Re: Identity implies logic

>
>  > No, the MT applies to RDF graphs. Your mentographs do not appear to
>>  be RDF graphs.
>
>Apart from the difference I mentioned above about sequence, what other
>difference do you see?

Well, the labels on your graphs do not appear to be URIs or literals, 
for a start.

>  >In fact, the MT shows that things like implications
>>  *cannot* be represented in RDF graphs
>
>Well would you agree that if we can represent an implication in N-Triples,
>then we can represent it in a RDF graph?

N-triples is just a linear notation for indicating a graph; in 
itself, with no semantics, it can't represent anything (except the 
graph itself, of course). If you understand it as a notation for RDF 
graphs, then it can't represent implication because RDF can't 
represent implication. As a notation for mentographs it presumably 
can say anything that a mentograph can say, but that's what I'm 
trying to find out.

>  > Well, for everyone who proposes to use RDF, DAML+OIL, etc., we can
>>  make that commitment, and indeed do. You (or anyone) are free to
>>  invent a multivalued version of RDF, of course, if you prefer it.
>
>Nope, I don't need to invent anything.   RDF already exists and is
>compatible with multivalued logics, AFAIK.

No, its not. Read the model theory again, and bear in mind that this 
is (a draft of) part of the very definition of RDF.  RDF is not just 
an uninterpreted notation.

>  That no model theory has been
>written for such deviant logics does not mean that some program can't
>respond to a set of RDF triples according to whatever brand of entailment
>the author (or owner) of the program intends.

Programs can do anything their authors like, of course. They can do 
things to RDF graphs that have no bearing on the RDF content of those 
graphs. So what? I can write code which renders English text into 
gibberish; I'm free to do so. However, the result is not English.

>  > >So I take it that we need to keep PNC and PEM separate until we commit to
>>  >classical binary logic and committing to binary logic is not something we
>>  >can just do willy nilly for everybody with a single stroke of the pen
>>  >  .. can we
>>  Yes,
>
>Agree ... because you have done it :)
>
>>>... should we ?
>>  and yes.
>
>Well I think this depends on the political ramifications of  this binary
>logic Model Theory.  The Internet has thrived on there being no authority
>that can say something like:  "your file is meaningless" ...  the way you
>just said "RDF cannot represent implications".

Nonsense. If you post a file with bad enough HTML in it, browsers 
won't be able to render it.  Nobody goes around complaining about the 
Priests of Hypertext, though.

>The Model Theory provides
>the liturgy for Priests of logic to stamp an RDF file as kosher or not.
>That is something that rubs me the wrong way.

You are living in a paranoid fantasy world. There are no Priests of 
logic. There is however a working group charged with defining a 
formal language called RDF, and the model theory (soon to be 
improved, BTW) is what that body says RDF means. Of course you are 
free to treat RDF files in any way you like; but just as a practical 
matter, if you plan to use RDF to communicate with others, it might 
be wise to adopt the same conventions that everyone else is adopting, 
if you intend to be understood by them. Or, you can use some other 
language; nobody is calling you to prayer here. The MT just sets the 
RDF standards into public view to help people avoid mutual confusion.

>Now  let me ask a technical question:  .. correct me where I go wrong
>because this leads me to an absorb conclusion:   The MT assigns an
>entailment (True or False) for every possible triple based upon a Vocabulary
>... right?

Wrong. It says how to determine the truthvalue of every triple in a 
given interpretation of V.

>  If the set of triples of the graph does not entail a triple,
>then that triple is called False in the interpretation of the graph ...
>right?

Wrong. See the definition of entailment in the MT document, and the 
comments there.

>   So here is my problem ... I assert a single triple in my graph ....
>something like {:Mary :loves :John}.  The MT seems to say that my assertion
>means that {:John :loves :Mary} is False.

I fail to see how you could possibly come to that conclusion. The MT 
says that of all the many possible interpretations of this vocabulary 
in which :mary :loves :john . is true, some of them also have :john 
:loves :mary . as true, but some others have it as false. So it is 
not entailed by your graph, since it might be true or false. The 
truth of your graph does not constrain the truthvalue of that other 
triple one way or the other.

>  > We can't use any logic in that context until we discover what we are
>>  both talking about.
>
>I couldn't agree more :))   ... see my closing note below.
>
>>RDF and DAML+OIL make a basic assumption that
>>  URIs are a universal naming convention; if you and I both use the
>>  same URI, then we are referring to one thing, whether we like it or
>>  not.
>
>Were that true, we would be living in a much different world.  Even in
>standards land, what a URI refers to,  is not a cut a dried thing ... there
>is much confusion as you well know.  When people bookmark a URI and then
>describe that bookmark with RDF are you quite sure they will all be talking
>about the same thing?

No; but right now, RDF being the simple first step that it is, if 
this happens then an RDF engine may give them misleading conclusions, 
because it, in its bumbling, naive, way, does make this admittedly 
oversimple assumption. Fixing this is however a longer-term effort 
that we are neither chartered, nor have the capacity, to tackle.

>  > > I see you have nicely excised the bug-a-boo of time from the MT.  But
>>  >time is not the only problem, Identity is a problem too .... isn't it ?
>>
>>  Actually, no, I don't think it is.
>
>Well using your own words above:  "We can't use any logic in that context
>until we discover what we are both talking about." .... That and only that
>is all I am saying too.  Thing is, we certainly *can* send each other useful
>RDF statements regardless of that contingency.

Wrong. If you use RDF to send a message without regard to the 
interpretation rules for RDF that are published by the W3C RDF 
working group, then you are simply mis-using the formalism. Again, 
nobody will stop you doing this, or declare any kind of RDF-jihad as 
a result; but if someone's software agent misunderstands your RDF, 
and he complains that you misled him, then the fault will be yours, 
not that of the RDF authors. We published the manual, after all; if 
you ignore it, you have only yourself to blame for any subsequent 
harm caused by your misuse.

>  You, and all logicians I
>have ever known, always assume that you are in a logical space where
>identity holds before you roll up you sleeves and start doing logic ... but
>that assumption does not hold on the semantic web

Not just logicians.  Everyone who ever uses the same name twice makes 
this assumption.  I do not even know what it would mean for that 
assumption not to hold. I doubt if you do, either. Under what 
circumstance could A not be the same as A, except when 'A' is an 
indexical or a demonstrative?

I have already agreed that URIs may be time-sensitive, and that RDF 
has no way to deal with that explicitly. But I don't think that 
rushing to embrace deviant logics is the best approach for dealing 
with this. We would do better to look at what is standard practice in 
industrial uses where time-sensitivity of information is critical, 
and adopt practices which are of proven utility, such as 
time-stamping. The sensible approach is to strengthen the logic, not 
to weaken it.

>... nor will it hold by
>edict ... nor would that be a good thing ... well at least I don't think it
>would be a good thing.  I am simply lobbying to eliminate that assumption
>from the model theory of RDF.

Frankly, tough shit.  As I said before, you are free to invent your 
own language. In fact, you may have already done so. We are free to 
invent ours.

Pat Hayes

PS. Disclaimer notice: The views expressed above are those of the 
author, and may or may not reflect those of the W3C RDF Core working 
group.
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Received on Wednesday, 3 October 2001 16:33:33 UTC