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

From: Pat Hayes <phayes@ihmc.us>
Date: Sun, 15 Sep 2013 04:29:43 -0700
Cc: Sandro Hawke <sandro@w3.org>, www-archive <www-archive@w3.org>
Message-Id: <15D55576-0CDD-463B-B9D0-88246478A387@ihmc.us>
To: David Booth <david@dbooth.org>

On Sep 13, 2013, at 9:07 AM, David Booth wrote:

> 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 the DEFINITION of "logically necessary truth". Please, go read a logic textbook.

>  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.  

The entire apparatus of model-theoretic semantics is based on some undewrlying assumptions about meaning and language. FOrget interpretations for a second. We have some sentences, written in a language with a grammar, which we use to try to communicate. You send me some sentences. If I know exactly what you are referring to when you use the names you use, then I can fully understand you, lets us suppose. I do this by parsing your sentences, then taking the names (at the tips of the parse tree), figuring out what (you intended) the names refer to, then use the semantic tules of the language to construct the more complicated meanings that are conveyed by the larger sentences.  This is the overall picture, and its clearly somehat idealized compared to actual language use. In particular, it presumes that there is no contextual effects, since I rely on the fixed grammar to give me the way to construct meanings of larger expressions from those of their subexpressions. It also assumes that you are truthful, not lying or being sarcastic or ironic or anything 'clever'. 

Now, the chief problem here is, when you use a name, I might not know exactly what you are intending to refer to. I can presume that you are being truthful, however, so at least I know that you intend your names to denote in such a way that your sentences will be true. And that is something to go on. If you give me enough sentences, maybe that truthfulness assumption will be enough for me to be able to figure out what it is that your names refer to. Or at any rate, close enough to get some useful information out of what you are saying. And to do that, I can use principles of inference which are "safe", in the following sense: *whatever your names denote*, if X is true then Y is true, where X and Y are sentences or, more usefully, sentence "patterns". Then I can use these safe principles on your sentences to get more sentences, and I know I am OK because *whatever your names refer to", as long as your sentences are true, so will these other ones I have derived from them using these safe rules. 

That is the intuition. What Tarski did was to formalize this intuition and make it into useful mathematics, and the result is model theory. So the  idea of 'no matter what your names mean' is captured by that of an interpretation, defined to be a mapping from names to referents, and that of 'safety' by entailment, where the definition of entailment is: X entails Y means: for any interpretation I, if X is true in I then Y is true in I. 
Or, put another way, every I which satisfies X, satisfies Y. 

Nowhere in this story is there any idea of using one interpretation to interpret one sentence and a different interpretation to satisfy a different sentence, becuase that idea simply does not make sense, given what "interpretations" are intended to formalize, which is a way to interpret ALL sentences. 

> Imagine that we are talking instead about houses (instead of interpretations)

But this analogy makes no sense. 

> 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.

Logically necessary truths ARE those that are true in all interpretations, assuming completeness of the logic under discussion (which is a given for all logics below first-order, and certainly for RDF.)

>> 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.

Of course. But that does not make some occurences of 'a' denote differently from other occurrences of 'a'. 

>>> 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.

It does not matter how many intepretations you talk about, they are still all interpretations, and satisfy the definition of an interpretation. 

>>>> (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.

It has no precise meaning, even in English. Maybe if you tried formalizing your intuition it might get crisper. 

>> 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

No, they are not. Each interpretation applies to ALL names in ALL graphs. An interpretation assigns a truthvalue to every RDF triple. 

> , 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.

Of course we can talk about different interpretations. But each interpretation applies to all occurrences of all IRIs in all graphs. It is an interpretation of the entire RDF language. That is what the idea of "interpretation" is intended to capture. 

>>> 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.

You have not yet actually made a sensible point, only demonstrated a quite extraordinary degree of obtuseness in failing to grasp the basic idea of model theory, and hallucinating some 'perspective' on me. 

Sorry to be so blunt, but I really have better things to do than keep on with this pointless conversation, and it is now 4.30 am here.


> David

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Received on Sunday, 15 September 2013 11:30:10 UTC

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