Re: [RIF] Extensible Design

> 
> From: Michael Kifer <kifer@cs.sunysb.edu>
> Subject: Re: [RIF] Extensible Design 
> Date: Thu, 04 May 2006 14:48:24 -0400
> 
> > 
> > > Well, it seems to me that the proposal by Boley et al advocates precisely
> > > this view.  My reading of the proposal is that several (perhaps many) RIF
> > > dialects will share the same syntax (or very similar syntaxes) for
> > > conditions but will diverge on semantics.
> > > 
> > 
> > Precisely. Semantics will be attached to dialects. There will be no grand
> > unified semantics. The idea is to design RIF with as much synergy between
> > its different parts as we can manage.
> > 
> > 
> > 	--michael  
> 
> But why then require the substitution interpretation for the meaning of
> free variables in conditions, particularly as this might give peculiar
> results in models where not all domain elements have names?
> 
> peter

We will have to define the semantics for each dialect. We were hoping that
this could be done modularly from the components of the dialects.  Perhaps,
this is unachievable, but such an exercise might still be useful.

Regarding the substitutions, as I said earlier, the semantics that we gave
can be easily generalized.  We can define the meaning of phi in M, M(phi),
where M is an interpretation appropriate for the dialect in question, to be
the set of all variable assignments to free vars in phi, which make phi
true in M.

For FOL, M would be an arbitrary first-order structure. For stable model
semantics, M would be an infinite 2-valued Herbrand interpretation. For
well-founded semantics, it will be an infinite 3-valued Herbrand
interpretation, etc.

So, there is no restriction on FOL models in this case.


	--michael  


PS. By the way, these infinite Herbrand universes were introduced in
    Kunen's paper in JLP 1987 (called Negation in Logic Programming).
    After that this idea was used for WFS and stable models.
    I don't think anybody gave a good name to this kind of semantics, and I
    admit that my term "infinite" is not a good one either.

Received on Thursday, 4 May 2006 19:34:46 UTC