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Re: Meta-classes? (layered architecture)

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Mon, 16 Oct 2000 17:35:56 +0100 (BST)
To: pat hayes <phayes@ai.uwf.edu>
Cc: www-rdf-logic@w3.org
Message-ID: <14827.10105.640296.627976@localhost.localdomain>
Firstly, my main point (with which I think Pat agrees) is that we
should define a simple "base" language, and then extend it as
necessary with -META -SECOND_ORDER or whatever.

My particular worry was the potential confusion that is derived from
building on top of RDFS, which is designed so as to be able to
describe itself. For example, according to the specification,
rdfs:Class is a type of rdfs:Class as well as being a subClassOf
rdfs:Resource, which itself is a type of rdfs:Class. An rdf:Property
is also a type of rdfs:Class.

Ian

On October 16, pat hayes writes:
> 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 12:55:11 GMT

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