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Subject: Why \$is for inverse (was Re: [xdi] Splitting \$is into \$is and \$ref)

• From: Drummond Reed <drummond.reed@xdi.org>
• To: Phil Windley <pjw@kynetx.com>
• Date: Thu, 13 Dec 2012 01:54:22 -0800

On Tue, Dec 11, 2012 at 7:56 AM, Phil Windley wrote:

I like this change because it makes \$is much more intuitive.  And I'm in favor of anything that gets rid of \$is\$is. :)

Drummond, sometime I'd like to understand why \$is functions as an inversion function. That doesn't seem intuitive to me.

Phil, great question. I’ll skip the long history; here’s the basic logic.

First, by analogy to English, a statement of the relationship between two people might look like:

Cain’s father is Abraham.

In XDI this would be:

=cain/+father/=abraham

In English, the inverse statement would be:

Abraham is the father of Cain.

In XDI this would be:

=abraham/\$is\$father/=cain

Now, looked at it from the standpoint of the graph model, as an assertion of logical of equivalence, \$is is effectively a self-referential arc, i.e., an arc that both starts and ends at the same node of the graph (it doesn’t technically do that, since XDI is a directed graph with no loops, but logically it equates to that). That essentially means you can traverse the arc in either direction and still get the same logical result. If =a/\$is/=b, then =b/\$is/=a.

So we concluded that, for the same reason it sounds logical in English, it made sense in the graph model to say that the \$is context represents the inverse context, i.e., whatever direction the arc +foo points, the arc \$is\$foo has the exact same semantics in the opposite direction.

Make sense?

=Drummond

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