Re: Draft Partitioning

pat hayes wrote:
> 
> >Brian McBride wrote:
> > >
> > > Frank Manola wrote:
> > >
snip
> > > >
> > > > I guess the answer is in two parts.  First, I assume we have to define
> > > > "n-triple" itself (that is, the thing that corresponds to a
> > > > "statement"), along with its components "resource", "predicate", and so
> > > > on.  Aren't those built-in types or classes?
> > >
> > > No - a triple in n-triple is a character string.  Rather
> >different from m&s.
> >
> >I agree that the *syntax* is a character string (as defined by the BNF),
> >but I don't think that quite captures the *semantics*!  And I thought in
> >the base layer we were defining an abstract syntax *and semantics*.
> 
> I wonder, could I ask what people in this group mean by 'abstract
> syntax'? In the usage I am familiar with, an abstract syntax is
> essentially an algebraic theory of syntax which does not specify any
> kind of textual or character string rendering, but treats each
> syntactic category as a class of abstract entities formed by
> construction operators. Propositional logic for example might have an
> abstract syntax in which the classes are base propositions,
> conjunctions, disjunctions and negations, all subclasses of
> expressions; and a disjunction (for example) might be constrained to
> have a list or bag of immediate subcomponents which are required to
> be base propositions, conjunctions or negations, and so on. A
> different abstract syntax would define a disjunction to have
> precisely two subcomponents but allow them to be any proposition.
> Clausal syntax would allow disjunctions of base propositions and
> negated base propositions only; and so on. Note that nothing in this
> says whether disjunction is written as 'OR' or 'V' or '+', whether it
> is prefixed, infixed, postfixed or not fixed at all, whether
> disjunctions are enclosed in parentheses, written as XML, etc. ; all
> those would be alternative concrete syntaxes which all correspond to
> the same abstract syntax. (So, BTW, would things like Sowa's
> conceptual graphs; concrete syntax doenst have to be a character
> string.)  The abstract syntax says just enough about the syntax to
> enable one to attach a model-theoretic semantics to it, but no more.
> 
> My understanding was that the RDF triples were to be thought of as
> the abstract syntax in roughly this sense, and that the semantics of
> RDF would be something like a simple model theory for this abstract
> syntax. N-triples and the XML lexicalisation would then be two
> different concrete syntaxes corresponding to this abstract syntax. If
> so, I don't quite see what we have to do, since the abstract syntax
> is already well-defined.
> 
> If this picture is wrong, please someone put me right as fast as possible!

I think you're picture is right (but that's just my opinion).  I was
happy with "model" (which I understood in the sense of "data model", not
the logic usage), and understood "abstract syntax" to be more or less
the same thing (which is consistent with your description).  Although
these days I sometimes get "triple" (the generic idea) and "N-triple"
(the specific syntax) mixed up.  However, concrete syntax or abstract
syntax, we still need to define the components (syntax and semantics).

> 
> > >
> > > >  In other words, I think that the base layer (and the
> > > > current formal model) ought to be reasonably closed, without appealing
> > > > to other specifications to complete the definition of its basic ideas.
> > >
> > > I completely agree with that principle.  I think that we can define
> > > n-triple without a notion of type.  You think that's not possible.
> > > How about we try, and if I'm wrong, I'll buy you a beer in Sebastapol?
> >
> >That's fine (right or wrong, I expect to have a few beers in Sebastapol
> >and maybe buy a few for other people too)!  I just want to make sure
> >(see above) that any "definition" adequately covers the semantics too.
> >I'd be interested in seeing what you have in mind;  my ideas about how a
> >type system would work aren't all that well worked out anyway.
> >(Actually, I can imagine a model-theoretic semantics that uses subsets
> >of the domain of discourse rather than actual types, so if that's the
> >sort of thing you have in mind that could work for me, depending on some
> >of the details about what goes in higher levels).
> 
> Hmm. In my world, 'actual types' ARE subsets of the universe of
> discourse, so I wonder what you mean by a type?
> 

I'm probably not expressing myself clearly enough.  I agree:  types are
subsets of the universe of discourse.  But I expect the definition of a
given type to tell me a bit more than that it's a subset of the universe
of discourse!  For example, the current formal model for RDF in the M&S
defines a set called Resources, and a subset of that called Properties. 
That's essentially all the formal model says about them (there's more
said in other sections of the M&S, of course).  I would expect a
definition of "type Resource" to express something of the additional
semantics about resources conveyed by the text in the rest of the M&S
(like, it's something identified by a URI, at least).  Similarly, I
would expect a definition of "type Property" to say something about the
intended semantics of properties.  I read the DAML model-theoretic
semantics as providing exactly this type of information about RDF
triples (and even defining some types!), dividing the work of definition
among the identification of the various domain subsets, the
interpretation functions, and the semantic constraints.    

--Frank

-- 
Frank Manola                   The MITRE Corporation
202 Burlington Road, MS A345   Bedford, MA 01730-1420
mailto:fmanola@mitre.org       voice: 781-271-8147   FAX: 781-271-8752

Received on Tuesday, 26 June 2001 17:00:05 UTC