Hello Drummond,
all your argumentations seem to be based one central notion: "canonical XRI".
Could you clarify in more details what a canonical XRI is? (sorry,
maybe I'm the only one to require this clarification, however want to
be sure that my understanding is correct...)
Thanks,
Giovanni
Def. Quota Drummond Reed <>:
> XDI TC Members:
>
> Having had the long weekend (in the U.S.) to think about it, plus Giovanni's
> email yesterday, I had an insight about defining a predicate for
> equivalence/synonymity that has owl:sameAs semantics. This could kill two
> current birds with one stone. Here's a summary of my thinking:
>
> 1) WHY WE SHOULD AVOID MULTIGRAPHS
>
> First, with regards to the option we discussed last Thursday of the XDI
> graph supporting multiple XRI arcs between the same XDI subject and XDI
> object -- a directed multigraph <http://en.wikipedia.org/wiki/Multigraph>.
> As I've pointed out before, this creates problems determining the canonical
> XRI for identifying an XDI context node. But over the weekend I realized
> there's a second reason to avoid multigraphs: RDF graphs are not multigraphs
> either. In RDF, you must use an owl:sameAs statement to create an
> equivalence statement between two distinct RDF graph nodes. The owl:sameAs
> statement is a way to assert that the two nodes represent the same logical
> subject, but the two nodes still remain distinct and separate nodes in the
> RDF graph. Thus RDF graphs and XDI graphs currently share the same quality:
> every graph node has exactly one arc (one URI) that identifies it.
>
> With XDI graphs this has the further advantage that *every arc in an XDI
> graph corresponds to exactly one XDI statement and vice versa*. This is not
> only conceptually very clean and easy to understand and teach, but it is a
> very computation-friendly rule.
>
> So I would submit that XDI graphs should to follow the same underlying
> architecture as RDF graphs, i.e., be simple directed
> graphs<http://en.wikipedia.org/wiki/Graph_%28mathematics%29#Simple_graph>and
> not multigraphs.
>
>
> 2) USE $SAME FOR OWL:SAMEAS SEMANTICS
>
> My second realization was that if we want to be able to express the
> owl:sameAs semantics for equivalence, which only expresses general
> equivalence and does not include the notion of canonical equivalence, then
> we should assign an XRI to have the same semantics as owl:sameAs. To keep it
> simple, I propose that we use $same.
>
> As a relational arc, a $same assertion of equivalence would NOT be
> canonical, i.e., any two XDI subjects could have a $same relational arc that
> asserts that they are equivalent, and this arc could go in either or both
> directions between them, i.e., $same would be its own inverse (like $is, see
> below). So we would say:
>
> =!1111/$same/=example.name1
> =!1111/$same/=example.name2
> =example.name1/$same/=!1111
> =example.name2/$same/=!1111
>
>
> 3) KEEP $IS FOR BOTH CANONICAL EQUIVALENCE AND ALGORITHMIC INVERSION
>
> Lastly, because $same solves the RDF-equivalence semantics issue, I
> recommend keeping $is for exactly what we are using it for right now, i.e.:
>
> 1. By itself, for canonical equivalence (as illustrated in slide #3 of
> the latest XDI Graph Patterns
> PDF<http://www.oasis-open.org/committees/download.php/42654/xdi-graph-patterns-2011-06-23.pdf>
> ).
> 2. As a prefix, for algorithmic inversion for any other XDI predicate
> (example: $is$do as shown in slide 9 of the latest XDI Graph
> Patterns
> PDF<http://www.oasis-open.org/committees/download.php/42654/xdi-graph-patterns-2011-06-23.pdf>
> ).
>
> There are three reasons for this recommendation:
>
> 1. Since we have a separate $word for owl:sameAs equivalence, $same,
> there is no longer a conflict with using $is for canonical equivalence or
> algorithmic inversion or both. The latter are both XDI-only
> concepts, so it
> makes sense to use an XDI-defined predicate for them.
> 2. The reason for using it for both canonical equivalence and algorithmic
> inversion lies in the underlying metagraph model. In short, $is
> represents a
> self-referential arc (a loop <http://en.wikipedia.org/wiki/Graph_loop>).
> Since you can't actually express a loop in a simple directed
> graph, you use
> the $is metagraph statement to do it -- that's how we express canonical
> equivalence. When you then put any other XDI graph statement in
> the context
> of a parent self-referential arc (loop), you are "turning it back upon
> itself", i.e., expressing the inverse.
> 3. $is for inversion reads very well in English. We have seen numerous
> examples over the past several years. One of the most frequent is using
> $is$a to express supertype, which is the inverse of $a to express subtype.
> Or in the current link contract proposal, using $is$do to express the
> inverse of $do. But it also works works with virtually any
> English word. For
> example, =abraham/+son/=cain has the inverse =cain/$is+son/=abraham.
>
> =Drummond
>
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