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Re: Re-expressing our formalisation of Language

From: Harry Halpin <hhalpin@ibiblio.org>
Date: Thu, 07 Sep 2006 19:45:32 +0100
Message-ID: <450068CC.4000407@ibiblio.org>
To: Pat Hayes <phayes@ihmc.us>
Cc: "Henry S. Thompson" <ht@inf.ed.ac.uk>, www-tag@w3.org

My attempt at reconciling your vocabulary is:

1. Henry says "textset" = Pat says "expression"
2. Henry says "interpretation" = Pat says "denotation (mapping)"
3. Henry says "informationSet" = Pat says "interpretation (structure)"

It's the ambiguity between 2 and 3 that are causing lots  problems.

Now for obscure philosophy :)
> Is an 'infon' something like a chunk of information (about something?
> About what?) or is it something more like a part of a world or a
> possible interpretation? Or could it be something like an topic, or a
> thing that some information is about?
    I believe Henry is probably unconsciously resurrecting the term
"infon" from "situation semantics" ala "Situations and Attitudes" by
Barwise and Perry [1] and the "What is Information?" paper by Israel and
Perry[2]. Israel and Perry formalize an "infon" as an abstraction over a
"state of affairs." A "state of affairs" can be thought of a collection
of "real-world atomic facts" like (a,b,c,...) where  the infon is a
parameter in an abstraction over the state of affairs << ...,_c_,....>> 
where 'a'  is some atom. So, the atomic facts of a state of affairs
could be s_1=(a='chair', b='table', c='rock'...) the infon
i_1=<...,_c_='rock'...> is then any state of affairs that has a rock in
the right paramter, so s_2=('a='Tim', b='Dan', c='rock) and s_1 would
satisfy the infon i_1.  In normal language, an infon is a "partially
defined state of the real world" or "constraint of the real world" -> so
maybe an XML Schema can be thought of as  kind of "infon" that can
constrain a set of XML documents. After all, they all exist in the "real
world" given XML's lack of a formal semantics :)

The main differences between situation semantics and other formal (i.e.
Tarksi/Montague) sort of semantics is in a nutshell the (using Pat's
vocabulary) the interpretations over situation semantics are supposed to
be *real world things* and they are usually abstracted to some formalism
like sets in Montague semantics. When someone in situation semantics
land is talking about the denotation being a member of a mathematical
set that we happen to name using the string 'rock', he means a big,
lumpy grey piece of matter in all its metaphysical glory.

 However, Montague semantics just points out we can't really talk about
the fuzzy real world using logic in a sensible way, so let's formalize
our interpretation structure as sets or something else  mathematically
defined. And that has proven to be an immensely productive move.
Situation semantics never got off the ground because they couldn't find
a way to talk about the informal  world without using formalism. There
is no "real world state of affairs" that can be objectively described as
a "set of facts" because as soon as you say that, you're in set theory!

All the formalities of situation semantics can be folded into the
Tarski-Montague story. And I think Barwise and  Perry did eventually
formalize all of it using the KPU set theory.
>  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* ?? 
Well, the word "functional" should probably be deleted because it's not
functional really because a TextSet could map to some many "real world"
state of affairs. So giving my TextSet that is a XML document to Firefox
may return different behavior than if I give it to Mozilla. Likewise,
the same behavior of Firefox might be produced by multiple text sets.
 
However, if there is some  sort of abstract notion of standard
compliance (like all text <h1> gotta be bigger than all text marked up
<h2> no matter if you're running firefox or mozilla), then that could
make it functional since no matter what, your textsets in that language
(HTML) better *all* make <h1> bigger than <h2>. I think that's what
Henry is trying to get at - using Pat terminology, the expressions all
denote some set that obeys some constraint in the interpretation structure.

So, to make this mathematically respectable we should probably normalize
the Henry/Pat vocabulary, and then think if we can find a good way of
saying "constraints over (Pat) interpretations" without using the word
"infon" which is kinda weird and confusing. And maybe even find a way to
give all of this madness a formal semantics  - I do think they're valid
intuitions here, but I do agree that unless we're careful it does all
sort of sound wacky and like speaking in tongues.

[1]http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=7372
[2]http://www-csli.stanford.edu/~john/PHILPAPERS/whatisinfo.pdf -


>
> ht
>
> [1] http://www.w3.org/2001/tag/doc/ext-vers-generic-uml-v4.png
> [2] http://www.w3.org/2001/tag/doc/versioning#terminology
> --
>  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
>             Fax: (44) 131 650-4587, e-mail: ht@inf.ed.ac.uk
>                    URL: http://www.ltg.ed.ac.uk/~ht/
> [mail really from me _always_ has this .sig -- mail without it is
> forged spam]
>
> -- 
>         -harry
>
> Harry Halpin,  University of Edinburgh
> http://www.ibiblio.org/hhalpin 6B522426
>
Received on Thursday, 7 September 2006 18:45:59 GMT

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