[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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