# RDF Concepts and Abstract Syntax: two comments

From: <herman.ter.horst@philips.com>
Date: Fri, 7 Nov 2003 13:42:16 +0100

Message-ID: <OFD68C8D4B.4A601072-ONC1256DD7.0040CE7D-C1256DD7.0045DB32@diamond.philips.com>
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RDF Concepts document.

"In the RDF abstract syntax, a blank node is just
a unique node that can be used in one or more RDF
statements, and has no globally distinguishing
identity."

It seems that the use of the word "globally" could
use a little further explanation.  A blank node has a
unique identity within an RDF graph (or within an RDF
document), which can be a very large thing.
There is some analogy with a global variable in a
computer program.
However, a blank node is not distinguishing over
different RDF graphs.

===

It seems that the definition of graph equivalence
could undergo some editorial improvement, by mentioning
explicitly that blank nodes are mapped to
blank nodes, and by leaving
out the reference to the graph G' in lines 1 and 2.
The definition would then become:

Two RDF graphs G and G' are equivalent if there is
a bijection M between the sets of nodes of the two
graphs, such that:
0. M maps blank nodes to blank nodes
1. M(lit)=lit for all RDF literals lit which are nodes of G
2. M(uri)=uri for all URIs which are nodes of G
3. The triple (s,p,o) is in G iff the triple (M(s),p,M(o))
is in G'.

In this way, since M is a bijection between the sets of nodes
of the two graphs (and since the sets of URIs, blank nodes
and literals are assumed to be pairwise disjoint), it
automatically follows that (as is stated in the current
definition) M(lit)=lit also holds for each literal lit in G'
and that M(uri)=uri also holds for each uri used as a node in G'.
Conversely, the current definition implies that blank nodes
are mapped to blank nodes.  So the two definitions are
equivalent.
This definition above seems to make more explicit than the
current definition what is going on in an equivalence.
Moreover, a disadvantage of the current formulation is that,
by speaking of M(lit) and M(uri) for nodes lit and uri of
G', it is implicitly assumed that these nodes lit and uri
are in the domain of the mapping M, i.e., that they are nodes
in G.  It would be preferable if a spec avoids implicit
assumptions.
Finally, try to prove with the current definition that
equivalence is transitive - one of the crucial properties
of an equivalence relation.  The implicit assumption just
mentioned needs to be invoked two times, in a somewhat
awkward way.  With the definition above, transitivity follows
immediately.

Herman ter Horst
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Received on Friday, 7 November 2003 07:43:05 UTC

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