Re: Availability of the ANSI standard proposal?

fritz@rodin.wustl.edu (Fritz Lehmann)
Date: Fri, 22 Mar 96 20:50:43 CST
From: fritz@rodin.wustl.edu (Fritz Lehmann)
Message-id: <9603230250.AA22956@rodin.wustl.edu>
To: cg@cs.umn.edu, ged@cs.rmit.edu.au, sowa@west.poly.edu
Subject: Re: Availability of the ANSI standard proposal?
Cc: goolsbey@cyc.com, interlingua@isi.edu, murray@cyc.com, srkb@cs.umbc.edu
Sender: owner-srkb@cs.umbc.edu
Precedence: bulk

Dear Conceptual Graphs, Interlingua and SRKB lists,

John Sowa recently mentioned the hierarchy on relations.  This is
essential.  There are a couple of subtleties to consider.  First.
decide what to do about converses of relations.  If x R1 y subsumes
x R2 y, and R2' is the converse of R2, then x R1 y subsumes y R2' x.
An algebraic formalization is in Henkin, Monk & Tarski's "Cylindric
Algebras". Keep in mind that, as Peirce noted, a triadic relation has five
"converses" and it gets much worse with higher valence relations.

Some time before I started working on Cyc, they decided to drop
converses entirely.  This was a very wise decision, I believe.  If
you think of a relation "floating" in abstract space, the converse(s)
are really matters of how the abstract relation is projected into
a string notation.  There is only one genuine relation represented
by all the converses.  As I said on these lists years ago,
West-Of(Kansas,Missouri) and East-Of(Missouri,Kansas) both represent
the SAME FACT.  Of course, to translate to other (string-based)
languages and logics, it may be necessary to choose one variant or another,
or all of them, depending on what the other language or logic requires.

For inference and other purposes, Cyc needs only one form for each relation.
If you want to switch the order then state it in a different order in CycL.
I recommend that Conceptual Graphs people and others consider making the same 
choice, especially since the superfluity of converses is due to the (hyper)graph
nature of logical relations.  Had linear string notations for logics (and
languages) never been devised, there would be little notion of "converse".
The existence of converses is due to the linear form of natural languages.
In the fundamental logic, i.e. abstract relational structures (directed
hypergraphs floating in the Platonic void), the converses don't exist.

This leads to an issue for relational subsumption though, and that is that
there is an extra element of the subsumption of relations, namely the 
particular projection (permutation if you preserve valence) of the subsuming
argument-positions into the subsumed argument-positions.  If the relation
is wholly symmetric then it doesn't matter.  If the relation is partly
symmetric (in only some argument-positions) then only the asymmetric
arguments are of concern.  For two arguments, allow for a swap, etc.

Another thing to address is whether a relation can subsume another relation
of different valence.  I temporarily recommend against this.  Consider also
the case of "polyvalence" relations -- there is no good reason to require
that a relation have fixed valence.  KIF fortunately allows polyvalent relations
(at least it used to in version 3.0).   So does Cyc.  In subsumption, handle
these with care, but there should be no serious problem.

(Note: My opinions on things like this are my own, not Cycorp's, especially
since Cyc people are unaccustomed to treating logic as "floating hypergraphs".
Other than that, my views are as authoritative, canonical and definitive as
they ever were.)

                              Yours truly,  Fritz Lehmann


Cycorp, 3500 W. Balcones Center Dr., Austin, Texas 78759     fritz@cyc.com