[RIF-RDF] rationale for a model-theoretic semantics for combinations

Dear all,

In the original e-mail [1] I sent introducing my proposal for RIF-RDF
combinations based on combined models [6], I included a short rationale
for choosing such a combination as the normative way for combining RIF
and RDF, rather than an embedding of RDF in RIF.

Some doubt has been raised [2] about the value of this approach.
In this e-mail I try to formulate my rationale for this model-theoretic
semantics of RIF-RDF combinations a bit more clearly.
Before I present my main argument, I will first try to put the issue in
its context by considering the relationship between RIF and other
semantic Web languages, and recount the main use cases for RDF in RIF.


Some background
====
RIF is a W3C working group in the semantic Web activity. Like the Basic
Logic Dialect (BLD) of RIF, RDF is a logical language with a declarative
model-theoretic semantics.
Since RDF is the primary semantic Web language, RIF needs to account for
this language; RIF needs to be compatible with RDF.
Now, "compatible" can be interpreted in various ways.  Extending the
model theory of RDF is a possible way to ensure a high level of
compatibility; the language OWL Full extends the RDF semantics in such a
way.  Despite it being mentioned as a possibility in the charter, the
RIF working group decided not to base its model theory on that of RDF,
but rather, like OWL DL, develop a new one.
There could never be any real compatibility between RDF and OWL DL,
because the description logic paradigm does not work well with the
syntactic freedom of RDF.
There is, however, a potential to achieve a high degree of compatibility
between RDF and RIF, because the RDF semantics has been carefully
crafted so that it works well with the rule-based reasoning paradigm.
In fact, the RDF semantics can be embedded in a simple Datalog-like
language [3], so that rule reasoners can be used for reasoning with RDF.


The use cases for RDF in RIF
===
Now, the RIF working group has identified two primary use cases related
to RDF compatibility: (a) using an RDF graph as an external data
model/data set and (b) exchanging RDF rules, i.e. rules which extend an
RDF graph (e.g. N3, [4]).

In both cases, we are essentially dealing with the combination of an RDF
graph (which may include an RDFS ontology) and a set of (RIF BLD) rules
[*].
The question now is: what is an appropriate semantics for this combination.


The semantics of combinations
===
Earlier [5], I proposed to base the semantics on an embedding of the RDF
graph and the RDF semantics in RIF. It can be shown that this embedding
behaves the same as the RDF semantics, with respect to entailment, if
the rule set is empty.
There is, however, no way (apart from anecdotal evidence such as test
cases) to determine whether the semantics of the combination behaves in
a natural way.
In fact, there is no way to see whether the combination is in any way
faithful to the RDF semantics, and it is very hard to reconstruct from
such an embedding how the RDF and RIF semantics interact.

These problems prompted me to reconsider the semantics of RDF and RIF
combinations.  Since both RDF and RIF have a model-theoretic semantics,
it is possible to give a declarative, model-theoretic account of their
combination, thereby providing a clear understanding of the semantics of
the combination. It is thereby possible to verify whether the
combination is "natural", and whether it has the properties you want off
a combination.
I am sure that an important property of an RIF-RDF combination is that
it is faithful to both the RDF and RIF semantics.  So, the combinations
is defined such that the models are based on the combination of RIF and
RDF models, thereby ensuring that the semantics is faithful to RDF and
RIF, on the model level.
The interaction between the semantics is defined through a total of 8
conditions, so that it is very easy to verify whether the interaction is
natural.
It turns out that satisfiability checking and entailment of combinations
can be reduced to satisfiability checking and entailment, respectively,
of RIF rules, through an embedding. This embedding gives implementers an
idea of these combinations could be processed, as did the RDF entailment
rules for the model-theoretic semantics of RDF.

Another concern which has been raised about the model-theoretic
semantics for combinations is that it is supposedly complex, and bothers
the reader too much.
Actually, I find this a non-issue: if the reader is not interested in
model-theoretic semantics, the reader would probably have already
skipped the definition of the RIF semantics, and will probably also skip
the definition of the semantics of combinations, and perhaps instead
read the embedding, but, most likely, he/she will just read the language
reference or the language guide.
In fact, the definition of the model-theoretic semantics is much clearer
and much more concise than the proposed embedding (also in [6]), so I
would argue that an embedding actually bothers the reader more than the
proposed model-theoretic semantics.


Best, Jos


[1] http://lists.w3.org/Archives/Public/public-rif-wg/2007Aug/0012.html
[2] http://lists.w3.org/Archives/Public/public-rif-wg/2007Aug/0039.html
[3]
http://www.inf.unibz.it/~jdebruijn/publications-type/Bruijn-Heymans-LogiFoun-07.html
[4] Herman J. ter Horst: Combining RDF and Part of OWL with Rules:
Semantics, Decidability, Complexity. International Semantic Web
Conference 2005: 668-684.
http://www.springerlink.com/content/366474250nl35412/
[5] http://lists.w3.org/Archives/Public/public-rif-wg/2007May/0077.html
[6] http://www.w3.org/2005/rules/wg/wiki/Core/RIF-RDF_Compatibility

[*] Not considering, for the moment, that RDF rules may require
additional constructs or symbols, such as (rigid) blank nodes and
certain built-ins.
-- 
                         debruijn@inf.unibz.it

Jos de Bruijn,        http://www.debruijn.net/
----------------------------------------------
In heaven all the interesting people are
missing.
  - Friedrich Nietzsche