Re: [xdi] golden triangle (was Re: [xdi] $is is the universal inverse re

Subject: Re: [xdi] golden triangle (was Re: [xdi] $is is the universal inverse restriction)

On Thu, Jul 1, 2010 at 5:10 PM, Giovanni Bartolomeo <giovanni.bartolomeo@uniroma2.it> wrote:

-1. I'd like "predicate" better, to maintain backward compatibility with RDF.

BTW there are currently many issues with the "golden triangle" which are still very obscure (at least to me), including: $is$a as $word relating predicates with objects, $is and self referencing arc definition, $has$a definition as traversal of subject and predicate, +x/+y/+y and +x/+y/+x+y reintroduced, after we agreed that they were not needed, etc...

Note that the current specs are totally based on the golden triangle: http://wiki.oasis-open.org/xdi/XdiOne/AddressingAndGraphModel

This way it becomes very difficult - or sometimes even impossible - to think at XDI productions in terms of description logic.

I think it would be better to rediscuss together the golden triangle, and probably revise the current specs page accordingly.

Kind Regards,
Giovanni

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

I don't think it's any more confusing than "predicate". "verb" is just a
role - the same XRI could be a subject, verb, and object (especially in an
XDI dictionary).

But that's just one person's view. What do others think?

=Drummond

On Thu, Jun 10, 2010 at 2:28 AM, Markus Sabadello
<markus.sabadello@xdi.org>wrote:

Oh nooo I'll have to rename lots of stuff in XDI4j :)

But seriously, isn't "verb" a bit confusing? +name, +address etc. don't
look like verbs to me.

Markus

On Thu, Jun 10, 2010 at 10:49 AM, Drummond Reed <drummond.reed@xdi.org>wrote:

On Thu, Jun 10, 2010 at 12:51 AM, Joseph Boyle <boyle.joseph@gmail.com>wrote:

On Jun 9, 2010, at 11:22 PM, Drummond Reed wrote:

Joseph, first, my apologies for not replying earlier - I had another trip
this week so my email is way behind.

But we have another XDI TC telecon coming up tomorrow so I wanted to move
discussion forward on the individual issues/questions about the example
PDX document <http://wiki.oasis-open.org/xdi/PdxExample>. Here are my
answers to your two questions about $is (copied from below to keep the
thread clean):

> 1) How do the two roles of $is form a single coherent concept? Right
now the modifier role (as a passive voice marker modifying the following
verb) and the standalone role (as the copulative verb) seem like distinct
definitions to me. I realize this is analogous to the English verb "to be"
that also serves in both these roles, but is there a philosophical /
semantic / formal (take your pick) argument that this should logically be
the case in XDI?

You phrase that question very well. I have been thinking that in the
spec, we need to define the semantics for each of the metagraph predicates
for each of the following uses:

1) Standalone, e.g., $is

2) As a restriction on another predicate (i.e., preceeding it, e.g.,
$is+foo)

3) As an extension on another predicate (i.e., following it, e.g.,
+foo$is)

Agreed, we must do this, and explain what the 3 usages for a given
predicate have in common. (Are these the only 3, or are there even more
possible uses?)

I left out the other six options: Using the metagraph predicate as a 1)
standalone subject, 2) subject restriction, or 3) subject extension, as well
as a 4) standalone object, 5) object restriction, 6) object extension.

For many of those, the answer may be "undefined", but for some there are
very good answers. For example, $ as a standalone subject is the XDI context
self-descriptor; and $has and $a are both used as the proposed subject
extensions to create link contracts as shown in the lower part of the example
PDX document <http://wiki.oasis-open.org/xdi/PdxExample>.

I believe the definitions in each of these three roles must be logically
consistent. For example, the definition of $is as a standalone predicate is
synonymity between the subject XRI and object XRI (they both identify the
same logical resource). This is as shown as a reflexive<http://en.wikipedia.org/wiki/Reflexive_relation>arc (self-referential -- originating and terminating in the same node) as
illustrated in the golden triangle<http://www.oasis-open.org/committees/download.php/37568/xdi-golden-triangle.png>.

The Golden Triangle diagram (I'm tempted to say the XDI Holy Trinity but
should probably refrain) itself shows S and O as separate nodes though
connected by arrows labeled $is. For the arc to be reflexive, S and O would
have to merge and become a single node. Sorry if this sounds too literal. We
do understand "$is" as making S and O equivalent - but this is something
that we have to explain with text external to the diagram. Looking at the
diagram alone naively, it is not obvious that the $is arcs merge S and O but
that the other $a, $has arcs do not make S and P equivalent or P and O
equivalent.

I agree that the Golden Triangle diagram by itself does not make it clear
that the $is arc is reflexive. It needs some text with it to explain that. I
have a separate intermediate diagram that explains the origins of the Golden
Triangle diagram that makes that much clearer. I propose we use both in the
final spec.

The definition of $is as a restriction on another predicate is that it
expresses the inverse of that predicate, e.g., the inverse of +b is $is+b
(example: +a/+b/+c <=> +c/$is+b/+a). The logical connection with $is as a
standalone verb is that $is, being reflexive arc, is being used to describe
the verb it is restricting. As a reflexive arc, it is literally "reversing"
the restricted verb. So $is+foo is the reverse (inverse) of +foo.

This is one simplest yet most powerful examples of the utility of
semantic (non-opaque) identifiers in XDI.

> 2) One difference I notice between XDI terminology and linguistics
terminology is that in the latter, "predicate" means verb together with
object, not simply the verb.

Ahhh, I didn't know that. As you know, I have no formal background in
either linguistics or formal logic, so I am constantly learning nuances like
this. What's the solution: are you suggesting we use the term "verb" instead
of "predicate"? As in: XDI subject, XDI verb, XDI object?

http://en.wikipedia.org/wiki/Predicate lists the differing meanings in
grammar, logic, etc.

XDI gets the term "predicate" from RDF which gets it from mathematical
logic, where it specifically means a boolean-valued function. In this case
both S and O would be considered arguments to the predicate, and the boolean
result True from P(S,O) is expressed by the fact that the predicate is being
stated / graphed at all while the boolean result False from P(S,O) would be
expressed by not stating / graphing anything. This makes sense in one sense,
but may not be the most intuitively obvious meaning, in addition to the
conflict with the natural-language grammar that most people are familiar
with.

I would vote for "verb" not "predicate" in line with the trend towards
using simple everyday natural-language-like terms in XDI, which has included
using "$is", "$has", "$a" to replace more technical terms. This would be
another break with RDF terminology, which may be good or bad depending on
your viewpoint. I think some other knowledge representation systems have
used "verb" in some way, but don't remember specifically. However, the only
programming language I can think of offhand where "verb" is part of normal
terminology is COBOL. :/

I agree with your logic, and with using "subject, verb, object" instead of
"subject, predicate, object". If anyone on the TC disagrees, please post,
else I will start using that in all the XDI-related text I'm writing.

Thanks,

=Drummond

----------------------------------------------------------------
Invito da parte dell'Ateneo:
Il tuo futuro e quello della Ricerca Scientifica hanno bisogno del
tuo aiuto. Dona il 5 x mille all'Universita' di Roma Tor Vergata
codice fiscale: 80213750583 http://5x1000.uniroma2.it

---------------------------------------------------------------------
To unsubscribe from this mail list, you must leave the OASIS TC that
generates this mail. Follow this link to all your TCs in OASIS at:
https://www.oasis-open.org/apps/org/workgroup/portal/my_workgroups.php

xdi message