Re: mappings between SWRL and Boley proposal

> From: Michael Kifer <kifer@cs.sunysb.edu>
> Subject: Re: mappings between SWRL and Boley proposal 
> Date: Thu, 18 May 2006 13:46:57 -0400
> 
> > > > > The proposal may not be sufficiently explicit about this,
> > > > > but it states that modeltheoretic satisfaction gives
> > > > > the meaning to conditions.
> > > > 
> > > > Yes, but where is this tied to the mappings?
> > > 
> > > This has not been made explicit in the proposal. So, 
> > > let's do it. [Harold and Michael, we are waiting for 
> > > your contribution to this.]
> > 
> > It was sufficiently explicit in the proposal and Peter knew exactly what
> > was meant.  The mapping is obviously supposed to satisfy the condition that
> >
> > I |= C  <->  I |= M(C)
> > 
> > for every interpretation appropriate for the dialect in question.  In a
> > more general case, M can also be a transformation on models, but this is
> > not required for Peter's case.
> 
> Well, where is the definition of interpretations and supports on the
> proposal side?  I don't see one.  Without such how can you talk about
> satisfying your condition above?

The proposal said:

    So, by semantics we mean the notion of satisfaction of a formula in the
    interpretations of the various RIF dialects.  For example, in FO, all
    first-order interpretations are appropriate. In LP, infinite Herbrand
    models are typically used. In LP with the well-founded semantics,
    3-valued Herbrand models are used. Stable model semantics uses only
    2-valued interpretations.

There are different notions of interpretations and each comes with its own
definition of |=. When we say "first-order semantic structure", we mean a
particular definition of |=. A "3-valued well-founded model" has its own
definition, etc.

This was the intention, if the above wasn't sufficiently clear. Given that
this is a first draft (which didn't even pretend to be completely formal),
I claim that we can get some slack here.  Will try to clean it up in the
next iteration.


> > By the way, the proposal didn't talk about these mappings, but it should
> > have been obvious that such mappings are needed and that the above
> > condition should be satisfied. Someone who proposed to define these
> > mappings in the telecon must have also had something like this in mind.
> 
> I had in mind, in part, trying to explicate what I felt was missing from
> the proposal and what was wrong with it.

This was too subtle for some of us to understand...


	--michael  

> peter

Received on Thursday, 18 May 2006 19:00:47 UTC