Re: a simple question

At 13:38 05/12/03 -0500, Drew McDermott wrote:


>    [Dan Connolly]
>    I suggest that checkable valid conclusions are
>    essential to anarchic scalability.
>
>A fond wish, but one that can't be granted.
>
>Suppose a web service offers a warehouse-truck scheduling algorithm.
>The algorithm is widely used and endorsed by several major truckers,
>but it comes with no optimality guarantee.  Your agent uses the output
>of the algorithm as one step in an inference concerning a
>preventive-maintenance schedule for your trucks for next month.
>
>In what sense are the outputs of the algorithm checkable _or_ valid?

In your last response [1] to my comments (which I found helpful, thank 
you), you said "Perhaps a better strategy is to stay away from particular 
statements
that we want to be theorems, and just look for logical theories with
lots of useful conclusions that are very rarely wrong."

Your above comment about an algorithm that is "widely used and endorsed by 
several major truckers" suggests a possibility that such might be adopted 
as part of the logical theory against which conclusions may be checked.  So 
there becomes an element of agreement required:  the conclusion is 
checkable, but only on the basis of accepting the particular logical 
theory, which is not.

I make this suggestion in full cognizance of your comment (from [1]): "The 
problem is that there is a trivial way to turn an inference of P into a 
deduction: add P as an axiom.  So you have to be careful in what you allow 
as an axiom."  The last sentence here, in particular, seems to me to be 
pivotal in bridging the gap between pure formalism and useful inference.

Hmmm... but this seems to be what you're trying to steer away from.  I 
can't see how domain knowledge becomes part of a deduction without being 
part of the logical theory.

[1] http://lists.w3.org/Archives/Public/www-rdf-rules/2003Dec/0015.html


>I fear that this is the usual case, not an outlier.  That's why
>"undisciplined" use of negation-as-failure doesn't scare me.  It's
>just allowing useful heuristicism to appear in small doses amidst
>logical inferences, on the grounds that the logical inferences will
>mainly be glue between large-scale computations permeated with
>heuristicism.

Yes.  I expect checkability has it that "useful heuristicism" be 
distinguishable from the "logical inferences" (deductions?).  I have often 
thought that the value of mathematical proof is not so much to assert that 
some statement is correct, but to identify (through the assumptions made) 
the conditions under which the statement is true.

>Maybe this is a good way to think about it: Many inferences are
>justified by statements of the form, "Here's my conclusion and my
>grounds for believing it; just try to refute it."  That is, checking
>is not just a matter of verifying that each step is actually justified
>by an inference rule.  It can also be a matter of trying to find a
>better conclusion than the one offered.

Hmmm... I don't think I follow.  I'm not sure if I'm stumbling on your "not 
just a matter...", or on what constitutes a "better conclusion".

#g


------------
Graham Klyne
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Received on Sunday, 7 December 2003 08:42:38 UTC