RE: definition/assertion (WAS rdf as a base for other languages)

> > Ah, now I have painted myself into a corner, since I never fully 
>understood the definition/assertion distinction myself, though it 
>seemed
>
> > central to many folk (and still does). Although to be fair, the 
>idea of a definition is a pretty common one in mathematics and life 
>generally, in > spite of its having no obvious logical content.
>
>...
>
> > Now, I can guess from your earlier emailings that you think of 
>these matters in a fairly strict model-theoretic way, as I do 
>myself, and within a > strict extensional model theory there really 
>is no principled way to make this distinction on logical grounds.
>
>It does indeed have an intuitive appeal -- I agree with you there is 
>no immediately obvious logical content, and I actually find that a 
>bit surprising. I have been pondering this issue, in one form or 
>another, in recent weeks as I have been interacting in my 
>professional life with engineers on constructing ontologies and 
>representational systems.

This has also been a hot topic in the SUO discussion list, as it 
seems to be of interest to ontologists generally. The semanticians 
(me a few others) stripped out the definitional syntax from KIF when 
designing the SUO-KIF (SKIF), on the grounds that it was silly, in a 
logic, to have an elaborate syntax for something with no logical 
content. The ontological engineers have been insisting ever since 
that they need the distinction, and some of them have used this as an 
argument for using a modal logic. (Fortunately, the modal logicians 
cannot agree on the intended meaning of the modalities they think 
they require.)

BTW, you can find a mine of information about this and many other 
'ontology' issues on John Sowa's fabulous website 
http://www.bestweb.net/~sowa/direct/

>Consider something simple like working with a "class of bachelors", 
>which by definition means that every instance of a bachelor must be 
>not married -- a married bachelor would be a logical error of an 
>intuitively different order than any other assertion, such as a 
>bachelor's place of residence or some such thing. I am seeking some 
>"logic grounded' way of expressing what is behind this, perhaps 
>using some combination if and only if statements, but have not been 
>satisfied yet.

I don't think you will be able to do it within normal extensional 
relational logic, since it requires a kind of asymmetry in resolving 
contradictions which has no basis in the ordinary truth-recursions. 
(Modality is one way to provide the asymmetry: bachelors being 
unmarried is necessary, not a mere truth. My worries about this 
(admittedly appealing) approach arise when one tries to give this 
modality a Kripke semantics, and asks what the alternativeness 
relation would be. It seems to be something like, any change to the 
knowledge base: but that doesnt seem like a relation between 
*worlds*.)(BTW, Sowa disagrees with me on this.)

>You are correct in concluding that my academic training has been in 
>hard-core model theory, and the interaction with software engineers 
>has been a bit jarring.

You have my utmost sympathy.

>In my opinion years and years of Object-Oriented dogma/brainwashing 
>has created a generation of engineers who cannot conceive of 
>representational modelling that does not reduce everything to simple 
>property/value pairs attached to objects -- this has apparently 
>affected the creators of RDF as well, hence the insistence on 
>triples, subject-predicate-object, etc. that has become so familiar 
>to readers of the threads on this list. The loss of expressiveness 
>that this mind-set may entail for the future Semantic Web will be 
>problematic IMHO.

In many other HOs as well, fortunately probably enough to provide a 
better future eventually.

>For example, it was pointed out in a recent posting on this list, I 
>cannot recall the exact one,

I think it was in a posting by Lynn Andrea Stein in reply to me a few days ago

> that a triple connecting a parent with a child, in a 
>subject-predicate-object format of person-parentOf-child, leaves 
>much unsaid -- a parent may have several children. If predicates 
>serve as functions, then this "function" might not have a 
>well-defined value precisely because the value could be any of a 
>number of children. Of course one could make the object a list, but 
>that too has drawbacks. Logic long ago handled these matters by 
>distinguishing between relations and functions. But because 
>relations can be multi-placed and do not always fall neatly into the 
>subject-predicate-object framework, they are anathema to many, to 
>the detriment of the representational tools.

To be fair to RDF, I think itis  based on the relational intepretation.

>The matter also relates to the definition/assertion issue. Suppose 
>that one wishes to express a common bank account for a couple. One 
>straightforward way would be to model this as a function on pairs or 
>2-tuples, so that one would have a function BankAccount(Homer,Marge) 
>= AZ3468 or whatever, and in a relational data-base this might 
>appear as a table with three columns. But of course, a function on 
>pairs is problematic to the folks who work with s-p-o triples, so 
>the suggestion I have heard is that one create objects called 
>Couples, so that e.g. one would have an object called Couple#34 with 
>Member1(Couple#34) = Homer, Member2(Couple#34) = Marge, 
>BankAccount(Couple#34) = AZ3468. This can work, but in the function 
>on 2-tuples case, the "definition" of the pair was "built-in" in the 
>sense that the function would automatically understand that it 
>should deal differently with a pair (Montgomery,Marge) as opposed to 
>a pair (Homer,Marge) because the identity of the pair is tied to the 
>identity of it constituents. Reducing it to the triples level means 
>that the function Member1 is on a par with the function BankAccount, 
>and it seems as if the "identity" of Couple#34 would be as little 
>changed by changing the value of Member1 from Homer to Montgomery as 
>it would if the value of BankAccount were changed from AZ3468 to 
>BX4579. Something, somewhere seems to have gotten lost in the 
>translation.

Or, it is all implicit in the relation names. But then if we accept 
that we are in a sense implementing a more complex structure inside 
the RDF model, this could be an acceptable way to encode the required 
information. Of course, it would only be meaningful to a suitable 
interpreter, but such is life.

Pat Hayes

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