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Re: Re-expressing our formalisation of Language

From: Dan Connolly <connolly@w3.org>
Date: Wed, 06 Sep 2006 22:12:39 -0500
To: noah_mendelsohn@us.ibm.com
Cc: "Henry S. Thompson" <ht@inf.ed.ac.uk>, Pat Hayes <phayes@ihmc.us>, www-tag@w3.org
Message-Id: <1157598759.9288.1272.camel@dirk>

On Wed, 2006-09-06 at 19:01 -0400, noah_mendelsohn@us.ibm.com wrote:
> Dan Connolly writes:
> 
> > 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
> 
> Gee, I'm really torn about that.  On the one hand, as one who's not expert 
> in those areas, I'm very excited to discover that these formalisms have 
> been so carefully developed.  Not reinventing the wheel seems like the 
> right approach. 
> 
> Having said that, David Orchard was on the call making the case that even 
> my relatively simple efforts to present set theoretic approaches 
> separately from programmatic descriptions like XML Schema were a step away 
> from the sort of approachable commonsense explanations that our readers 
> will be looking for.  Honestly, I find that wikipedia article tough going, 

yes... it took me about 18 months, somewhere between 1998 and 2003, to
get it. I got some invaluable individual tutoring from Pat and
from Massimo Marchiori, but I learned a lot by reading various
course notes too; one of my favorites is Logical Systems
by Peter Suber.
http://www.earlham.edu/~peters/courses/logsys/lshome.htm


On the other hand, 18 months is not all that long compared to the
lifetime of the TAG versioning issue, especially when you consider
that the issue has been there since long before the TAG started
tracking it. And a lot of our discussions do feel like reinventing
the wheel.

On the other hand, now that I sit down to work on this, I'm not
sure how a lot of the terms (satisfaction, entailment in particular)
work/help when the language is not first order logic or any logic
at all, but something like SVG, where an interpretation of a document
isn't True nor False, but an assignment of colors to the (x, y) plane,
or HTML, where the meaning of a document is a vague notion
of importance of headings, sequence of paragraphs and lists,
2-d coherence of table cells, and so on.

Pat, maybe you could help. How would you define/discuss/explain
a backward compatible evolution of HTML or SVG in terms
of the 50 year old terminology?

I think we discussed an even simpler example at
our June ftf meeting (I don't think the minutes will help
all that much but they're available...
http://www.w3.org/2001/tag/2006/06/12-tagmem-minutes.html#item04 ).
It's the language of a street light: green for go,
yellow for caution, red for stop. If you could set that
up with the 50 year old terminology, and then introduce
blinking red or left turn arrow or something into
the syntax/vocabulary and discuss the extensibility,
versioning, and compatibility issues, that could
be a big help.

Returning to the analogy between the "functional" terminology that
you objected to, Pat, and the conventional terminology, here's
what I have in mind...

In the conventional terminology, "An argument is valid if the truth of
its premises guarantees the truth of its conclusion" (odd; that's
easy to find in Suber's stuff, but I can't find it in wikipedia).
That glosses over a bunch of stuff that you have to elaborate
in order to talk about multiple (versions of) languages.
To elaborate, an argument P to Q is L-valid iff for
all L-interpretations I, if I(P) is true, then I(Q) is true.
(the Wikipedia article calls them L-structures rather
than L-interpretations, I think.)

To map to the "functional meaning" terminology, flip things
around just a little bit and let the "L-meaning" of P be a function
from interpretations to True/False. Then we'd say:

 an argument from P to Q is valid iff for all interpetations I,
 if L-meaning(P)(I) is true, then L-meaning(Q)(I) is true.

Does that make sense, Pat? And do you see how it allows
us to speak of _the_ meaning that SVG version 1.23 gives
to the text "<svg>...</svg>"?

> and I have to believe that many readers of a TAG finding on versioning 
> will seek something much easier to understand.  Trying to head in the 
> direction you're signaling while writing something that typical finding 
> readers will grok looks like a bit of a challenge.  If we can do it, cool!

Well, I have said all along that what we've taken on w.r.t.
extensibility and versioning deserves a book-length treatment.
We're trying to squeeze a PhD thesis into a TAG finding.
Indeed, if we can do it, cool!


-- 
Dan Connolly, W3C http://www.w3.org/People/Connolly/
D3C2 887B 0F92 6005 C541  0875 0F91 96DE 6E52 C29E
Received on Thursday, 7 September 2006 03:12:50 GMT

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