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Subject: Re: [xdi] Proposal to kill two birds with one stone with $same

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...)


Def. Quota Drummond Reed <drummond.reed@xdi.org>:

> 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:
> 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.
> 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
> 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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