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Re: AtomList infinite or cyclic in all models

From: Henry S. Thompson <ht@inf.ed.ac.uk>
Date: Mon, 19 Feb 2007 12:10:14 +0000
To: Bijan Parsia <bparsia@isr.umd.edu>
Cc: drew.mcdermott@yale.edu, www-rdf-rules@w3.org
Message-ID: <f5babzaz6u1.fsf@hildegard.inf.ed.ac.uk>

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Bijan Parsia writes:

> Are these anomalies? I'm not so sure. It makes nil a bit more like
> the empty set. One might find that anomalous on some readings of
> lists, but not on others.

Fools rush in. . .  I'm curious as to what you are appealing to for
your judgements about 'real' lists.  I've struggled with this a fair
bit myself in the context of trying to build a satisfactory ontology
for XML itself.  I ended up concluding that

 a) Lists were sequences (*);
 b) A sequence is best understood as a function from the integers
    [1..|sequence|] to its members.

So I'd say that what's been discussed so far in this thread should be
called OFLispList or some such, since as already remarked it's
modelling lists using cons-pairs that's causing all the trouble.  Then
some further work is required to axiomatise a useful definition of
List and/or Sequence.  AtomList is also misleading as a name in that
there's no constraint that its members be atoms, AFAIK!

ht

*[At least Python distinguishes lists from sequences in that the
  former are mutable and the latter aren't, but I don't _think_ that's
  a dimension we're interested in at this level of discussion.]

[[The 'OF' above is for 'old-fashioned', as in some languages the empty
  list is not unique, e.g. Python and (BC Smith's) 2- and 3-Lisp.]]
- -- 
 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 Monday, 19 February 2007 12:10:40 UTC

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