Re: A Rough Guide to Notation3

> > > Following the RDF philosophy that any RDF graph,
> > > particularly non-tree graphs, should be allowable, non-tree versions
> > > of the logic's sentences should also be allowed.
> > 
> > I don't completely accept that last sentence.   DAML+OIL says the RDF
> > graph 
> >     _:x daml:differentIndividualFrom _:x.
> > is not allowed.  
> 
> DAML+OIL does indeed not say that at all.
> 
> _:x daml:differentIndividualFrom _:x.
> 
> is a perfectly good DAML+OIL knowledge base.  It just happens to be
> inconsistent, and thus have no intepretations, but this does *not* prevent
> it from being a DAML+OIL knowledge base.

Good point.  I wasn't being precise about the situation of having
self-referencial statements in the KB.   When I said "not allowed", I
meant "disallowed by the axioms", which causes the sitation you
describe: it makes the KB have no models.

> By the way, _:x pl:negation _:x is only a very simple example of the kind
> of sentences that cause problems.  More complex ones can easily be
> constructed, such as
> 	_:x pl:negation _:y .
> 	_:y pl:conjunct _:x .
> 	_:y pl:conjunct _:x .
> 
> > Each new vocabulary can do that.  The RDF philosophy
> > of "anyone can say anything about anything" does not extend to the
> > point of a receiver having to make sense of a contradiction.  
> 
> Why not?  DAML+OIL makes sense of these contradictions.  (DAML+OIL has its
> own lossage, by the way, but a different sort of lossage.)

I don't see how a logically inconsistent sentence (or KB) conveys any
useful information.  In fact, only satisfiable sentences seem useful
for communication, but that's perhaps going on a tangent.

> [...]
> 
> > Can't we just just disallow RDF graphs which describe self-referencial
> > sentences (or at least self-negating) ones?
> 
> How can you do this, in RDF?  They are still RDF graphs, and need to be
> handled by the model theory.  In fact, there is no real problem with
> self-negating sentences, by themselves, in RDF (as opposed to the situation
> is some other styles of providing semantics).

Such RDF graphs exist, but their meaning to someone respecting the LX
vocabulary is nil, much like me sending you a message saying "The sky
is blue; the sky is not blue."  (Presumably, you'd think have to "go
meta", and think about how to make sense of a nonsense message.  But
that's an issue beyond defining the language of the message.)
Similarly, someone respecting the Widgets vocabulary might get an RDF
graph that was clearly in error (in terms of what it says about
widgets), and have to take some corrective actions such as ignoring
it, reporting an error. etc....

> The problem is not their (potential) existence.  It is their existence
> everywhere.  The problem is that if you allow self-referential
> sentences and also need to have sentences exists everywhere, removing just
> the problematic ones is problematic. 

I don't quite follow that, sorry.

   -- sandro

Received on Saturday, 24 August 2002 17:53:33 UTC