about what you'd see in RDF if each of RDF triple was "reified", as
described here:
http://www.w3.org/TR/rdf-primer/#reification
(Although, based on this primer, I can note that while reification is
not "quoting", my set-up for triples in Arxana is quoting; so the two
systems are not identical. Some further critique of RDF focusing on
its lack of quoting are here: [1]. Must say, I haven't quite grokked
the details of the critique.)
Anyway, lack of originality doesn't necessarily mean make an idea any
worse! However, it does seem to mean that if Arxana is to wins in
anything, it would probably be in applications, not in terms of basic
theory, because the basic is apparently all developed (whether or not
there is a viable implementation).
All that said: in plain language, everyone agrees that the "reified
triple model" will be valuable whenever it is valuable to make
assertions about assertions. (The example in the RDF primer talks
mainly about recording the "provenance" of assertions. I'll just
mention that of course there are other things one might want to say
about assertions.)
(Note: One place where some additional theory may to be needed is in
describing "side-effects" of making an assertion or taking other
actions. It is one thing to be able to talk about an assertion once
it exists -- but it is certainly also good to be able to make
assertions about ACTIONS. I don't know if RDF talks or "thinks" about
actions at all -- but since they are already "semantic" in the sense
of having a "physical meaning" I think it would be very helpful to be
able to modify semantics; e.g. notify me if the price of this stock
falls or rises more than 3 points.)
Application-wise, just because a model exists for RDF does not mean
that there is necessarily any good way to compute using that model at
present...
Here are some other perhaps more interesting examples, again related
to PlanetMath.
Example 1: Evolution of metadata as basic objects evolve.
Currently, objects are owned by one person. (E.g. the object "Group"
is owned by user Drini.[2])
This is very different from the model used by Wikipedia, where anyone
can edit any object and the changes are applied directly to the object
in question.
I've been considering the idea of allowing anyone to edit an object on
PlanetMath, but splitting these versions off as "variants" until they
are either approved by the original owner (in which case they
supercede the original object) or adopted by a new owner. A third
party might choose between different objects that define or discuss
the same term based on metadata like:
"Group" hasEducationalLevel "Undergraduate"
"Group" hasLevelofDetail "Low"
Suppose that these metadata carry over to new variants and suppose
that someone comes up with a much more detailed and advanced
definition. (Such definitions can exist; cf. the Encyclopedic
Dictionary of Mathematics.) The triples above are no longer accurate,
but the metadata is owned by the new owner of the object. So, it
would be good for a third party to be able to annotate the bogus
metadata. (Currently, such annotations would just go into text
fields: "dear owner please change your 'level of detail' metadata
field, its wrong!!", but more specific/directed commentary would
probably be helpful for everyone involved.)
The details here may be a bit complex -- but the basic principle is:
when objects change, their metadata may sometimes change too; so, we
need some language for talking about changing metadata.
Example 2: Building, maintaining, and interacting with learning
resources.
Right now PlanetMath is mainly a "reference work". I envision it in
the future being useful as a full-fledged learning resource. In other
words, if I want to learn Abstract Algebra or some other math topic, I
should be able to log into PlanetMath and reach some desired level of
proficiency using resources I find there.
In order for this to work, the system will need to know which types of
problems I've solved, which things I have "mastered", which things I
need work on. Obviously all of this can be stored as triples. The
assertions about assertions come in with things like: "if Joe knows
the First Isomorphism Theorem and the Sylow theorems, then he should
be able to solve problem A1287g." So they throw me this problem and I
can't solve it, and a new fact is added to the database: Joe bombed
another problem. The system needs some recourse: perhaps give me an
easier problem or give me a hint on how to solve the problem I was
given.)
*killer app* ;)
Some User Interface Considerations
Well, I have thought about this some, maybe not in much depth.
Rendering as hypertext is what I was focusing on in an earlier
prototype -- links that attach to certain pieces of text are of course
overlayed on top of the text itself; markup with different attributes
may appear with different colors; overlapping links (the most basic
case being multiple targets for the same words) could be switched out
either by switching the whole rendering (e.g. by using a scroll wheel)
or by choosing between multiple targets after "right-clicking". My
prototype stuff has been in Emacs.
For an AI-style view, you could have a node rendered with slot
relationshps running down the screen, links to known entities provided
where suitable, annotations lined up in a second column --
JoeCorneli
[ResidesAt]: [421 Cedar Avenue] (became true in Feb 2004)
Again for "hypertext": Note that typesetters have been dealing with
"scholia" for centuries. Marginalia, inline annotations, different
fonts... all kinds of great ideas can be found in historical
manuscripts. So, for textual views, a LaTeX renderer that could pull
of some of these old-fashioned tricks would be great.
The simplest "graphical" systems would just be adaptations of typical
link-node semantic net frontends. 3D and color would be cool of
course.
Finally, in some of my best day-dreams, I imagine a graphical system
that specifically deals with partitions of space. Why? Because
categorizing assertions move objects from partition to partition.
(Generally there are many different ways to partition up a space.)
This is where my old interests in Riemann geometry start to come back
to light... but I haven't worked out (m)any details.
[1]: http://www.mulberrytech.com/Extreme/Proceedings/html/2004/Stickler01/EML2004Stickler01.html
[2]: http://planetmath.org/encyclopedia/Group.html
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