On Wed, 2009-10-07 at 00:05 +0000, Len Yabloko wrote:
> ...
> Of course Semantic Web technologies are expanding now into these old
> territories you have referenced with such detail and accuracy. But one
> has to be very careful not to confuse semantic modeling with data
> modeling and data linking with data integration. And, indeed, not to
> confuse model-theoretic semantics (developed by Tarski for first order
> logic and claimed by RDF) with various other semantics. (01)
By saying RDF has "claimed" model theoretic semantics, do you mean
anything more than that it has been provided with a model theoretic
semantics? That's a good thing, right? (02)
> I believe OWL itself is an attempt to go around the inherent
> limitations of Semantic Web. (03)
I'm not sure what limitations you have in mind. OWL is an attempt to
provide a standardized ontology language built upon a logical framework
in which questions of consistency, validity, etc are decidable. In
general, such questions are not decidable, and that is certainly a
limitation, but it predates the Semantic Web by several decades. (04)
> I have been following these forum long enough to have heard all kinds
> of claims about what is Semantics and many of these claims were tying
> it directly to FOL, like no other logic or semantics ever existed. (05)
Really? I can't remember anyone ever having made any such claim. I
frankly doubt whether you could find a single example. What people
*have* said is that, whatever representational medium you choose, it
must have a clear model theoretic semantics (regardless of whether it
happens to be that of classical first-order logic) so that the meanings
of its primitive logical vocabulary and its basic grammatical constructs
are well-defined. Without that, questions of consistency and questions
of whether one thing follows from another are, quite literally,
nonsense. (06)
I believe this is what Ed had in mind when he wrote: (07)
> >Formal logic is a means of expression, in which the basic elements of
> >the language have well-defined meanings and a set of well-defined
> >manipulations retain those meanings, and nothing more. (08)
I think by "well-defined manipulations" Ed means the inference rules of
a logic -- whose legitimacy is justified by the underlying semantics.
But, importantly, model theoretic semantics is very limited; it is
restricted entirely to the assigning meanings to the basic logical
expressions and telling us how to interpret the grammatical
constructs of a language in terms of their simpler parts. For
nonlogical vocabulary, a model theoretic semantics tells us only the
*kinds* of things signified by each grammatical category: e.g., names
refer to individual things (whatever those are), predicates refer to
classes, etc. But *which* things the names of an ontology refer to and
*which* classes its predicates pick out and exactly which classes a
given individual belongs to and exactly what logical connections relate
the classes we're interested in --- all of that is the job of what we
might call "applied" semantics, a.k.a. ontology. And model theoretic
semantics is entirely silent on those questions. As Ed put it: (09)
> >As to whether the snark actually is a boojum, classical formal logic
> >offers only two possible interpretations: it is either true or it is
> >false, and it cannot be both. And if you make a set of statements
> >that allow the well-defined manipulations to produce a result of
> >"true", then it does. That's all there is; there ain't no more.
> >Formal logic is about "how to think"; it is not about what you think
> >about. (010)
That is pretty much spot on. (011)
Chris Menzel (012)
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