Re: Re-expressing our formalisation of Language

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Pat Hayes writes:

> Well, there are some reasonably accessible accounts. I tried to
> briefly convey the general idea of 'set-theoretic' (horrible and
> misleading terminology) semantics, aka model theory, aka Tarskian
> semantics, using non-mathematical language, in the RDF Semantics
> document
> and especially 
> and the linked glossary entries.

My shot at this (uses the "snow is white" example) is at

> But the best way to relate this kind of semantics to operational
> issues, I suggest, might be through talking about entailment, a
> *relationship between* texts which is very close to being an
> operational idea already. A entails B (see
> if B is true whenever A
> is.

As Dan Connolly has already said, my immediate problem with this
suggestion is that we don't generally think about the texts in our
languages in terms of truth or falsity.  What would it mean to ask if

 "(gcd 63 42)"


 "<svg:rect y='221.0' x='246.0' height='16.25' width='64.1' id='rect221'/>

is _true_?

> So, here are a few of the kinds of relationship between languages and
> texts that can be defined. Say that a language is a set of texts with
> an associated semantics, which for our purposes we can simply *define*
> as an entailment relationship En between texts of a language Ln. Say
> that L1 *syntactically extends* L2 if every text of L2 is also a text
> of L1, *semantically extends* it if in addition E1 is a superproperty
> of E2, i.e. if A E2 B then A E1 B.

Yes, that's certainly the _kind_ of thing we're working towards,
except that entailment relations between texts can't be the foundation
(see above), as far as I can see.  What kind of entailment relation
could there be for the texts of HTML, or SVG, or W3C XML Schema?

> a 'markup' example might be E1 and E2 both being XML entity
> vocabularies but E1 being larger than E2. In all these cases one can
> see the idea, that E1 extends E2 by allowing an interpreter to draw
> more conclusions than E2 is allowed to sanction.

Indeed, at _this_ level of detail, you're where we started a year
ago.  But I need help connecting up the dots - - I don't see what,
in this story, the entailment relationship could be between two texts
in E1, say.  

> And in all these cases, the entailment relation can be
> directly related to a model-theory style semantic theory in which
> the extension amounts to having a richer notion of what counts as an
> interpretation, so that one gets E1 interpretations by imposing
> extra constraints on E2 interpretations and maybe by also adding
> some more structure to them. As the language can say more, the
> worlds it can describe get more complicated, but you can also rule
> out more of them by saying more stuff.

And language like this makes me think you're still taking
interpretation out into some domain of real discourse, i.e. that it
matters that the marked-up texts are _about_ something, and you need
to appeal to that intentional relationship to say what you want to
say.  For better or worse, I think we were trying to avoid having to
make that step.

- -- 
 Henry S. Thompson, HCRC Language Technology Group, University of Edinburgh
                     Half-time member of W3C Team
    2 Buccleuch Place, Edinburgh EH8 9LW, SCOTLAND -- (44) 131 650-4440
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Received on Wednesday, 13 September 2006 14:04:57 UTC