Labelling propositionsRobert MacGregor <firstname.lastname@example.org>
To: Michael Genesereth <email@example.com>
Subject: Labelling propositions
Date: Mon, 17 Sep 90 09:31:45 PDT
From: Robert MacGregor <firstname.lastname@example.org>
Responding to some of Mike's comments.
> (3) On quotation. ... In
> my own work I have encountered many cases of knowledge that was best
> represented with quote (even before considering the intermachine
> communication problem). Often, i want to represent knowledge aboiut
> knowledge. Some of this knowlegde can be written with a believes
> modal. However, some of it requires syntactic treatment, e.g. when I
> want to say something about the form in which I plan to write all of
> my knowledge, when I want to give the machine advice on
> representation, when I want to encode problem solving hints (e.g.
> prove this lemma befoire attempting the main theorem). The quotation
> operator is just right for this.
On the contrary, the quotation operator is frequently an extremely
clumsy means for accomplishing reasoning with knowledge about knowledge.
Let us take Mikes own example: If one wishes to state that a particular
lemma should be proved before a particular theorem, Mike suggests that
we quote each, and place the quoted forms inside of some predicate like
"prove-before". An obvious (and better) strategy is to give the theorem
a name (e.g., Theorem-3) and to give the lemma a name (Lemma-4), and
"(prove-before Lemma-4 Theorem-3)"
In Mike's quotation scheme, if one happens to change the text of the
theorem (e.g., by swapping two arguments to a commutative function
within the text of the theorem) then all statements that reference the
theorem via quotatation cease to apply, even though the meaning of the
theorem has (in this case) remained invariant.
While Mike has continuously advocated the virtues of the quotation
scheme, in each of the examples he has provided thus far, there always
exists an alternative that looks much more attractive than the quotation
device. As far as I can tell, one reason we are being asked to suffer the
inconveniences of the quotation device is for the sake of avoiding paradox
(although I believe someone mentioned that adding Len's definition
facility reintroduces the possibility of paradox). To me, this argues
strongly for the admission of paradoxical sentences into the Interlingua.
> However, we cannot flush quote or I would
> npot be able to transmit my knowledge baseswith those problem solving
I am not suggesting that we flush quote. I would just like to see it's
role made very small and inconspicuous, so that those systems (almost
all of them) that don't use quote can ignore it completely.
> But I think itis important for US (who are designing
> the interlingua) to pay it careful attention, even if our users (who
> areusing the interlingua) rarely see it.
Again I disagree -- I think quotation has served mostly as a time sink.
We have not yet, for example, explored alternative possibilities for
labelling individual propositions. In fact, we haven't explored any
such possibilities, since quotation labels sentences rather than
propositions. Len's definition facility may represent a means for
achieving this (labelling propositions), but so far the discussions on
Len's definition facility have focused on such things as the semantics
of recursive definitions. Many systems solve the problem of labelling
propositions by turning statements into (named) objects. The
Interlingua ought to provide a standardized means (not using quotation)
for translating such constructs.
> ... I do not think we should
> emphasize quote. I think it should be used rarely in everyday
> transmissions. ...
If the Interlingua doesn't provide an alternative to quotation for
labelling propositions, then we may find ourselves using it frequently
even though we would prefer not to.