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Subject: Re: [xdi] EquivalenceLinks - XDI Wiki

Very good point, Markus. We need to be strict about what can be implied and what is actually an arc in the graph.

On Sat, May 4, 2013 at 2:02 PM, Markus Sabadello <markus.sabadello@gmail.com> wrote:
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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