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Subject: Re: [xdi] Proposal for separation of subject/predicate and parent-subject/child-subject semantics

• From: Drummond Reed <drummond.reed@xdi.org>
• To: Giovanni Bartolomeo <giovanni.bartolomeo@uniroma2.it>
• Date: Thu, 22 Apr 2010 08:54:49 -0700

This thread is missing the point I made in my reply yesterday, which I definitely want to discuss on today's telecon.

The point is that, as now proposed:

+a/\$has/+b <=> +a/+b
+a/\$has\$a/b <=> +a+b

However neither of these implies the other. In other words

+a/\$has/+b != +a/\$has\$a/+b
+a/+b != +a+b

I can show this logically with this proof:

1) \$has as a predicate is an assertion that its object is a predicate of its subject, e.g. +a/\$has/+b is asserting that the subject +a has the predicate +b. It thus implies logically that +a/+b AND asserts that the XDI statement +a/+b exists in the XDI graph where the +a/\$has/+b statement exists.

So the OBJECT of a \$has metagraph statement is by definition a PREDICATE.

2) \$a as a predicate is the assertion that its object is the object of a predicate that is its subject, e.g., +a/\$has\$a/+b means that +a is a predicate and +b is an object of that predicate. And

So the OBJECT of a \$has\$a metagraph statement is by definition an OBJECT.

Since a PREDICATE is not an OBJECT, the two statements are not logically equivalent. And neither by itself in the graph implies that the other exists in the graph.

I have spent the last two months thinking through the implications of the path where +a/+b implies +a+b and vice versa, and I am convinced it does not work.

What +a/\$has\$a/+b defines in an XDI graph of the subset of predicates +b of +a that are also an object of +a. That subset by definition is a single object which we can then identify itself in the graph as +a+b. That is why +a/\$has\$a/+b <=> +a+b and vice versa.

That set - consisting of a single object - is NOT equivalent to the set identified by +a/\$has/+b, which implies +a/+b, which identifies the XDI graph of all objects that are the object of the predicate +b on the subject +a. That set is by definition zero-to-n, and thus cannot be either logically or resolution equivalent to +a+b.

=Drummond

On Thu, Apr 22, 2010 at 3:08 AM, Giovanni Bartolomeo wrote:
Yes, that's correct. The "magic" you are referring is called "reasoner" and should be placed at the XDI endpoint which receives the incoming query.

As a side note, the difficulty about implementation is not to implement the reasoner itself (there are already available products, open source, in java) rather, to provide a formal, *consistent* model for XDI documents and XDI query which could be described to the reasoner in terms of Description Logic.

Talk with you all in today's phc,
Kind Regards,
Giovanni

Okay I understand.. And you call this behavior "logical equivalence", right?
Whereas "resolution equivalence" is based on \$is statements?

So from your point of view, both "logical equivalence" and "resolution
equivalence" would affect how an XDI endpoint works, i.e. add some "magic"
to the plain data in a low-level XDI store/document?

Markus

On Thu, Apr 22, 2010 at 11:06 AM, Giovanni Bartolomeo <
giovanni.bartolomeo@uniroma2.it> wrote:

Thank you Markus and Drummond for your replies.

I think Markus got the point. Here our views are probably different here.
My answer to Markus is that this query

=markus
\$get
/
=markus+email

should return

=markus+email
\$1

This might be not an asserted statement (there is no need that a human
writes this in the document) but an inferred one (a reasoner produces this).

In this, my opinion is that XDI should behave more similarly to RDF/OWL
rather than to XML (i.e. XDI is more an ontology language rather than a
simple markup language).

As Bill pointed out that +a <=> (+a), I'm saying that there are also other
logical equivalences and that +a/+b <=> +a+b is one of them (and that's why
I see no need for \$has\$a) - sorry, I'm disagreeing here with you Drummond.

But you're probably right in saying that I'm not fully understanding what
you're proposing ("semantically linked" and the golden triangle). So looking
forward to talk with you for a clarification on this.

Kind Regards,
Giovanni

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

It's late so I will just put short replies inline.

On Wed, Apr 21, 2010 at 9:11 AM, Markus Sabadello

So if I send the following XDI message to an endpoint:

=markus
/
=markus
+email

and then I send this XDI message:

=markus
\$get
/
=markus+email

What will be the XDI response?

Markus

would be no such subject exists (in other words, the response would be
null). In order to get a response to the second query, you would have to

=markus
/
=markus+email
...

where ... is whatever the contents of the subject =markus+email is.

Giovanni,

I understand what you are saying below, but you may not  understand what I
am saying. I am saying that +a/+b and +a+b are neither logically
equivalent
or resolution equivalent.

I am only saying that they are *semantically linked* - in other words,
that
if you have +a/+b in the graph, it implies that +a+b would be a
semantically
valid XRI in the graph, and vice versa. However it does NOT imply that
+a+b
exists, or vice versa.

The reason this is semantically consistent -- and I agree with you that of
course XDI needs semantic consistency -- is because in the analysis I have
been doing of the implications of what it would mean IF +a/+b and +a+b
were
logically equivalent, I keep finding deeper and deeper problems.

I don't have time to go into in more deeply now, but I would summarize
that
the golden triangle model I posted yesterday reveals the crucial
difference
between \$has, as a predicate that identifies another predicate, and \$has\$a
as a predicate that identifies an object.

Because of this, \$has and \$has\$a, as now proposed (vs. some of the
discussions of this topic over the last year that you reference below) are
not logically equivalent, and thus obviously not resolution equivalent
either.

Let's definitely make this the subject of tomorrow's XDI TC telecon.

Talk to you then,

=Drummond

On Wed, Apr 21, 2010 at 11:10 AM, Giovanni Bartolomeo <
giovanni.bartolomeo@uniroma2.it> wrote:

Hello Markus and Drummond,

thanks for your replies. I think there is however some confusion which I
want to clarify once for all. I'm not saying that +a/+b is resolution
equivalent to +a+b. I think we are now all agreeing on this (at least I
think :-).
Logical equivalence is a different concept. It means that if +a/+b is
resolvable then also +a+b must be. Note that they DO NOT resolve to the
SAME
node (this is instead resolution equivalence).
The requirement I'm talking about (if +a/+b is resolvable then also +a+b
must be and viceversa) is needed to ensure consistency in my semantic
model.
For instance, having in a graph

=example
\$has
+email

will allow to deal with =example+email as the set of emails which
=example
owns (=example+email), and consequently make assertions on them (pls
refer
to http://lists.oasis-open.org/archives/xdi/201004/msg00004.html for
details on this, btw I can clarify them in next phc). This is also
highlighted in point 1) of
http://lists.oasis-open.org/archives/xdi/201003/msg00014.html.

Note that resolution of certain statements is needed, even if not
asserted
in the graph, but inferred using a reasoner (again pls refer to my mail
for
details) in order to implement what we have discussed in

http://lists.oasis-open.org/archives/xdi/201001/msg00047.html

=bill.barnhill: We can get the graph containing statements about any

statement in the graph, and that graph will only exist if and only if
the
statement is in the graph. put more simply (+a/+b) is resolvable, or
R(+a/+b) = True. Generalizing this we see that if R(X) = True then
R((X)) =
True, meaning  and (X) are logically equivalent
Drummond: It seems the import of what you are saying is that +a <=>
(+a)

is

false

=bill.barnhill: but not  +a = (+a)

Drummond: Yes!
Drummond: A \$is statement in an XDI graph establishes what Bill calls
"resolution equivalence"

where we used symbol <=> to address logical equivalence, and = to
resolution equivalence.

Now my point is: either the TC has a different semantic model to propose
for XDI (in this case, I would be glad to know more and discuss about
it),
or the TC wants to discard semantic consistency for XDI. If the latter
is
the case, then, frankly, I think the TC is underestimate a tremendously
powerful feature which could instead change the whole concept of web
it.

Thank you,
Giovanni

What I'm afraid of is that people will never understand resolution

equivalence, and that it would be difficult to implement at the storage
and
messaging levels of an XDI stack.

Can't we just have logical equivalence without resolution equivalence?
On the logical level a high level application/reasoner/etc can infer
lots
of
stuff based on some \$is, \$has, \$is\$a, etc rules we make up, but I'm
really a
bit scared of having to implement such extra XDI "magic" just for plain
XDI
storage and messaging..

Markus

On Tue, Apr 20, 2010 at 5:21 PM, Giovanni Bartolomeo <
giovanni.bartolomeo@uniroma2.it> wrote:

Dear Drummond, All,

thank you for this proposal - two main thoughts from my side:

1) it is FUNDAMENTAL that if +a/+b is resolvable then also +a+b MUST
be,
and viceversa. We used the symbol <==> to say this, +a/+b <==> +a+b.
Obviously the stored document can only contain one of the two, e.g.
the
document only contains +a/+b, but +a+b MUST be resolvable as well.
This is about the relationship between asserted and inferred
statements
which I illustrated in the second part of my email
http://lists.oasis-open.org/archives/xdi/201004/msg00004.html - we
didn't
discuss this yet because we ran out of time last week, but it would be
good
to address this in next phc.

2) About the following statements (in which the symbol <==> is used in
a
somehow different way than in point 1)

+a/\$has/+b      <==>    +a/+b

+a/+/+b <==>    +a+b
+a/\$/\$b <==>    +a\$b
+a/=/=b <==>    +a=b
+a/@/@b <==>    +a@b
+a/*/*b <==>    +a*b
+a/!/!b <==>    +a!b
+a/()/(b)       <==>    +a(b)

note that the statements on the left side in their own give origin
to
metastatements like +a/\$has/+, +a/\$has/\$, +a/\$has/() which in turns
are
logically equivalent to +a+, +a\$, +a() whose semantics is totally
unknown to
me.

Kind Regards,
Giovanni

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

Per my action item from Thursday's telecon, following is more about
my

analysis and proposal for solving the "\$has semantics problem" once
and for all.

*** ANALYSIS ***
My first conclusion, on which I think we all agree, is that while
+a+b
might imply +a/+b and vice versa, that does not mean that: a) they
have the same semantics, or b) that they identify the same XDI graph.
Indeed, since one is an XDI subject and the other adds an XDI
predicate, by definition they cannot identify the same XDI graph.

To illustrate in English, most English verbs can be made into nouns
by
putting them in their infinitive form (“to be”, “to run”, “to
shout”).
But “run” and “to run”, while clearly linked semantically, do not
have
the same meaning. They cannot be interchanged with each other.

Thus my second conclusion is that none of the three XDI graph
examples
we were discussing on our telecon two weeks ago were in fact
equivalent. They were each different XDI graphs that had similar but
not identical semantics.

My third conclusion is that this means that we do in fact need
clearly
distinguished ways of semantically and syntactically of expressing
that an XDI subject (e.g., +a) : 1) has a child subject (e.g., +a+b),
and 2) has a predicate (e.g., +a/+b).

My fourth conclusion was that this is the problem we have been
struggling with for the last year: by using \$has (with or without
variants like \$has\$a) to express both parent subject/child subject
relationships (+a+b) and subject/predicate relationships (+a/+b), we
have wrapped ourself in a classic Gordian knot.

*** PROPOSAL ***

Once the problem was framed this way, it became much easier (for me
anyway) to see that a clean solution would be to dedicate the \$has
predicate to only one semantic – either the parent subject/child
subject relationship or the subject/predicate relationship. Of those
two options, I strongly prefer dedicating the \$has verb to expressing
the subject/predicate relationship (+a/+b), since this is the simpler
and more intuitive to understand, and mirrors the semantics of the \$a
predicate, which expresses predicate/object relationships.

If \$has is dedicated to that expression, then we simply need a
different predicate (or set of predicates) to express parent
subject/child subject relationships.

For that, an obvious answer is to use XRI delimiters as predicates.
This is intuitive since it is syntactically required to have a
delimiter between XRI subsegments, and each of the six XRI delimiters
(not counting parentheses for cross-references) has its own
XRI-defined "semantics", e.g., * means reassignable identifier, !
means persistent identifiers, etc.

So to summarize using +a and +b notation:

+a/\$has/+b      <==>    +a/+b
+a/+/+b <==>    +a+b
+a/\$/\$b <==>    +a\$b
+a/=/=b <==>    +a=b
+a/@/@b <==>    +a@b
+a/*/*b <==>    +a*b
+a/!/!b <==>    +a!b
+a/()/(b)       <==>    +a(b)

Semantically, it would still be true that +a+b/\$is\$a/+b (and the
inverse that +b/\$a/+a+b). And while +a+b would imply that +a/+b is
valid, and vice versa, the existence of one in an XDI graph would not
imply the existence of the other.

So, if =example wanted to do a query to determine if +a+b and +a/+b
both existed in an XDI graph, it would be:
=example
\$get
/
+a
\$has
+b
+
+b

I have been trying out this proposal in sample XDI documents for the
past week and it seems to work very well. Please consider and
experiment with it and post your thoughts. We'll put it on the agenda
for next week's telecon.

=Drummond

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