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RE: first and rdf:rest as functional property

From: Jeremy Carroll <jeremy@topquadrant.com>
Date: Fri, 20 Mar 2009 10:36:40 -0700
To: "'Michael Schneider'" <schneid@fzi.de>, 'Reto Bachmann-Gmür' <reto.bachmann@trialox.org>
Cc: "'Semantic Web'" <semantic-web@w3.org>, "'Bijan Parsia'" <bparsia@cs.man.ac.uk>
Message-ID: <002401c9a982$6d976210$48c62630$@com>
Joining this thread late ...
(or maybe rejoining - I seem to remember such a conversation, from a few weeks back, ... and a few years back).


Another type of ill-formedness[*] is a list with anti-foundation.


If we start at list node _0, its rest cell is _1, whose rest cell is _2, etc.
The list does not end.

And it is pretty hard to distinguish that case from a similar case, where we also have list cells

a_n for n from { ... -3, -2, -1, 0, 1, 2, 3 ... }
also forming an rdf:rest chain.

Distinguishing  cell _500 (which is finitely link to the start node _0) from cell a_500 which is not, is pretty difficult. Of course, nothing prevents cell _0 from being the object of an rdf:rest triple from cell _-1.


Jeremy

* Note words like 'ill-formedness' have an emotive quality that is unhelpful. When we have a narrowly conservative world view, such structures are surprising. The most likely error is our narrowly conservative world view. Better words to described such surprising structures might be 'surprising', 'elegant', 'creative', 'unconventional', 'imaginative' or 'beautiful'.




> -----Original Message-----
> From: semantic-web-request@w3.org [mailto:semantic-web-request@w3.org] On
> Behalf Of Michael Schneider
> Sent: Friday, March 20, 2009 10:00 AM
> To: Reto Bachmann-Gmür
> Cc: Semantic Web; Bijan Parsia
> Subject: RE: firts and rdf:rest as functional property
> 
> >-----Original Message-----
> >From: semantic-web-request@w3.org [mailto:semantic-web-request@w3.org]
> >On Behalf Of Reto Bachmann-Gmür
> 
> >The example 2 violates what's the convention described by RDF semantics,
> >however I see no way to add tbox statements with the (current)
> >expressivitiy of OWL that would contradict this graph.
> 
> Me neither.
> 
> [...]
> 
> >> (2) Lists should not be cyclic, though this is possible with RDF lists:
> >>
> >>       A -> B
> >>       ^    |
> >>       |    v
> >>       D <- C
> 
> Try to express such a general cycle prohibition axiom! This would roughly
> need to say something like:
> 
>   For any non-negative integer n:
>     there must not be nodes x1,...,xn
>     such that
>        x1 rdf:rest x2
>        x2 rdf:rest x3
>        ...
>        xn rdf:rest x1
> 
> If the cycle size would be restricted, one could express this by a finite
> set of axioms (I'm not necessarily talking about OWL here). But the cycles
> may be arbitrarily large, so this is not possible.
> 
> Michael
> 
> --
> Dipl.-Inform. Michael Schneider
> Research Scientist, Dept. Information Process Engineering (IPE)
> Tel  : +49-721-9654-726
> Fax  : +49-721-9654-727
> Email: michael.schneider@fzi.de
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Received on Friday, 20 March 2009 17:37:29 GMT

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