Re: Re-expressing our formalisation of Language

On Wed, 2006-09-06 at 01:06 -0600, Pat Hayes wrote:
[...]
> >  Interpret, a functional mapping from TextSet to InformationSet,
> >    i.e. a subset of TextSet X InformationSet such that if a,b and c,d
> >    are in Interpret, then a==c implies b==d
> 
> Why do you call this 'interpret'? Is this supposed to imply something 
> to the effect that 'infons' are interpretations?
> 
> Main question: Why is this *functional* ??

Hmm... yes, that is arbitrarily different from conventional
mathematcial logical terminology. I'd be happy to go with
the conventions. I find the wikipedia article pretty
nice to start from
  http://en.wikipedia.org/wiki/Mathematical_logic

I _think_ that what Henry is proposing is consistent with
(i.e. analagous to) the conventional terminology. I was
going to spell out the details of the analogy, but that's sorta
beside the point. We might as well use the conventional terminology...

> This general style of associating meanings to 
> texts by defining semantic *constraints* on *denotation mappings* 
> from expressions to *interpretation structures*, with its concomitant 
> notions of satisfaction, entailment and so on, is extremely 
> general-purpose, established, successful and supported by a huge 
> amount of precise and well-understood mathematical development.

Meanwhile, I really like the UML diagram. I think maybe I
could present the terms Pat is talking about in a UML
diagram and the differences might be manageable. I hope
to give it some thought...


-- 
Dan Connolly, W3C http://www.w3.org/People/Connolly/
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