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Re: firts and rdf:rest as functional property

From: Pat Hayes <phayes@ihmc.us>
Date: Fri, 20 Mar 2009 12:43:46 -0500
Cc: Reto Bachmann-Gmür <reto.bachmann@trialox.org>, "Semantic Web" <semantic-web@w3.org>, "Bijan Parsia" <bparsia@cs.man.ac.uk>
Message-Id: <EC6DC910-FFF5-4638-8B73-E264535CFA12@ihmc.us>
To: "Michael Schneider" <schneid@fzi.de>

On Mar 20, 2009, at 11:59 AM, Michael Schneider wrote:

>> -----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.

Yes. This isn't a problem that can be hacked around. Basically, FOL  
plus a min-fixed-point recursion is intrinsically more expressive than  
plain FO logic.  We've been exploring this space in the Common Logic  
effort, in order to make better sense of the sequence-marker  
construction, which provides a form of recursive extension. In CL,  
this axiom would do what you want here:

(forall (x y ...)(not (and (rdf:rest x y)(RestLoopEnd x y ...))))

(forall (x y)(iff (RestloopEnd x y)(= x y)))
(forall (x y z ...)(iff (RestloopEnd x y z ...)(and (rdf:rest y z) 
(RestloopEnd x z ...)

Pat

>
> Michael
>
> --
> Dipl.-Inform. Michael Schneider
> Research Scientist, Dept. Information Process Engineering (IPE)
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> Email: michael.schneider@fzi.de
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Received on Friday, 20 March 2009 17:44:29 GMT

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