Re: [xdi] XDI dictionary, reasoner...

On Sun, Apr 27, 2008 at 8:13 PM, Giovanni Bartolomeo <giovanni.bartolomeo@uniroma2.it> wrote:

Hello Markus,

to my understanding, the underlying idea is that there may be one node (literal in this case) which can be accessed with different XDI RDF statements provided that, through a reasoner, all the statements are expressing exactly the same concept. Let's consider them synonyms. A "mod" message simply changes the node's value, so that all three statements are automatically modified. I think this is a good feature, I see that e.g. any object oriented programming language allows you to define more than one pointer to the same object, and the benefits are huge.
What do you think?

Giovanni

At 05.44 26/04/2008, Markus Sabadello wrote:

Sorry for having been quiet about this so far, but I don't understand it. What does it mean to say that the three statements "identify the same literal":

#1
=giovanni+phone+home
          $type$xsd$string
                      "+39 06 4451843"
#2
=giovanni
          +phone+home
                      "+39 06 4451843"
#3
=giovanni+phone
          +home
                      "+39 06 4451843"

Assuming they do "identify the same literal", does that mean that there is just one literal node in the graph, which is shared by three predicates? If I apply a $mod message to one of the statements, will they all change?

And is this what you are trying to prove with the dictionary?

Also, the obvious question I have to ask, what would an application look like that demonstrates this functionality? What problems would you expect an XDI library to solve here?

Markus

On Thu, Apr 24, 2008 at 12:09 PM, Giovanni Bartolomeo < giovanni.bartolomeo@uniroma2.it> wrote:

Hello Drummond, All,

as for last week's request, I'm reintroducing this issue. After receiving your answer, I tried to figure out how to prove that two XDI RDF statements

=giovanni+home+phone/$type$xsd$string/

=giovanni/+home+phone/

does identify the same node. In order to recall the whole issue, which is now also on the wiki thanks to Drummond, http://wiki.oasis-open.org/xdi/XdiReasoners I report hereafter the whole message, at the end my elaborations:

********** Drummond replies **********

I am so glad someone finally asked this question in black and white – I have been thinking about this issue of "XDI expressivity" for months now given the fundamental capabilities of XDI RDF. Forgive me for providing an extended answer, but I think the question can be so revealing about the power of XDI RDF.

First, to answer your question right up front, "Do those three XDI addresses identify the same literal node?", my answer is: "You cannot know deterministically without reference to the XDI dictionaries used by the statements."

The reason is that the three statements represent three different paths through the XDI RDF graph, and as you pointed out, each path represents different semantics. So you you really have to drill all the way down into the graphs, and the statements represented by each graph, in order to answer your question.

To do this, let's start by looking at the three graphs visually in X3 Simple (one reason I love X3 Simple is that it lets you see the visual pattern of the graph while at the same time seeing the addresses).

#1

=giovanni+phone+home

          $type$xsd$string

                      "+39 06 4451843"

#2

=giovanni

          +phone+home

                      "+39 06 4451843"

#3

=giovanni+phone

          +home

                      "+39 06 4451843"

Now, let's "fully explode" each of these into ALL the XDI statements they represent.

#1 (5 statements)

=giovanni

          $has

                      +phone

=giovanni+phone

          $has

                      +home

$type

          $has

                      $xsd

$type$xsd

          $has

                      $string

=giovanni+phone+home

          $type$xsd$string

                      "+39 06 4451843"

#2 (3 statements)

=giovanni

          $has

          +phone+home

+phone

          $has

                      +home

=giovanni

          +phone+home

                      "+39 06 4451843"

#3 (2 statements)

=giovanni

          $has

                      +phone

=giovanni+phone

          +home

                      "+39 06 4451843"

Isn't it fascinating that the first graph represents five statements, the second three, and the final one only two?

In any case, all three options here (plus more - see below) appear to be completely valid chains of XDI statements between the XDI subject =giovanni and the XDI literal "+39 06 4451843". But none of them asserts exactly the same semantics (the only way to do that would be to use XDI synonyms, i.e., $is statements). However using an XDI reasoner and an XDI dictionary (which itself is just a set of XDI statements comprising definitions), you could verify that according to that dictionary, all these statements identify the same literal node.

In fact the dictionary is pretty short. Here it is:

+phone

          $is$a                                        <--1-->

                      +

                      $type$xsd$string

          $has                                         <--2-->

                      +home

          $a$has                                      <--3-->

                      +home

          $has$a                                      <--4-->

                      +home

          $a$has$a                                  <--5-->

                      +home

+home

          $is$a                                        <--6-->

                      +

          $has                                         <--7-->

                      +phone

          $a$has                                      <--8-->

                      +phone

          $has$a                                      <--9-->

                      +phone

          $a$has$a                                  <--10-->

                      +phone

$type

          $has

                      $xsd

$type$xsd

          $has

                      $string

As short as it is, the semantics represented by those statements – while crystal clear from a pure XDI semantics point-of-view – represent a surprising range of grammatical relationships a human POV. Roughly translated to English, the first ten statements say:

1) A phone is both a subject (noun) and a label for a type of data (typically called a "phone number", but often abbreviated in English as just "phone").

2) A phone can have a home, i.e., as a noun, it can have a possessive relationship with another noun, home.

3) A phone is something a home can have (possessive relationship).

4) A phone has an attribute of home.

5) Phone is an attribute of a home.

6) Home is a subject.

7) A home can have a phone (possessive relationship – inverse of #3).

8) A home is something a phone can have (possessive relationship – inverse of #2).

9) A home has an attribute of phone (inverse of #5).

10) Home is an attribute of a phone (inverse of #4).

Armed with that dictionary, an XDI reasoner can quickly prove that all the following XDI statements identify the same literal:

=giovanni+phone+home/$type$xsd$string/

=giovanni+home+phone/$type$xsd$string/

=giovanni/+home+phone/

=giovanni/+phone+home/

=giovanni+phone/+home/

=giovanni+home/+phone/

However, if you remove any of those XDI dictionary statements, some of the above are no longer provably true. For example, if you remove the statements:

+phone

          $has

                      $home

+home

          $a$has

                      +phone

Then you could no longer prove that the following two statements identify the same XDI object as the rest:

=giovanni+phone+home/$type$xsd$string/

=giovanni/+phone+home/

They MIGHT identify the same literal as the rest, but now you have nothing you can prove that with.

There's much more I'd like to say about this simple dictionary, but I'm out of time. However I encourage everyone who is interested to study it closely. To test your knowledge, here's a quiz question:

          "Given the dictionary above, how can you prove that it is valid for the XDI object of all six statements to be a literal string?"

=Drummond

Now, I think the most important part to understand is related to the semantics underlying the dictionary sentences:

+phone

          $has                                         <--2-->

                      +home

          $has$a                                      <--4-->

                      +home

which in English means

2) A phone can have a home, i.e., as a noun, it can have a possessive relationship with another noun, home.

4) A phone has an attribute of home.

$has, according to XDI RDF model v9, is aggregation, meaning that

Any two XDI subjects with a $has relationship can be concatenated into a single XRI representing this relationship.

Thus +phone+home is the way how aggregation is expressed.

Whereas $has$a is defined as a composition. The object in the RDF statement is therefore an "attribute" belonging to the subject.

Example similar to the one in XDI RDF v9: =giovanni/$has$a/+hair+color; thus =giovanni/+hair+color/+black should be a valid XDI RDF statement, expressing composition.

Quoting from wikipedia, difference between aggregation and composition: Aggregation differs from ordinary composition in that it does not imply ownership. In composition, when the owning object is destroyed, so are the contained objects. In aggregation, this is not necessarily true. For example, a university owns various departments (e.g., chemistry), and each department has a number of professors. If the university closes, the departments will no longer exist, but the professors in those departments will continue to exist. Therefore, a University can be seen as a composition of departments, whereas departments have an aggregation of professors. In addition, a Professor could work in more than one department, but a department could not be part of more than one university.

Now, I tried to work out a formal proof using the assertions 1)-10) but I failed in proving

that all the following XDI statements identify the same literal:

...

=giovanni+home+phone/$type$xsd$string/

=giovanni/+home+phone/

...

Probably I'm missing something (probably some underlying semantics), however, can you give some hints? Maybe we can work out the prove once for all and report this in the wiki/deliverable, as reference?

Thanks,

Giovanni

At 01.32 24/04/2008, Drummond Reed wrote:

4) TECH TOPIC: XDI DICTIONARY AND XDI REASONER

On last week's call Giovanni requested that our tech topic this week be the

XDI dictionary and XDI reasoner discussion we started on the list. Wikipedia

has a good article on semantic reasoners:

         http://en.wikipedia.org/wiki/Semantic_Reasoner

Drummond created a wiki page to capture the email thread for further

discussion:

         http://wiki.oasis-open.org/xdi/XdiReasoners

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