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Subject: Re: [xdi] EquivalenceLinks - XDI Wiki

I think it's okay to say that =a/$ref/=b and =b/$ref/=c does imply =a/$ref/=c.

But it doesn't mean there's actually a =a/$ref/=c arc in the graph.


On Sat, May 4, 2013 at 10:38 PM, Drummond Reed <drummond.reed@xdi.org> wrote:
On Sat, May 4, 2013 at 1:23 PM, Joseph Boyle <boyle.joseph@gmail.com> wrote:
Yes, I think this is clearer than link. Although in math http://en.wikipedia.org/wiki/Equivalence_relation implies reflexive, symmetric, and transitive. $is meets all three conditions while $ref and $rep meet none of them.

Part of the reason we created the https://wiki.oasis-open.org/xdi/EquivalenceRelations page is to define the different types of equivalence that XDI supports. We split off first $ref and then $rep so that $is could meet the very strict reflexive, symmetric, and transitive requirements of a "Leibniz equivalence" test. $ref and $rep are not supposed to meet these requirements.

Actually, when we say $ref is non-transitive, we are saying =a/$ref/=b and =b/$ref/=c does not imply =a/$ref/=c. However is it even possible to have both =a/$ref/=b and =b/$ref/=c in the first place? If not, how are we avoiding it? If it is possible, then how do they behave?

Actually, reading this, I think we were wrong to say $ref is non-transitive, i.e., =a/$ref/=b and =b/$ref/=c does imply =a/$ref/=c. Does anybody disagree?

If not, Joseph, can you update that page to correct this?



On May 4, 2013, at 1:02 PM, Drummond Reed <drummond.reed@xdi.org> wrote:

I believe it's important to keep XDI literal nodes fully aligned with RDF literal nodes.

$ref and $rep (and $is) are, IMHO, not special types of nodes, but special types of relations. That's why we have special treatment for them. 

In fact, this is such a good point that I don't know why we originally decided to call them "equivalence links". To be consistent with the XDI graph model should have called them "equivalence relations".

So I just did a search-and-replace edit on the page to change "links" to "relations" (it reads wonderfully) and then renamed the page to:

Just FYI, to rename a page on the wiki requires two steps:
  1. Use the "Copy Page" function on the drop-down menu to copy the page to the new page name.
  2. Edit the old page to replace all the content with a single line:
                           #REDIRECT NewPageName


On Sat, May 4, 2013 at 2:31 AM, Joseph Boyle <planetwork@josephboyle.net> wrote:
Drummond reminded me that $ref or $rep preclude not only literal but any other child nodes. This is such a strong constraint that a node originating a $ref or $rep looks to me less like other context nodes, and if anything more like literal nodes. Can we make them an additional category of nodes, on a par with context nodes and literal nodes? Better yet, can we subsume literal nodes and alias nodes (originating a $ref or $rep) under a category called value nodes.

On May 3, 2013, at 3:56 PM, Drummond Reed <drummond.reed@xdi.org> wrote:

Markus, I was just discussing this with Joseph and I think he's got a point that, in that proposal, we'd be better off calling them equivalence arcs than equivalence links. All arcs are a form of link, but "link" has a lot of Web semantics, whereas "arc" is pretty much just a standard graph concept.

What do you think?


On Fri, May 3, 2013 at 7:48 AM, Markus Sabadello <markus.sabadello@gmail.com> wrote:
I would say "arc" and more specifically "relational arc" are low level terms in the graph model. We can always use these terms. An "equivalence link" is a relational arc that expresses equivalence. I don't think we're using just the term "link" by itself.


On Friday, May 3, 2013, Joseph Boyle <planetwork@josephboyle.net> wrote:
> When should we say "link" vs. saying "arc" or "relational arc"?
> https://wiki.oasis-open.org/xdi/EquivalenceLinks?highlight=%28%5CbCategoryProposal%5Cb%29
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