On Dec 29, 2009, at 9:14 AM, John F. Sowa wrote:
> CM> As to why you characterize pointing out weak points in an argument
>> as "picking holes"... (01)
Just to clarify, this was said in response to Chris Partridge, not you. (02)
> What I was objecting to is the repetition of unqualified statements
> like the following, which you just repeated in the most recent note:
> CM> Here, more explicitly, is the basic argument.
>> 1. There is no restriction on the first-order statements one can
>> use to build an ontology.
>> 2. Consistency/validity/entailment are undecidable in first-order
>> 3. Therefore, it is possible that questions of consistency/validity
>> /entailment will be undecidable on the Semantic Web. (03)
> 1. Every major programming language in use today is undecidable
> in the sense that there can be no general proof that a program
> written in it will terminate.
> 2. But no programmer would ever dream of asking for a less
> expressive language.
> 3. For all kinds of computation, including the Semantic Web
> and relational databases, there is a question that is vastly
> more important than undecidability or even intractability
> -- namely, *efficiency* .
> 4. Decidability is usually defined as computable in finite time,
> and tractable is defined as computable in polynomial time.
> But when you have millions or billions of data items, any
> polynomial with an exponent greater than 1 is a disaster.
> 5. If you want an answer within your lifetime, the difference between
> a thousand years, a billion years, or forever is irrelevant.
> I agree that computational complexity is important for both logic
> and programming. But we must make it clear that reducing the
> expressive power of a language can *never* solve any problem.
> It merely makes certain problems impossible to state. (04)
I agree that these points are very important for filling out the larger
picture. I don't want the relatively small points of disagreement between us
obscure the very large points on which we agree, particularly the fact that it
is both confused and wrong-headed to think that the way to avoid intractability
is to tie your hands with an expressively impoverished representation language.
That's like choosing to live life as a couch-potato to avoid the risk of
accident or failure. :-) And as you rightly point out, and the specter
intractability, indeed undecidability, already lurks in every Turing complete
programming language. I think we disagree only with regard to the extent that
intractability will need to be addressed in the maintenance, use, and sharing
of ontologies. (06)
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