# Synthetic Dimensionality

Bruce Schuman <origin@rain.org>
```Date: Sat, 14 Jan 1995 12:54:26 -0800 (PST)
From: Bruce Schuman <origin@rain.org>
To: Discussion List ONTOLINGUA <ONTOLINGUA@HPP.Stanford.EDU>
Cc: Nicola Guarino <guarino@ladseb.pd.cnr.it>, Jorn Barger <jorn@mcs.com>
Subject: Synthetic Dimensionality
Message-id: <Pine.SUN.3.91.950114122157.13748A-100000@coyote.rain.org>
Mime-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII
```
```Hi, People --

Just want to mention that I'm firing up a little online discussion on
"conceptual dimensionality" through my BRIDGE-L@ucsbvm.ucsb.edu mailing
list.  And it would be interesting to draw into this discussion some
serious knowledge representation engineers, and anybody else with an
interest in the algebraic foundations of conceptual structure.

"Synthetic Dimensionality" represents an attempt to *generalize* these
ontological foundations, in ways which are based on the isomorphism
between the concepts "dimension" and "ordered class".

There is apparently a profound algebraic simplicity here, that seems
amazingly in compliance with Occam's Razor.  This logic is so simple, the
entire thing is based on the concept of "cut", -- analogous to the
"Dedekind Cut" in the real number line definition at the foundation of
mathematics.

In other words, there are no algebraic primitives, -- and no axioms or
postulates.  These approaches involve "arbitrary and heuristic"
ontological choices, which narrow the implications of the logic.

But Synthetic Dimensionality attempts a "top-down stipulative" semantics,
which postulates an extreme simplicity by fiat, then explores the
mappings to natural language semantics, and a zillion other things.

The exploratory claim is made that this logic does, in fact, generalize
the form of conceptual space.  From this point of view, all natural
languages are specific interpretations of this general form, and subject to
various sorts of adaptive historical and heuristic distortions.  In other
words, there is a "pure and universal logical form", of which existing
"natural" forms are blurry interpretations.

If you're interested in looking at some of these issues, we're going to
consider them on an occasional basis through the SEMANTICS topic of the
BRIDGE-L mailing list.

For those who don't know, L-Soft listserv lists can be partitioned into
as many as 11 independently addressable topics, that function like
mini-mailing lists.  To sign on exclusively to this discussion, send the
two-line subscription command

set bridge-l topics= semantics

to

listserv@ucsbvm.ucsb.edu

I hope to see a few of you ambitious analysts over there.

- Bruce Schuman
http://rain.org/~origin/

PS, the basic paper on Synthetic Dimensionality is at
http://rain.org/~origin/sr/sr2
Another related paper, on "The Universal Hierarchy of Abstraction", is at
http://rain.org/~origin/sr/sr1

```