- From: Michael Kifer <kifer@cs.sunysb.edu>
- Date: Tue, 16 Oct 2007 10:48:54 -0400
- To: Jos de Bruijn <debruijn@inf.unibz.it>
- Cc: public-rif-wg@w3.org
> Michael Kifer wrote: > > Just wanted to infuse a healthy doze of a reality check regarding the > > following: > > > > Jos wrote: > >>>> g- the value space is required to be a subset of the domain. This > >>>> means that every interpretation includes all value spaces of all data > >>>> types. This is unnecessary. > >>> So what? It makes the definition simple and uniform. > >> It makes every domain infinite. For most kinds of rules (especially > >> those without equality in the head) this is not really a problem. > >> However, as soon as we have full use of equality, or deal with > >> extensions in the direction of FOL, then one often wants to talk about > >> finite models. > >> > >> > >> It also makes rule sets which only contain rules such as Forall ?x,?y > >> (?x=?y) inconsistent. I claim that this is undesirable. > > > > Apart from everything that was said about it, you should remember that we > > have function symbols. So, the domain is infinite whether you have data > > types or not. > > This would be the case if you use a Herbrand universe. Otherwise, it is > not necessarily the case that the domain is infinite. Recall that unsatisfiability reduces to unsatisfiability problem over Herbrand models. Only "uninteresting" models would have finite domains. I hope that you realize that your argument about finite models in the presence of function symbols is a red herring. --michael
Received on Tuesday, 16 October 2007 14:49:33 UTC