[Corpora-List] Is a complete grammar possible (beyond thecorpus itself)?

[Yorick Wilks]

Rob
just for the record (because John cares about these things), I didnt  
mean to equate decidability to completeness, only to say that the  
second is a necessary condition for the first for a calculus (but not  
vice versa).
best
YW

On 9 Sep 2007, at 06:52, Rob Freeman wrote:

> John,
>
> You'll confuse the issue with so many words.
>
> For "completeness" I am happy to agree with Yorick Wilks and equate  
> it with "decidability". I'm indebted to Yorick for pointing out  
> this was how the problem was seen by generativists.
>
> What it means to be "computable" was first defined by Alan Turing  
> (and Alonzo Church?) I do not intend my sense to differ in any way.
>
> The question of decidability is a technical one within this  
> framework. According to Turing's theory there are computable  
> problems which are not decidable. It is not a question of adding  
> more information, "semantic" or otherwise, to make them decidable.  
> They are not decidable because they have too much power, not too  
> little.
>
> I am suggesting natural language might be such a system.
>
> That would not be a bad thing by the way. Decidability acts as a  
> kind of straitjacket on computability. It is a limitation on its  
> power. A generally computable model of natural language would be  
> more powerful than a decidable model. It could be powerful enough  
> to account for the detail of collocation and phraseology, for  
> instance.
>
> To get that power we would only need to lose the ability to _label_  
> language definitively. That is the content of decidability: the  
> ability to fit language to a grammar, nothing more. I personally  
> would not be bothered it if turned out that tags and tree-banks  
> were officially meaningless, and corpora the most complete  
> description of a language possible, especially if that meant we  
> could recognize speech accurately, and index information effectively.
>
> Anyway, I think the possibility is worth considering.
>
> -Rob
>
>  On 9/9/07, John F. Sowa <sowa at bestweb.net> wrote:
> Rob,
>
> The original definition of "generative grammar", which is used
> for formal languages, very explicit defines "completeness":
>
>     A language L is defined as the set of all and only those
>     sentences that can be generated (or parsed) by a grammar G.
>
> This definition has proved to be very useful for artificial
> languages, such as programming languages and formal logics.
>
> But it quickly became obvious that no grammar and parser could
> come anywhere close to generating or parsing all and only the
> sentences commonly used in any NL.  Therefore, Chomsky qualified
> it by saying that G would only describe the "competence" of an
> "ideal" speaker, not the performance of any actual speaker.
>
> But even that definition is woefully inadequate, because there
> is no grammar/parser combination in existence today that can
> correctly parse more than about 50% of the sentences published
> in well-edited texts.  (Many parsers can produce parses for more
> than 50% of the sentences, but if you eliminate any parse that
> has one or more errors, as judged by a competent linguist, even
> the best have difficulty in reaching 50% completely correct.)
>
> > Take the opposite point of view. Assume only that language is
> > generally computable. Then it may be undecidable.
>
> I don't know what you mean by "computable".  But the question
> of undecidability is trivial to show for any NL grammar in
> existence today.  Just pick up any any well-edited book, magazine,
> or newspaper you can find around the house.  Then run the sentences
> from the first page through the parser.  That will demonstrate
> that at least 99% of the grammars fail on a small finite set.
> In the unlikely event that one of the parsers actually produces
> correct parses for all the sentences, just try it on the next
> book, magazine, or newspaper.
>
> By the way, you can get higher percentages of correct parses *if*
> you supplement the grammar with semantic and pragmatic tests.
> But that is harder to implement, and it violates Chomsky's
> assumption of the autonomy of syntax.
>
> John
>
>
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