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Re: What do the ontologists want

From: pat hayes <phayes@ai.uwf.edu>
Date: Wed, 16 May 2001 19:54:19 -0500
Message-Id: <v04210109b728b316e929@[205.160.76.173]>
To: Dan Brickley <danbri@w3.org>
Cc: Jonathan Borden <jborden@mediaone.net>, <www-rdf-logic@w3.org>
Hi Dan

> > >pat hayes wrote:
>
>[...]
> > So it has no semantics at all? I doubt if that is really what you
> > mean, since then it would have no point to it, as far as I can see.
> > Certainly the RDF literature seems to *want* RDF to actually mean
> > something.
>
>I consider RDF content to be meaningful largely by proxy: RDF
>piggybacks on URIs, which are meaningful by virtue of
>a quasi-mystical social/legal process involving the devolution of naming
>rights (via various URI schemes) to individuals and organisations. I'm not
>sure how this aspect of meaning (ie. theories of reference) fits with the
>DAML+OIL formalisms (the Model-Theoretic and the Axiomatic semantics). The
>DAML+OIL documents provide (very useful) rules for inferring
>DAML+OIL expressions from other DAML+OIL expressions, but are rather
>quiet on the grounding of those structures in social / legal reality.

Logic has little, if anying, to say about social/legal reality, 
indeed. (If you want to get involved with that area,  seems to me 
that y'all ought to be recruiting lawyers and sociologists to be in 
RDF-Core..?)

>http://www.daml.org/2001/03/model-theoretic-semantics.html says "This
>document ignores all aspects of naming" while appealing to a notion of
>DAML+OIL semantic structures being _true_ ("A semantic structure
><AD,IC,IO,IR> is a model for the DAML+OIL ontology if the constraints
> resulting from the mappings from the ontology are true in the
>structure.").

That is true *in the structure*, notice. Do not read that as meaning 
'true' simpliciter, ie true in the real world. Logical semantics - 
model theory - does not purport to be able to say anything much about 
the actual, real, world. Which is entirely appropriate, since its 
purpose is to analyse the validity of inference processes, and that 
depends not on what is true (in this world) but on what could 
possibly be true, given the semantic rules of the language. The fact 
that P can be inferred correctly from (P & Q) is entirely independent 
of what P and Q *actually* mean: they could mean naything, and it 
would still be valid. It would be valid even if P were false.

One way to think about this is to regard the logical semantics (the 
model theory) as a process by which meaning is carried from small, 
atomic, basic expressions - names, typically - and transferred to 
large, complex, expressions. (In case Uche Ogbuji ever reads this, I 
should maybe explain that by "expression" here I mean to refer not 
just to surface syntax, but any structured representation of 
propositional content. KIF expressions are LISP Sexpressions, for 
example, rather than strings, and McCarthy's abstract syntax provides 
a very abstract characterisation of logical syntax independently of 
the details of surface rendering. RDF triples for example are 
'expressions' in this sense.) It defines the rules of meaning 
composition. All the machinery of inferential logic depends on how 
this composing of meaning is done, and all the issues of designing 
inference engines, strategies for determining meanings, and so on, 
depend on it also. The validity of the inference machinery is usually 
independent of the base meanings, which is just as it should be, of 
course: one wouldnt usually say that the particular referents of 
names are a matter for *logical* analysis. So there is usually no 
particular role in logical langauge design for the details of the 
'base' meanings. Thus the model-theoretic semantics for DAML  just 
says that an interpretation is defined by three mappings from the 
basic symbols to three classes of entities. It says almost nothing 
about those entities or those mappings: not because that is 
unimportant, but in order that the theory can be applied as widely as 
possible. Whatever the names denote, this is saying, the 
grammatical/logical machinery of the language will work in the same 
way.

So I think that your concerns - which seem to be entirely focussed on 
the base meanings, the referents of the logical names, which here are 
URIs - and our concerns, are not opposed, but nicely complement each 
other. If we can find a way to put them together, we will have a much 
more powerful theory.

>I find it difficult to understand how the truth
>condidtions for DAML+OIL expressions can in practice be usefully reasoned
>about by Web applications unless DAML+OIL acquires a theory of reference
>/ naming. Without some specification that tells us what (if anything) a
>DAML+OIL expression *refers to*, DAML+OIL content will be meaningless.

No, since DAML+OIL largely talks about classes and their 
relationships. One can make true assertions about classes without 
knowing exactly what the classes contain, or even without exactly 
identifying the classes. For example, I might draw some conclusion 
about the class of all people who have at least two children who work 
for Boeing. I have no idea who is actually in this class, and I might 
not need to know that. Many representational languages are able to 
express useful information without fully identifying the things they 
are talking about.

>Maybe I'm misreading the specs, but an account of meaning that ignores
>naming / reference is missing something. (Maybe KIF has an attempt at
>this? I should probably re-read the KIF docs...)

KIF uses exactly the same approach to model theory. All logical and 
representational languages do, in fact. I agree something is missing, 
if you want an formal account of reference. But are you sure that you 
really do want that, especially since it seems to be embedded in a 
kind of a quasi-mystical social/legal cloud that seems likely to 
resist any kind of precise analysis? Let me ask you in return: what 
extra leverage would a theory of reference get you, compared to a 
model theory? In a word, what do you see it as being useful FOR?

>I'm not complaining about DAML, and I'm not claiming that RFC 2396 (the
>URI syntax spec) embodies an adequate theory of reference. Just that we're
>in the same boat, in that there's an aspect to meaning (ie. reference)
>that all these specs have a problem with.

If they were expected to deal with it then they would have a problem, 
I agree. Also, this is not an aspect that logical semantic theories 
are likely to be much direct help with. You are right to point out 
that the model-theoretic semantics of DAML (or any other assertional 
langauge) says very little about reference. Reference and naming is 
not a topic that logic has much to say about: model theory treats 
names simply as symbols that denote, and says nothing about *how* 
they denote, or how their denotation is supposed to be determined.

To get back to the orginal discussion, when I was talking about the 
semantics of RDF, I meant it in the sense of logical , perhaps 
'structural' semantics: that is, given that the basic symbols denote 
something (by some means we need not go into for now), what 
determines the meanings of more complex RDF expressions? You refer to 
'piggybacks', which is fine, but I want to know the piggybacking 
rules. Simple triples seem easy enough, but it isnt entirely clear 
whether or not relations can be objects (if so, the model theory 
required is going to be a bit more complicated) and it isnt clear 
what the anonymous nodes range over (I see they are like existential 
quantifiers, but what domain do those quantifiers range over? A lot 
turns on the answer, if that domain contains relations). (It is a bit 
worrying when one sees triples being used to encode things that seem 
to have no obvious relational interpretation, but never mind....) And 
when reification appears, it seems that we have to put the triples 
themselves into the domain. What *is* a triple, then? What kinds of 
properties does it have? Are the triples in the domain of 
quantification the same triples used in RDF syntax, or are they 
abstract things denoted by the RDF syntax? And so on... those are the 
kinds of questions that I want to see answered. (Its not that it is 
particularly hard to answer these questions, by the way, only that 
someone in a position of authority needs to provide them, just to 
keep things clear, and the current picture seems to be confused on 
just what the answers are. Some people have sharply clear views on 
some of these question, but others have different, sharply clear 
views.) Notice that the basic terms can denote anything (any 
'resource'), in this discussion: this is orthogonal to a theory of 
reference.

BTW, the utility of doing this stuff is not just to keep some crabby 
Floridian ex-logician happy. The model theory provides the 
mathematical machinery that enables people to make very precise 
statements of just how expressive the formalism is and isn't, for 
example.

Pat

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Received on Wednesday, 16 May 2001 20:54:17 UTC

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