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Subject: RE: [xdi] RE: [External] [xdi] Re: Update on $is and $is!
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I need to clarify some of the terminology being used. By your description Drummond it is not symmetric.
Symmetric: a binary
relation R over
a set X is symmetric if
it holds for all a and b in X that
if a is
related to b then b is
related to a
Drummond, you said that "$is statements are "symmetric but directional". So =a/$is/=b does NOT imply that
=b/$is/=a" - the last part is specifically saying $is is antisymmetric. The meaning of 'directional' in the context of relations is undefined, but I'm going to assume you mean that $is is a function.
Curiously, you could think of $is as an ordering of aliased contexts by follow order, i.e., $(A)/$is/$(B) and $(B)/$is/$(C) means that $is is an ordering of the linked contexts (a subset of the contexts in the graph)
like so $(A)->$(B)->$(C).
Given that, and based on the thread so far, it seems to me that $is is an injective function that is also a partial order, where two contexts (elements) of the graph (of the set)
are comparable if and only if traversal must follow from one of the contexts to the other.
I think part of my confusion,at least, is that the semantics of 'is' in the English language are ambiguous, e.g., If Bob is Ted then Ted is Bob, but Bob is Republican does not imply
Republican is Bob. Part of the problem lies in the implicit 'a ', i.e. Bob is a Republican does imply that a Republican is Bob (though it reads weird). In some cases there is also an implicit 'Thing', 'Red' in Bob is Red goes to Bob is a Red thing. The
semantics of $is seem more appropriate to a word with a more antisymmetric slant, like links or in. $in has set semantics, which is I believe the rational behind it not being adopted when I proposed it as a replacement for $is a while ago. I still think it's
better to think in terms of set semantics rather than pseudo-equivalence, but with $in out, how about changing $is to $links?
As for $is$is, my issues with that are:
.. Reads awkwardly
.. Unclear from reading it what it means
.. $is has two completely different meanings in the same segment, let alone in the same graph
I've proposed alternatives to $is for inverse several times before, notably $inv, and still advocate not using $is for this purpose. There are benefits to $is as the inverse, and
I understand that, but the disadvantages far outweigh the benefits in my mind. As a result here is a new idea, somewhat radical: a new symbol in XDI for inverse: ', e.g., $is' is the inverse of $is. This also has the benefit of being the mathematical symbol
sometimes used for inverse instead of a superscript -1. Also, RFC 1738 suggests that an
apostrophe does not need to be URL encoded. What do you think? If there is some interest from the TC I will write it up as a proposal and put it on the wiki.
Definitions:
A partial order is a binary relation "≤" over a set P which is reflexive, antisymmetric, and transitive, i.e., for all a, b, and c in P, we have that:
Injective: A function
is called injective (or one-to-one,
or an injection) if f(a)
≠ f(b)
for any two different elements a and b of
the domain
Definitions are from wikipedia.org, with gratitude.
Kind regards,
Bill Barnhill
Booz Allen Hamilton - Belcamp,MD
Cell: 1-443-924-0824
Desk: 1-443-861-9102
From: drummond@respectnetwork.net [drummond@respectnetwork.net] on behalf of Drummond Reed [drummond@connect.me]
Sent: Wednesday, November 21, 2012 12:45 AM To: Barnhill, William [USA] Cc: Markus Sabadello; OASIS - XDI TC Subject: Re: [xdi] RE: [External] [xdi] Re: Update on $is and $is! I'm not sure if I can follow all of this thread because it's getting very deep. But let me just clarify one thing: $is statements are "symmetric but directional". So =a/$is/=b does NOT imply that =b/$is/=a. Rather there is a specific inverse of $is, which
is $is$is. So =a/$is/$b (one direction) implies =b/$is$is/=a (other direction). The first direction is canonical (a context may have zero or one $is statement) but the inverse is not canonical (a context node may have zero to n $is$is statements).
Hope this helps,
=Drummond
On Tue, Nov 20, 2012 at 3:44 PM, Barnhill, William [USA]
<barnhill_william@bah.com> wrote:
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