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Re: [ontac-forum] Semantics (1, 2, and 3), Ontology and Semiotics

To: ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Mon, 29 May 2006 22:27:33 -0500
Message-id: <447BBBA5.7030107@xxxxxxxx>
Adrian Walker wrote:
> Someone pointed out at a meeting a while back the irony that
> "semantics" is one of the most ambiguous words that we use when
> talking about ontologies and the like.  (Perhaps the ambiguity is a
> plus for funding, but a minus for productive technical discussions?)
> I have made a modest attempt to start clearing out the ambiguous
> underbrush by suggesting the terms:
>    Semantics 1   Interleaving of metadata with data, e.g. as in RDF
>    Semantics 2   what conclusions a reasoning engine *should* be able
>                          to infer from any set of rules and facts
>    Semantics 3   the meaning of English concepts at the author- and
> user-interface
>                          of a system.
> There's more about this in [1,2].
> From a practitioner point of view, the three kinds of Semantics have
> to "play nicely"  together in one system, e.g. as in [3].
> If one takes this admittedly unconventional point of view, it seems at
> least to help to keep the history of philosophy and AI in
> perspective.   One can then start to focus on more recent technical
> issues, such as how to be more ambitious about robust processing of
> natural language without falling off the "AI-complete" cliff.
> What do you think?
Well, since you asked... ;-)  I don't think either of your first two
senses of "semantics" has much of anything to do with semantics at all. 
Well, in the case of Semantics 1, I guess it would be more accurate to
say that I don't understand Semantics 1 well enough to see the
connection.  But given that you use RDF as an example, I'm pretty sure
that it is not anything like what I would call semantics.  RDF itself is
just a language; there is nothing semantic about it in and of itself. 
It *has* a semantics -- specifically, the model theory defined for it by
Pat Hayes (http://www.w3.org/TR/rdf-mt).  But RDF itself is just not a
semantical thingy.  Moreover, RDF proper is, expressively speaking,
*extraordinarily* weak; any "interleaving" of data and metadata in RDF
has no formal foundation at all, but rests only upon the intuitive,
informal meanings that users assign to certain of its syntactic
primitives.  Only with RDFS do you begin get a framework capable of
making some reasonably robust assertions; much moreso with OWL.    (01)

As for Semantics 2, I'd have to say that I find the use of "semantics"
something purely proof theoretic to be, well, somewhat perverse. :-) 
Proofs and interpretations are *utterly* separate things, though if God
smiles and we've set up our system properly, we can prove a completeness
theorem to show that our proof theory and our model theory are in a sort
of pre-established harmony wherein provability and semantical entailment
are in complete agreement.    (02)

Moreover, what can it even mean to say that a reasoning engine *should*
be able to infer a sentence B from a set S?  Given a (well-defined)
reasoning engine, for any sentence B and set S, either the engine will
(eventually, given proper initial tweaking perhaps) infer B or it
won't.  (Of course, we may never be able to prove which, but one or the
other is the case.)    (03)

Semantics 3 of course says something about meaning, so it is, in my
eyes, a genuine notion of semantics, but it is so vague that it is
difficult to see how it could be useful.    (04)

I don't think that my own idea of semantics is complicated or at all out
of the ordinary. In fact, I think there are now two related but quite
different notions in the wind, one of which is primary.  Semantics in
the more traditional sense has to do with the word/world connection
(with "world" understood in the broadest sense); a semantics for a
language identifies the types of meanings appropriate to the various
syntactic types in the language and accounts for the manner in which the
meanings of complex syntactic expressions depend upon meanings of their
simpler parts.  Most notably, a semantics in this sense tells us how the
*truth* of a sentence depends on the meanings (typically, the
denotations) of its semantically significant component parts.  Classical
model theory for formal languages is the most rigorous example of
semantics in this sense.    (05)

A secondary sense of is the one that seems meant by the word "semantic"
in "semantic web".  "Semantic" in this sense doesn't have much of
anything to do with providing a systematic account of meaning for a
language.  Rather, one "adds semantics" to the terms of the language by
writing axioms that *constrain* their interpretations -- their semantics
in the above sense, and hence which both convey a clearer sense of their
intended meanings to users and provide automated reasoners sufficient
grist to be able to draw useful inferences from input containing those
terms.     (06)

Since axioms constrain the interpretations of terms, semantics in the
second sense presupposes semantics in the above sense, conceptually at
least.    (07)

So sez I, anyway. :-)    (08)

Best wishes,    (09)

Chris Menzel    (010)

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