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Re: Meta-classes? (layered architecture)

From: pat hayes <phayes@ai.uwf.edu>
Date: Mon, 16 Oct 2000 11:22:02 -0500
Message-Id: <v04210104b610d61cdea8@[205.160.76.86]>
To: Ian Horrocks <horrocks@cs.man.ac.uk>
Cc: www-rdf-logic@w3.org
Ian Horrocks writes:
>We need to be clear as to whether or not it is intended that DAML-ONT
>classes (relations) denote classes of objects (binary relations
>between objects) or whether they could also denote classes of classes,
>classes of relations etc. .....
>
>In OIL, it was explicitly decided that, in the base language, the
>denotation of classes and relations should be sets of objects and
>binary relations between objects, and that meta-extensions, if
>required, would be provided in additional language layers (yet to be
>defined)......

........

>It has been suggested that DAML languages will also have a layered
>architecture, and that further layers (DAML-RULES, DAML-LOGIC) will
>follow. If this is the case then I think it makes sense to stick to
>the simple thing for now and leave meta-classes for DAML-META.

I would like to express a howl not about what Ian has said (with 
which I think I agree) but about the way he has said it. There are 
two ideas which we should try not to get confused. One is allowing 
classes (or predicates) as first-class entities, including allowing 
classes of classes (predicates on predicates) and so on. This is 
often referred using the terminology 'second-order'or 'higher-' or 
'omega-' (rather than 'first-'), and it usually requires extending 
the language in certain characteristic ways.  The other is the idea 
of allowing a language to describe its own syntax, so that 
expressions and their syntactic parts become first-class objects. 
(KIF for example does this by treating its own expressions as list 
structures, which are themselves a KIF category.) This is often 
referred to using the terminology of 'meta', as in 'metalangauge' 
(the term 'reflection' is also often used in this context.) This also 
requires extending the language in characteristic ways, but - and 
this is my point - these are completely different from each other. 
KIF for example is rigidly first-order and richly meta-expressive, 
whereas classical type theory is as higher-order as anyone except a 
category theorist could wish for, but hasn't a trace of 
meta-expressiveness. These two ideas involve different kinds of 
language extension, different kinds of semantic construction, and 
they have different kinds of pardoxical dangers to avoid 
(respectively Russel's and the liar paradox).  There are many subtle 
connections between them, but they really are not the same thing, and 
confusing them muddles things so much that one cannot even see these 
relationships properly. It would be a real shame to get them confused 
when so many smart people have managed to get them unconfused for us.

I think (?) Ian really means second-order, not meta-linguistic. It 
may be that Ian's usage of 'meta-classes' comes from a different 
intellectual tradition, but it is likely to cause a lot of confusion 
if it is just left hanging.

Pat Hayes

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Received on Monday, 16 October 2000 12:19:01 GMT

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