Re: RDF Semantics, non-lean RDF graphs, and redundancy of content

>Dear all,
>
>I have a minor comment to the characterisation of non-lean RDF graphs. In
>short, I wonder what "redundancy" means in the context of non-lean RDF
>graphs (in RDF Semantics).
>
>The longer version:
>
>In ...
>
>RDF Semantics
>W3C Working Draft 10 October 2003
>http://www.w3.org/TR/2003/WD-rdf-mt-20031010/#graphdefs
>
>...the text reads (graph labels and blocks added):
>
>----------snip-
>An RDF graph is lean if it has no instance which is a proper subgraph of
>the graph. Non-lean graphs have internal redundancy and express the same
>content as their lean subgraphs.
>For example, the graph
>
>G1: {
><ex:a> <ex:p> _:x .
>_:y <ex:p> _:x . }
>
>is not lean, but
>
>G2: {
><ex:a> <ex:p> _:x .
>_:x <ex:p> _:x . }
>
>is lean.
>----------snip-
>
>I don't quite understand the sentence "Non-lean graphs have internal
>redundancy and express the same content as their lean subgraphs." From the
>modelling point of view, this seems rather important. Perhaps the concept
>"redundancy" should be defined in this context?

Well, it was intended only as a helpful remark: 
the formal definition stands by itself. The point 
of the word 'redundancy' is that the content of 
one part of the graph can be inferred from other 
parts. For example if the graph contains

ex:pat rdf:type ex:human .
_:x rdf:type ex:human .

then it is redundant in this sense: the second 
triple adds no new content to the first triple, 
and can be inferred from it. This graph says in 
effect, Pat is human, and a human exists.  So 
this graph is equivalent in content to the first 
triple alone, and could be removed without 
changing the meaning of the graph.

>What kind of example would illustrate the "removal or redundancy"? G2 is
>an instance of G1 but G2 is not a subgraph of G1 (two different blank
>nodes would be accidentally identified) so the example in the text will
>not do(?)

No, that is the point of the example. Mapping _:y 
to <ex:a> gives an instance of G1 which is a 
subgraph of it (the first triple).  The triples 
which 'vanish' under the instantiation mapping - 
which become identical to some other triple in 
the graph - are redundant; in this case, the 
second triple. You could delete them from the 
graph and it would express the same content, 
since stronger assertions (the triples which they 
map to under the instance mapping) are already 
made in the graph itself. So, G1 is not lean. 
There is no such instantiation of G2, so G2 is 
lean.

>
>I'm asking this because I can't figure out how to write the content of G1
>"without redundancy" -- all changes seem to change the design and thus the
>potential interpretations

Just omit the second triple. G1 is equivalent to the singleton graph

<ex:a> <ex:p> _:x .

>(e.g. G1 has more models than G2). (The
>definition of an instance does not assume the vocabulary of the particular
>graph. This seems sensible since an agent might have a rich inner
>vocabulary which it tries to match with the blank nodes?)

Quite.

>
>Perhaps the text should read something like: "If a non-lean graph A has a
>lean subgraph B, then A and B express the same content i.e. A is
>redundant." ???

No, that would not be quite correct.

>(And personally, I would still be interested to see an example how to
>reduce "redundancy" from G1 without affecting the content.)

See above.

>What am I missing? (Expect for common sense, of course.) I can only
>suspect that I "disagree" either about the concept "redundancy" or about
>the role of blank nodes in taking subgraphs.

Hope the above helps.

Pat Hayes

>Best regards,
>
>--Ossi
>
>
>--
>Ossi Nykänen                              Tel   +358 3 3115 3544
>Tampere University of Technology          Fax   +358 3 3115 3549
>DMI / W3C Finnish Office                  Email ossi@w3.org
>P.O. Box 553, FIN-33101 Tampere, Finland  Web   http://www.w3c.tut.fi


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Received on Thursday, 4 December 2003 11:18:01 UTC