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Re: Formal Semantics of RDF

From: Pat Hayes <phayes@ihmc.us>
Date: Thu, 16 Jun 2005 14:52:20 -0500
Message-Id: <p06200709bed788bff671@[]>
To: "Hardgrave, Terry \(Contractor\)" <Terry.Hardgrave@ed.gov>
Cc: www-rdf-comments@w3.org

>RDF Team--
>My suggestion is that you base the formal semantics of RDF on
>the work of Chris Strachey, Dana Scott, etc.  --  i.e. on 
>"denotational semantics" and set theory--
>rather than on model-theory/graph-theory.  The primary reason is 
>that graph theory
>will not (easily) support Boolean query languages on the structures. 
>To support the semantics
>of Boolean query languages, you need to use set-theory directly.

Thanks for the observation. A few quick comments:

1. The semantics of RDF, like everything else about RDF, is now 
fixed: it has been published as a W3C recommendation and cannot be 

2. The semantics of RDF is based on set theory, like most semantic 
theories, and it is in fact a denotational semantics. It also uses 
set-theoretic terminology directly, as you suggest.  (It would be 
slightly misleading to say that the RDF semantics uses set *theory* 
as it is too elementary to require any nontrivial set theory.)

3. RDF uses 'graph' terminology to describe its (abstract) syntax, 
not its semantics. But in any case, the word "graph" may be 
misleading, as the RDF graph idea bears very little relationship to 
the 'graphs' of graph theory. If you check out the formal 
definitions, an RDF graph is defined simply to be a set of triples. 
We could have called it "set syntax" rather than "graph syntax" with 
equal justification: the term "graph" was used simply because one 
could draw RDF as graph-like diagrams.

3. The field you may be referring to, of which Strachey and Scott 
were pioneers, is that of providing a denotational semantics for 
programming languages (and functional calculi more generally, such as 
the lambda-calculus). This is now a huge, mature field with many 
ramifications and connections to other parts of semantics, logic, 
mathematics and even philosophy. It would be a mistake, though, to 
think of RDF as a programming language: it is more closely aligned 
with assertional languages such as logics (indeed, RDF is essentially 
a fragment of quantified binary logic). Model theory really is the 
appropriate semantic framework for such languages, rather than 
programming/functional semantics. For example, there are no recursive 
or iterative structures in RDF, so no reason to restrict it semantics 
to domains which satisfy the Tarski fixedpoint theorem, a basic 
assumption of the Scott-Strachey tradition.

4. A W3C working group is designing a fully featured query language 
for RDF, to be called SPARQL. The current draft can be seen at 

Best wishes

Pat Hayes

>Chris Strachey developed something based on triples years ago, but I 
>have not been able to
>find the reference to it.  I would need to ask some of my colleagues 
>to hunt it down.
>Here is one reference.  If you are interested in pursuing this 
>further, please let me know, and
>I will provide additional references.
>Terry Hardgrave

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Received on Thursday, 16 June 2005 19:51:40 UTC

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