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. Best, Jos > > > --michael -- debruijn@inf.unibz.it Jos de Bruijn, http://www.debruijn.net/ ---------------------------------------------- In heaven all the interesting people are missing. - Friedrich Nietzsche
This archive was generated by hypermail 2.2.0+W3C-0.50 : Tuesday, 2 June 2009 18:33:43 GMT