# Re: Availability of the ANSI standard proposal?

sowa@west.poly.edu (John F. Sowa)
Date: Sat, 23 Mar 1996 12:37:09 +0500
From: sowa@west.poly.edu (John F. Sowa)
Message-id: <9603231737.AA04801@west>
To: cg@cs.umn.edu, fritz@rodin.wustl.edu, ged@cs.rmit.edu.au
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

Fritz Lehmann raised some questions about the relational hierarchy.
Following is the approach that I recommend:
1. A relation may be defined by a lambda abstraction over a logical
expression or graph by specifying one or more variables (or concept
nodes) as formal parameters.
2. Two different abstractions over the same expression or graph that
specify different formal parameters or the same parameters in a different
order are considered distinct.
3. Implication induces a preordering (which can be converted to a partial
ordering by factoring out logical equivalences) over expressions or
graphs. That partial ordering can be extended to lambda expressions
in a straightforward way:
If expressions x<y, then the lambda abstractions x'<y' ONLY IF the
corresponding variables or concept nodes in both x and y have been
designated as formal parameters.
4. Point #3 implies that if you select different formal parameters (or
the same formal parameters, but in a different order), you won't
preserve the partial ordering x'<y'.
5. Point #3 also implies that relations of different valence (arity,
adicity, or whatever you want to call it) are not comparable in the
partial ordering.
I agree with Fritz that converse relations are an unnecessary redundancy.
But if anyone throws them into the pot, they won't be placed in the same
point in the partial ordering.
John Sowa