alternative interlingua

pfps@allegra.tempo.nj.att.com (Peter F. Patel-Schneider)
Message-id: <9008101725.AA26723@vaxa.isi.edu>
Date: Fri, 10 Aug 90 13:24:49 EDT
From: pfps@allegra.tempo.nj.att.com (Peter F. Patel-Schneider)
To: bobrow@parc.xerox.com
Cc: interlingua@vaxa.isi.edu
In-reply-to: Danny Bobrow's message of Thu,  9 Aug 90 22:26:02 -0700 (PDT) <IakYJeQB0V0wA1R40O@nero.parc.xerox.com>
Subject: alternative interlingua

Here is an example showing how hard it is to use the current interlingua.

I have the following assumptions about how the interlingua is to be used:
1/ No information is to be lost when translating into the interlingua.
2/ When translating into the interlingua, no knowledge of the system that
   will eventually be translating out can be used.
3/ When translating out of the interlingua, no knowledge of the system that
   the information was initially represented in can be used.


Consider the following CLASSIC knowledge base:

	(cl-define-role r)
	(cl-define-concept y '(prim classic-thing 1))
	(cl-define-concept x '(and y (at-least 5 r))
			     '(at-most 4 r))
	(cl-define-concept w '(at-least 10 r))

How am I to translate this into the interlingua?

The obvious way is to translate into defrelation, resulting in:

	(defprimrelation r ($x $y) )
	(defprimrelation y ($x) (classic-thing $x))
	(defrelation x ($x) (and (classic-thing $x)
				 (y $x)
				 (at-least 5 ($y) (r $x $y))))
	(defrelation w ($x) (and (classic-thing $x)
				 (at-least 10 ($y) (r $x $y))))
	(forall $x (implies (x $x) (at-most 4 $y (r $x $y))))

where at-least and at-most have complicated axiomatizations, but are
non-problematical.  

The problems start with the definition of "implies".  In CLASSIC, rules
(third and subsequent arguments to cl-define-concept) are forward-chaining
rules, and not material implications, so some axiomatization of implies,
probably in terms of partial procedures, and definitely using some
quotation mechanism, is required.

However, suppose I wanted to translate this out of the interlingua into
LOOM.  LOOM has rules, which I will suppose to be similar enough to
CLASSIC's rules that the best translation of a CLASSIC rule is a LOOM rule.
>From assumption 4, I cannot just realize that the interlingua
axiomatization of CLASSIC rules is the result of translating from CLASSIC,
so I cannot do a textual match to see if the axiomatization is the same as
one that I was told CLASSIC results in.  This means that I have to
determine that the axiomatization of "implies" is close enough to the
meaning of rules in LOOM.

My contention is that this is essentially impossible, regardless of the
exact axiomatization of "implies".  This the basis of my argument that
extensions using quotation are undesirable in an interlingua.

Even more difficult problems surface when "defrelation" and
"defprimrelation" are considered.  In CLASSIC, definitions have a modal
component so there must be some axiomatization of defprimrelation beyond
the simple extensional axiomatization in the manual.  Even if some modal
flavour is added to "defrelation" and "defprimrelation" in the interlingua,
it is extremely unlikely that it will correspond to concept and role
definitions in CLASSIC, so some extra axioms, also using quotation, will
have to be added.  Again, determining the equivalence of these to the
meaning of concept and role definitions in LOOM will be impossible.


There is, however, a way to use the constructs of the current interlingua
to translate between CLASSIC and LOOM.  It goes like this:

	All players will agree that concept and role definitions will be 
	represented by defprimrelation and rules will be represented as
	above. 

Then translation (of at least these parts of CLASSIC and LOOM) will be
easy.  This agreement does not use the quotation aspects of the current
interlingua, and ignores the axiomatization of "implies", "defrelation",
and "defprimrelation", instead treating them as syntactic primitives.


Peter F. Patel-Schneider