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RE: rdf as a base for other languages

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Sat, 02 Jun 2001 15:18:24 -0400
To: ziv@unicorn.com
Cc: www-rdf-logic@w3.org
Message-Id: <20010602151824D.pfps@research.bell-labs.com>
From: "Ziv Hellman" <ziv@unicorn.com>
Subject: RE: rdf as a base for other languages
Date: Sat, 2 Jun 2001 17:55:38 +0200

> I am beginning to lose sight of what the terminology "ground facts" is
> supposed to mean in this context.
> 
> At the risk of being a considered a dreary pedant, I will sketch out
> here how I was taught one constructs a logic, and then ask where this
> fits into the terms of the debate raging in this interests list:
> 
> a.  Determine a group of "logical" symbols that are "reserved" and
> assumed to be a part of any language that one will define and use --
> this is where connectives, quantifiers, modal operators, etc. are
> declared, perhaps also variables
> b. Determine that a language may contain "non-logical" symbols that play
> the roles of relations, or functions, or constants etc.
> c. Determine rules for deciding what constitutes a well-formed statement
> built out of these logical and non-logical symbols
> d. At this point, either build a proof theory or a model theory or both.
> For a proof theory, declare logical axioms and rules of inference that
> enable one, given certain statements as assumed, to infer other
> statements as conclusions. For a model theory, one needs to explain how
> and when statements in the language are to be considered "satisfied" in
> possible worlds or structures or models, etc. 
> 
> What are "ground facts" this picture? Where in this picture does RDF fit
> in? Where would another language "built atop RDF" fit in? Or is all this
> irrelevant to the debate?
> 
> 
> Cheers,
> 
> Ziv


[Here is my reconstruction of RDF as a logic.  It is missing a few minor
details.]


RDF is precisely such a language.  It has one logical construct, namely the
triple, with various surface syntaxes.

Let's make this simple and say that triples are all of the form <p,s,o>.
Only '<', ',', and '>' are logical symbols, all other symbols are
non-logical.  

An RDF input is a sequence of such triples.  A semantic structure is a
finite set of three-tuples over a domain, with some extra conditions.  A
semantic structure is a model of an RDF input if there is a mapping from
the non-logical symbols used in the input into the domain such that the
obvious mapping from each triple in the input into a three-tuple results in
precisely the set of three-tuples in the semantic structure.


Now a ground fact is either a triple in the input or a three-tuple in the
semantic structure.  The reason that we can call it a ground fact is
because it is in the semantic structure.  However, there is a morphism
between the triples and the three-tuples, which makes it easy to be
less-than-precise about whether a ground fact is a triple (syntax) or
three-tuple (semantics).


How can you build another language on top of RDF?  Well, you can either
take RDF as it stands and provide another meaning for its triples or you
can take the semantic structures and provide a subsequent meaning for
them.  (The two approaches work out just about the same, and have no
inherent serious problems.)

However, the approach that has been put forward on this group is to keep
the RDF semantics and put another alongside of it.  This sibling semantics
that would have more logical constants (such as OR) and more conditions on
what makes a semantic structure into a model.  The problem with this
approach is that the triples (because that is the only construct that RDF
has) still have their RDF meaning.


peter
Received on Saturday, 2 June 2001 15:20:25 GMT

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