+x/+y/+x+y

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

On the last telecon we discussed the set of XDI RDF statements that Markus
and I concluded are inferred the XDI subject +x+y:

#1) +x/$has/+y
#2) +y/$is$has/+x		;inverse of #1
#3) +x/+y/+x+y
#4) +x+y/$is+y/+x		;inverse of #3
#5) +y/$a/+x+y
#6) +x+y/$is$a/+y		;inverse of #5
#7) +x/$has$a/+y
#8) +y/$is$has$a/+x	;inverse of #7

At the end of the telecon, Giovanni asked "Is #3 above, i.e., +x/+y/+x+y,
really an inference from +x+y, or does that follow from a specific graph
notation?" I had the action item to pen an answer.

My answer is that yes, since the XDI subject +x+y represents the XDI
metagraph statement +x/$has/+y, then it infers all 7 of the other statements
above, irrespective of any particular graph notation. In fact, the RDF
relationship represented by +x+y has a direct RDF graph that doesn't require
any of the XDI metagraph predicates toe express. In ASCII art (where [] is a
node and --- label ---> is an arc):

      [+x] --- +y ---> [+x+y]

Note that all three XRIs are needed to capture this graph in standard RDF.
In other words, the $has statement +x/$has/+y does not constrain the subject
+x to just having a singleton predicate +y. +x may in fact have any number
of predicates +y (if so, that means +x/$has$a/+y). However the statement
+x/$has/+y is the assertion that +x has EXACTLY ONE +y predicate AND that
the object of that predicate MUST have the identifier +x+y.

Another way to put it is that, in contrast to a $has$a statement, a $has
statement is a way of expressing the English article, "the". So while
+x/$has$a/+y is a way of referring to "a" predicate +y on +x (i.e., the
class of all +y that are predicates on +x), +x/$has/+y is a way of referring
to THE (exactly one) +y that serves as a unique path to the object node,
which by definition has the path (address) +x+y. (Like any XDI subject, it
can also have other XRI synonyms, but this one is know a priori.)

Hope this helps,

=Drummond