There has been a lot of discussion about various notations. Partisans
or inventors of one version or another make many claims about them.
Over the years, I have used, implemented, evaluated, compared, and
written about many different notations for many different purposes. (01)
As an example, I wrote an article "Semantic Networks" for the 1987
edition of the _Encyclopedia of AI_, revised it for the second edition
(1992), and updated it with more recent info about the Semantic Web
and other developments: http://www.jfsowa.com/pubs/semnet.htm (02)
I sometimes get unsolicited requests from people who have invented
a YAN (Yet Another Notation). At the end of this note is my response
to somebody who asked me to consider a notation I'll call XGraph (XG). (03)
In general, I don't believe that there is any notation that is
(a) ideal for all purposes or (b) significantly better than all other
notations even for its prime purpose. But there are many notations
that are significantly worse than others for many purposes. (04)
John (05)
 Slightly edited version of a note to the inventor of XG  (06)
Some observations: (07)
1. The claim that XGs aren't nested is misleading, because you
assume a linear order for reading them. (08)
2. In predicate calculus, for example, the order of quantifiers in
a formula such as ∀x∃y∀zP(x,y,z) has the same effect as nested
parentheses in ∀x(∃y(∀z(P(x,y,z))) or the nested ovals in EGs. (09)
3. The critical issue is not the external notation, but the structure
that gets mapped to and from the semantics (i.e., model theory)
and the rules of inference that apply to that structure. In the
papers cited below, Peirce's EGs and the linear EGIF have exactly
equivalent mappings, even though they look very different. (010)
4. Some structures have a cleaner, simpler, or more general mapping
to the model theory or to the rules of inference than others.
But a simple diagram is not convincing. It's necessary to prove
theorems that show which versions are equivalent to, more general
than, or more specialized than other better known versions.
Even if you prove such a theorem, you have to explain why the
point you proved is relevant for any practical application. (011)
5. Showing a picture of a wiring diagram of a monkey brain and
a picture of an XGraph proves nothing. Neuroscientists would
be the first to tell you that (1) an enormous amount has been
learned about the brain in the past half century, (2) the amount
that is still unknown is far greater, (3) even when connections
are known, the question of what information flows along those
connections is mostly unknown, and (4) the most that can be
inferred from such research is to say that some theories are
clearly wrong and some are less wrong than others. (012)
For some slides that introduce Peirce's existential graphs and relate
them to other notations, see http://www.jfsowa.com/talks/egintro.pdf (013)
But those introductory slides require much more detail to back up the
claims. See http://www.jfsowa.com/pubs/egtut.pdf (014)
And it's also important to show how different theories are related
to one another. See http://www.jfsowa.com/pubs/eg2cg.pdf (015)
For a survey of issues about the brain, language, and reasoning,
see http://www.jfsowa.com/talks/goal2.pdf (016)
All these papers and slides have many references to other research.
It's essential to dig into those details before making any claims
about one notation or another. (017)
If you want to get anybody to evaluate XGraphs, you need to publish
articles in journals and give presentations at conferences  and/or
implement software that other people *want* to use. Just look at
SourceForge for thousands of examples of software that nobody uses. (018)
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