Re: Re-expressing our formalisation of Language

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Dan Connolly writes:

> 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.

Yes, this is what was troubling me when I said in my previous message
that "I'm not sure that a mathematical logic is really what we're
building here."  Our languages don't consist of sentences, there's no
notion of proof or axioms in them, and whatever else you can say about
what we meant by InformationSet, truth or falsity are unlikely to be
properties attributable to its members. . .

> 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>"?

Could you elaborate a bit, Dan, as I don't get this yet.  In the SVG
case, what kind of things are the 'P' and the 'Q'?  What is the space
of interpretations -- all possible bitmaps?

- -- 
 Henry S. Thompson, HCRC Language Technology Group, University of Edinburgh
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Received on Wednesday, 13 September 2006 13:28:31 UTC