Re: mappings between SWRL and Boley proposal

> 
> > > 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.

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.


	--michael  


> 
> It seems clear to me, that if the RIF core has a model-theoretic
> semantics in the form of a preferred/intended model operator
> Mod assigning a set of intended models to a set of formulas
> (as a borderline case, giving you what you prefer, all models 
> may be considered intended models), then we want to have that
> for any RIF condition formula C
> 
>    Mod(C) = Mod'(M[C])
> 
> where M is the mapping from RIF to the target language, and
> Mod' is the adapted model operator definition working on 
> formulas of the target language.
> 
> Considering also the inverse mapping N from the target 
> language to RIF, we get the additional requirement that
> 
>    Mod(C) = Mod(N[M[C]])
> 
> which is, however not sufficient to guarantee semantic 
> equivalence.
> 
> > > The proposal mentions the option of typing terms and 
> > predicates/atoms.
> > > So, I just made use of this option (in the spirit of the proposal).
> > > Of course, you are free to suggest another style of typing...
> > 
> > How about adding K and A modal operators?
> 
> This would be another extension that we could think about,
> if we find arguments to justify it.
>  
> > > >> The extended proposal syntax with optional typing also
> > > >> allows a faithful inverse mapping of typed atoms to SWRL.
> > > > 
> > > > Oh?  Which atoms?  All of them?
> > > 
> > > Yes all of them (modulo some subtleties concerning restrictions
> > > and the generic datatype rdfs:Literal).
> > 
> > Even predicate applications with 5 arguments?
> 
> No, you are right, in some cases, like this one, we may
> need to apply special transformation techniques (which
> are well-known for this reduction from n-ary to binary),
> or we may even have to give up. As I said already, typically, 
> mappings will be partial.
> 
> -Gerd
> 
> 
>

Received on Thursday, 18 May 2006 17:47:19 UTC