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

[Drummond Reed <drummond.reed@xdi.org>]

Giovanni,

The golden triangle has been working very well -- at least for me -- as a vehicle for explaining the simplicity at the heart of the XDI metagraph predicates/verbs.

See inline for more responses.

On Thu, Jul 1, 2010 at 8:10 AM, 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,

The golden triangle only explains the origins and semantics of the metagraph predicates. It doesnt' literally say that $is$a related a predicate to an object. For example, in the XDI statement

=drummond
  $is$a
    +person

all the standard XDI model applies, i.e., =drummond is the subject, $is$a is the predicate (or "verb" as Joseph suggests), and +person is the object.

The semantics of the $is$a statement simply say that +person is an arc that points at the subject =drummond. That's what it means to assert that a resource is of a certain type.
 

$is and self referencing arc definition,

Please do explain what the issue here is. When I present XDI, this is the first example I use to explain why identifiers in XDI are non-opaque, and it usually fires off "the big light bulb" in the audience. Suddenly they start to understand the power of XDI - that you can algorithmically state the inverse of any XDI predicate just by restricting it with $is.
 

$has$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...

I don't understand. We spent several months figuring out the new definitions of $has and $has$a. That was the "big ahha" that triggered the change in the metagraph model, and thus the revision to the spec. Can you send a writeup of what you believe the issue is?

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 too am very interested in figuring out how the metagraph model maps to conventional description logics. But I am not so interested in that topic that I believe it should delay us issuing XDI 1.0. The practical value of the metagraph model and in particular the great utility of restriction/extension of XDI subjects, predicates, and objects is enabling us to start building some very compelling XDI solutions. I don't know about the rest of the XDI TC members, but after six years (2004-2010) of developing models, it really feels like time to start putting out XDI 1.0 specifications along with real code that shows what can be done with them.

If that attracts the attention of the DL community and, with their help, we figure out there is a better metagraph model, that can become XDI 2.0, just as the OWL community has put out OWL 2.0 and the RDF community is now looking at RDF 2.0
 

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

If you have specific issues that you believe are problems -- especially fundamental logic or semantics problems -- please do post them together with your suggestions about how to fix them.

Thanks,

=Drummond

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

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