to work. This is
analogous to the role of good comments in code when writing software.
But I'm okay with it being deleted if you want.
Pat
<<Other in-line responses, below, are part of our continuing, um,
debate, and are aside from discussions of the RDF documents.>>
On Oct 4, 2013, at 10:51 AM, Peter Patel-Schneider wrote:
In my opinion the divergence boils down to Pat believing that
this informative section should be more informal and David
believing that it has to be more formal.
I don't exactly think it has to be more formal, but just that: (a)
it needs to mention interpretations, because that concept is so
central to the formal semantics; and (b) the statement about the
conditions under which a graph is true *needs* to be scoped to an
interpretation to make any sense at all.
That is exactly what it should *not* be, in order to convey the point
it was intended to be conveying.
The point to which you allude appears to reflect a particular intuition,
but apparently I don't agree that that is the only valid intuition that
is supported by the mathematics. More on this below.
If one talks about a graph being true, without mentioning an
interpretation, IMO the most sensible way to understand such a
statement is to take it as meaning that the graph is *satisfiable*
No, that is not the right way to understand it. Truth and
satisfiability are not the same thing at all. (That pigs can fly, is
satisfiable.) To say that a graph (or any other assertion or
sentence) is true, is to say that when it is interpreted *in the
actual world*, its truth-value is true.
There are multiple problems I have with that last sentence. First of
all, AFAICT the formal semantics makes no claim whatsoever about the
real world: the semantics leaves it up to the user to choose
interpretations. Second, the phrase "*the* actual world" betrays an
assumption that there exists only *one* valid interpretation -- that
"single-interpretation assumption", as I've been calling it -- whereas
AFAICT the formal semantics makes no such assumption.
That is the pre-theoretic,
intuitive, notion. Someone says something, you figure out *what* they
are saying, and you judge whether it - what they are saying - is
true. Nothing in that account mentions interpretations. It does
mention, implicitly, the truth conditions (section 5) and we could
say that it *presumes* an interpretation that the speaker and hearer
have in common.
Ah, now we're starting to get closer to the heart of the issue. I'll
come back to this below.
And that is where the naivitée of this naive account
is displayed, of course, that implicit assumption of a common
interpretation; because when we have the kind of distancing between
publisher and reader that is inevitable on the semantic web, and
communicate using IRIs which have no assumed common background of
linguistic meaning, we cannot presume this common shared
interpretation, this "common ground"
(http://semantics.uchicago.edu/kennedy/classes/f07/pragmatics/stalnaker02.pdf,
or
http://plato.stanford.edu/entries/discourse-representation-theory/.)
Agreed.
So this is where the interpretation idea comes in, because we have
to, as it were, survey the possible things you might mean when you
publish some RDF. We don't know what world you are talking in, so we
have to consider all *possible* worlds. Which is what interpretations
are (the thin, pale shadows of formalizations of).
Yes, excellent so far.
Long - very long - story short, the analysis of real linguistic
communication - including Web communication - between cognitive
agents (people, mostly) involves model-theoretic ideas, but it also
involves a *lot* more. RDF, indeed the entire semantic web, is a tiny
part of this larger picture, and can be fitted into it in one small
corner. But in order to be useful, it does need to be fitted into it
accurately.
: that there *exists* an interpretation under which the graph is
true, and hence we can take the graph as being true. (Conversely,
if the graph is not satisfiable then we cannot take it as being
true.) OTOH, such a statement could be taken to mean that the
graph is true **in some unspecified interpretation**
The one that is presumed when we talk (pre-theoretically) about what
people are referring to when they say "Everest" (for example), and
when we make judgements of the truth or otherwise of their utterances
in the actual, real, world we are all talking about. Yes, exactly.
First of all, I really like this explicit distinction between the
pre-theoretic or real world notion of truth, and the truth value that is
assigned to an RDF graph by the formulas in the formal semantics. That
helps the discussion.
With that on the table, although real world truth should be a *goal* --
just as one resource per URI should be a goal -- I don't believe that it
is the right criterion for making engineering decisions in the semantic
web world. Rather, *usefulness* is the more relevant criterion by which
we should evaluate our engineering trade-offs when designing the
semantic web. This will take more explanation, so I'll attempt to
provide that. But with respect to interpretations, this translates into
the notion that a more agnostic view toward interpretations should be
taken, rather than making the single-interpretation assumption that
always attempts to understand every RDF utterance in terms of a single
notion of pre-theoretic real world truth.
Now to attempt to explain. First of all, note that there is nothing
whatsoever in the mathematics that limits us to a single interpretation:
the mathematics works perfectly fine without modification whether we
eventually talk about one or more than one interpretation. I've
pointed out several times that it is perfectly possible to have two
interpretations I1 and I2 and two graphs G1 and G2, such that
I1(G1)=true and I2(G2)=true (in the non-pre-theoretic sense), whether or
not these graphs share some of the same URIs. "So, what of it?" you may
ask. I'll get to that.
The second point to observe is that different graph authors have
different interpretations in mind when they write their graphs. This
can be either conscious or unconscious. Although I agree that there is
a single notion of pre-theoretic truth in the real world, different
people have different -- and sometimes *very* different -- ideas of what
that single truth is. Correspondingly, they also make different
assumptions about the resource to which a given URI maps, within those
interpretations. Again you may object and assert that if they are
making different assumptions then one or more of them should be
considered wrong. But again, as I've tried to point out, such a
requirement is not generally *possible* to obey.
Asssuming that a URI owner has the right to say what resource his/her
URI denotes (as described in the Web Architecture), there are several
reasons why different well-intentioned URI users may make different
assumptions about the identity of a URI's resource:
1. The URI owner may not know or may not understand a particular
resource distinction that matters to some user of that URI. We cannot
expect every URI owner to be omniscient about his/her URI's resource.
2. The URI owner may not care about a particular distinction. We cannot
expect the URI owner to have the same concerns as all users of the URI.
3. The URI owner may *intend* the URI definition to be ambiguous to some
degree, so that the URI can be used in a wider variety of ways.
4. The URI owner may not be reachable to clarify a particular point of
ambiguity.
5. The URI owner may want to keep the resource definition simple,
without cluttering it up with distinctions that 99% of the
URI's target users would not care about. Complexity has a cost.
6. The URI owner may not wish to expend the resources necessary
to figure out what finer distinctions might be made.
7. When a URI definition is provided in a machine processable form such
as an RDF graph -- and that of course is the point of the Semantic Web
-- it is generally not possible to make that definition unambiguous.
So the reality is that different authors *do* make different assumptions
about the resource denoted by a particular URI. This is very neatly
captured by the notion that different authors have different sets of
intended interpretations in mind when they write their graphs. In other
words, when an author writes an RDF graph, the author's intended meaning
of that graph does *not* generally boil down to a *single*
interpretation, but an ambiguous *set* of interpretations, all of which
are licensed interpretations falling within the author's intent.
This leads to the question of what exactly are the author's intended
interpretations for a given graph. That of course may be hard to know
-- just as it may be hard to know what *single* interpretation the
author intended if one assumes that the author only intended a single
interpretation. But given that the author could (in principle at least)
if desired supply whatever constraints he/she chooses as triples within
the graph, a reasonable assumption is that the intended interpretations
are the satisfying intepretations of the ontological closure of that
graph. (By ontological closure I mean the union of the graph with the
transitive closure of the URI definitions for the URIs within the
graph.) This makes for a very "what you see is what you get" notion of
the intended interpretations, and I will note that it has the further
advantages of: (a) removing nearly all "then a miracle occurs" steps
http://blog.stackoverflow.com/wp-content/uploads/then-a-miracle-occurs-cartoon.png
in the determination of interpretations; and (b) being completely
aligned with the intent of the Semantic Web of facilitating machine
processing.
In other words, to my mind the notion of interpretations provided by the
RDF Semantics aligns very well with: (a) the inescapable ambiguity of
resource identity; and (b) the fact that people do *not* have the same
view of the world, nor do their software applications have the same view
of the world.
. But that would be a very bad way to write
Try telling that to linguists. Or to literary theorists, or
historians, or philosophers of language, or indeed pretty much anyone
who uses language professionally. Not only is this not a bad way to
write, its the ONLY way to write if we are trying to anchor model
theory in an intuitive description of how communication actually
happens.
I can't comment on literary theory or such, but to my mind, in formal
semantics, variables should *always* be bound.
Except, calling the actual world "unspecified" seems a
little strange.
Amusing. :) But I don't view the actual world as being very relevant
to the semantics, perhaps because I have a different intuitive view of
the semantics than you do, as I tried to explain above.
, because the interpretation under which the graph is true would be
an implicit unbound variable, which as we all know is a big no-no.
It is implicit, yes, but I don't know what kind of assumptions you
are appealing to by calling this a big no-no. Contexts are usually
implicit, right?
Yes, but we try hard to make them explicit, especially in formal specs.
Instead, the problem can be easily solved by adding "under a given
interpretation" to the sentence. (Of course, the notion of an
interpretation should first be explained. But that is a different
omission that should be addressed anyway.)
And regarding this:
http://lists.w3.org/Archives/Public/public-rdf-wg/2013Oct/0079.html
[[
I know, from extensive off-line email discussions with David, that
he does not properly understand the intuitive foundations of
semantics in any case, so I am not inclined to accept his rather
condescending advice. ]] (Wow, you're calling *me* condescending,
after repeatedly telling me to "go read a book"???) That's both:
(a) quite a projection; and (b) *really* unfair and unhelpful.
Fortunately I'm thick skinned and I have a good sense of humor.
:)
Well, you weren't meant to read that, obviously. But my dear fellow,
*have* you read the books, in fact?
I've read what I could find on the web on model theory, but not books.
The best resource I've found has been the Stanford Encyclopedia of
Philosophy, which I like a lot:
http://plato.stanford.edu/
For example, here is their entry on model theory, which corresponds
beautifully with your explanation:
http://plato.stanford.edu/entries/model-theory/
Incidentally, I wrote to the author of that particular article for some
minor clarification, and he was quite nice and confirmed a particular
point of understanding about interpretations. If there are other
references on the web that you'd suggest, I would certainly be
interested in looking at them. But thus far, all that I have read has
confirmed the understanding that I initially got from your writings,
which I've found most informative, BTW.
Is it really condescending for me
to suggest that you might want to read up something a little more
extensive than a few paragraphs that I wrote about RDF,
I certainly have done so, and read it quite carefully too.
before
claiming that you have discovered a new way to understand model
theory, or setting out to correct my misunderstanding of it,
NEVER have I made any such claim.
or
telling me that my perspective is too limited? I don't mean to pull
rank on you here, but I have been studying this stuff now, as well as
teaching it, for about 40 years. For a few years, I invented new
model theories for a living. God knows there are a lot of things I
don't fully understand, but model-theoretic semantics is one topic I
really do have pretty thoroughly grokked.
Okay, stop right there. Clearly you have grossly misunderstood my
intent, as I have never once questioned your understanding of model
theory, nor have I made any claims of discovering a new way to
understand model theory or any other such grand claims. All I have done
is tried to point out that, **based on the mathematics given**, there is
another valid way to think about the RDF Semantics. Furthermore, AFAICT
it is a *useful* way to think about the RDF Semantics, as it helps
explain real world use of RDF in a way that is not explained under the
single-interpretation assumption. It is not in any way intended to
extend model theory or make any grand claims about any new discoveries.
It is just a simple and straightforward way to use the semantic
formulas defined by the RDF Semantics that perhaps uses a slightly
different intuition of what they mean. Formulas are formulas and can be
viewed in different ways. Although many people may think intuitively of
E=MC^2 as meaning that matter can be converted to energy, it can also be
just as well taken to mean that energy can be converted to matter.
I hope this helps to clarify my intent.
Thanks,
David
