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Re: Re-expressing our formalisation of Language

From: Pat Hayes <phayes@ihmc.us>
Date: Wed, 6 Sep 2006 01:06:59 -0600
Message-Id: <p06230902c123bfaac668@[10.20.7.190]>
To: ht@inf.ed.ac.uk (Henry S. Thompson)
Cc: www-tag@w3.org

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>Wrt the minutes (forthcoming) of today's call, and in particular the
>diagram at [1] (from Editorial Draft] Extending and Versioning
>Languages Part 1 [2]), here's my take on where we might have ended up:

Sorry, but I have to comment on this. Insofar as I can understand 
this at all, this seems to have the semantics exactly backwards. See 
below for details.

>A Language is a n-tuple, consisting of
>  TextSet, a set of strings
>  InformationSet, a set of infons (intentionally vague)

Too damn vague. We already have no idea what a 'resource' is supposed 
to be or what it means to 'identify' one. Could the Tag please make 
an effort to avoid speaking in tongues, when matters get basic? At 
least give some guidance, or point to some kind of supporting theory 
or external account. 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?

>  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* ?? The most standard notion 
of meaning that we have, applied successfully for 50 years throughout 
logic, mathematics and formal linguistics, and incorporated as a 
foundation in at least three, soon to be four or five, W3C standards, 
involves a semantic mapping which is  emphatically NOT functional. 
Rather than project expressions to mysterious 'infons', which AFAIK 
have no supporting theory or mathematical basis *at all*, these 
mappings relate expressions to what it is that they denote in an 
interpretation, and an interpretation is then an organized account of 
how basic denotations (those associated to the syntactically simplest 
members of TextSet, the 'atoms' of the parsing grammar, typically the 
lexical names of the language) are related to denotations of more 
complex expressions. 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. It is 
the basis for semantic theories of natural human languages (by 
Montague and others), for classical logical languages (Tarski), 
generalized to modal logics by Kripke, to constructive logics, to 
programming languages of many kinds (generalized to concurrent and 
parallel computing architectures by Milner and others) and more 
recently is the basis of all the various restricted logics underlying 
OWL, and provides the ground theory for all the inference engines 
used in practical DL and LP reasoning systems. I have applied it to 
diagrammatic representations including cartographic maps. It is hard 
to think of a more successful or more widely accepted general view of 
meaning and semantics. So, why are you defining terms which not only 
ignore all this established, successful, absolutely standard science, 
but seem to be actively at odds with it?

>If Function is a class with three properties, namely Domain, Range and
>Mapping, then Language<Function, with TextSet<Domain,
>InformationSet<Range and Interpret<Mapping.
>
>I think it's useful to _also_ say that a Language has zero or more
>Grammars, which are, informally, expressions of characteristic
>functions for the TextSet, using e.g. regexps, BNFs, schemas, . . .
>
>And that there are zero or more Interpreters, which are, informally,
>effective computations from members of TextSet to members of
>InformationSet.

Interpreters *compute* infons? What on earth does that *mean*? Take a 
programming language, for example. LISP interpreters compute 
functions on Sexpressions. An interpreter for a scripting language 
computes, maybe, functions on data strings. What about other kinds of 
language? What *is* an interpreter for, say, OWL-DL?  Do you mean an 
inference engine? What that computes, if the term even applies to it, 
is entailment relationships, or perhaps subsumption relationships, 
between OWL-DL *expressions*. Where are the 'infons' in any of these 
cases?

>Likewise, finally, zero or more Models, which are, informally,
>expressions of characteristic functions for the InformationSet.

I have no idea what any of this means, and I strongly suspect that it 
does not mean anything at all. Apparently you do not mean 'Model' in 
the sense of "model theory", so what is the terminology supposed to 
suggest? What is a 'characteristic function' (even informally) for an 
'infon' ?

>Note that the 'expressions of characteristic functions' may be formal,
>or informal, or a mixture of the two (e.g. "[1-9][0-9]*" plus "the
>corresponding number per the standard decimal numeral interpretation
>is prime"

OK, take that last one. What *function* is indicated by that English 
phrase? It seems to be talking about a number, not a function. And 
what kind of 'infon' does it apply to? (Is a number an infon? Are all 
numbers infons? Are all infons numbers?)

>).
>
>I'm not sure how to do this in UML

First, I would suggest, try to say more clearly what it is that you 
are doing. Right now there is no way to know if you are doing it in 
UML or not, even if the UML were done.

Pat Hayes



>, i.e. whether it changes the diagram
>beyond relabelling Syntax as Grammar (1 to many), Semantics to Model
>(1 to many) and ActOfInterpretation as Interpret, as well as adding
>Interpreters (1 to many) with input and output relations to TextSet
>and InformationSet respectively.
>
>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]
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Received on Wednesday, 6 September 2006 20:59:30 GMT

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