Key implications of new metagraph $has definition

["Drummond Reed" <drummond.reed@cordance.net>]

It was an extremely productive XDI TC telecon this last week (see the
minutes at http://lists.oasis-open.org/archives/xdi/200905/msg00000.html)
because it resulted in, I believe, a precise definition of Giovanni's
proposal for the definition of $has statements. I want to reiterate that
definition here and discuss two key implications that need to be reflected
in the XDI Addressing & RDF Graph Model spec.

1) REVISED DEFINITION OF $HAS PREDICATE

An XDI RDF $has statement between +x and +y, i.e., +x/$has/+y, asserts that
+y is a predicate on the subject +x. It infers the following two XDI RDF
subjects exist:

(+x/+y)
+x+y

These two XDI RDF subjects are synonyms, i.e. this means the following two
XDI RDF statements are true:

+x+y/$is/(+x/+y)
(+x/+y)/$is/+x+y

In addition, both the subjects (+x/+y) and +x+y identify the set of all XDI
RDF nodes that are objects of the XDI RDF statement +x/+y.

Lastly, this definition is recursive. So the XDI RDF statement +x+y/$has/+z
identifies the set of all XDI RDF nodes that are objects of the XDI RDF
statement +x+y/+z, and that this set can be identified by either of the
following two XDI RDF subjects:

((+x/+y)/+z)
+x+y+z

This recursion repeats to any depth; ordering is always left-to-right.


2) THREE PART XDI RDF STATEMENTS

Giovanni's email
(http://lists.oasis-open.org/archives/xdi/200904/msg00017.html) also
proposed that +x/+y/+z infers +x+y+z. However the above definition does not
allow this. +x+y+z expresses +x+y/$has/+z, which is equivalent to
((+x/+y)/+z). Rather, if there is a need to refer to a complete three-part
XDI RDF statement such as +x/+y/+z, the entire statement becomes a
cross-reference (+x/+y/+z). There is no shorthand for this statement.


3) $HAS$A STATEMENTS NOT NEEDED

Another key implication of this new definition is profound: $has$a
statements no longer appear to be necessary. Rather $, $a, $is, and $has
appear to be the complete set of metagraph predicates needed to express the
fundamental relationships in an RDF graph:

	$a is an incoming arc relationship (inverse: $is$a)
	$is is a self-referential arc relationship (and is its own inverse)
	$has is an outgoing arc relationship (inverse: $is$has)

This actually solves some longstanding issues around clarifying the
relationship of $has and $has$a

If everyone is in agreement with these conclusions, I will update
http://wiki.oasis-open.org/xdi/XdiOne/RdfGraphModel to reflect them, which
will move us one step closer to publishing it as a spec.

=Drummond