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 21:22:07 -0400
> 
> > 
> > "Peter F. Patel-Schneider" <pfps@inf.unibz.it> wrote:
> > >
> > > From: Michael Kifer <kifer@cs.sunysb.edu>
> > > Subject: Re: mappings between SWRL and Boley proposal 
> > > Date: Thu, 18 May 2006 15:00:32 -0400
> > > 
> > > > > 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.
> > > 
> > > OK, so if in addition the proposal is extended by adding in the standard
> > > way of providing meaning to non-atomic syntactic constructs, then it can
> > > finally talk about satisfying the condition bove, provided that the rule
> > > formalism *exactly* matches up with one of the RIF "dialects" (to the
> > > extent of having the exact same set of interpretations).
> > 
> > It is actually more general than that. There are only a few different types
> > of interpretations (2-valued, 3-valued, etc.) so it would work for any kind
> > of dialect that uses one of these in its definition of semantics.
> > (Recall that the proposal talks only about the notion of satisfaction in an
> > interpretation.)
> 
> How is it more general?  You are requiring the same interpretations on
> either side of your condition,

Not quite. If mappings between interpretations can be established then they
don't have to be the same.

> so it looks to me that two rule systems that
> differe at all in their model theory will require a different RIF dialect.

but basically - yes. If somebody comes up with a rule system that uses
an unheard-of model theory then this would require a new dialect. I see no
way around this short of telling people to stop innovating.


> > > However, what has the proposal provided beyond an alternative syntax for
> > > rules, then?
> > 
> > It was not an attempt to provide something new. And, if you noticed, there
> > was no syntax for rules -- only for their conditional part.
> 
> OK, rule conditions.
> 
> > We are facing a pretty daunting task of providing an interchange format for
> > a bunch of very dissimilar formalisms whose only common theme is that they
> > are somehow "rule-based."  One way to approach this (we thought) was to try
> > to abstract some common parts of the syntax and semantics and then compose
> > dialects using building blocks. So, we abstracted the conditional part.
> > Other people (Paula&Francois) suggested that the event part can also be
> > abstracted.  The more we abstract -- the more uniform the resulting spec
> > will be.
> 
> Sure.  But I don't see that the proposal does much abstraction, if any, as
> it drags each rule system's semantics into the RIF.


Abstraction was a wrong word. Factoring out common parts is a better term.


> > > > 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.
> > > 
> > > How many RIF dialects (i.e., semantics) are there going to be?
> > > 
> > > The proposal identifies four:
> > > 
> > > - FO (first order)
> > > - LP (logic programming)
> > > - PR (production rules)
> > > - RR (reactive rules)
> > > 
> > > But this can't be right, as the proposal has two different semantics for
> > > LP, and doesn't have a semantics for PR or RR.
> > 
> > More than that. The semantics of PR & RR wasn't touched because there are
> > people here who can do this better. 
> 
> It would be interesting to find out whether it can be done at all.
> 
> > But the idea was to construct dialects
> > out of building blocks. I hope that this could be gleaned from the
> > taxonomy, which I sent on Monday. Although it is cluttered, the point is
> > that many of the features there are orthogonal to each other and can be
> > combined in various ways. This is why there were so many nodes in that
> > taxonomy and many other nodes didn't even fit.
> 
> OK, there may be a way of organizing the dialects, but that doesn't reduce
> their number.


This wasn't a goal.


> > > As well, the proposal is
> > > going to need a semantics for rule systems using RDF, as the model theory
> > > of RDF is not exactly standard.  I forsee this approach leading to a
> > > different dialect for each rule system.
> > 
> > Not if we use the hybrid approach.
> 
> But even if you use the hybrid approach, isn't that a change to the
> semantics and thus still generate a new dialect?

Not really. If you treat OWL and RDF predicates as base relations whose
extension is determined by their own semantics then no new semantics is needed.
I am not sure about the existentials. They might have to be approximated by
Skolem constants in some dialects.


> > > > 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.
> > > 
> > > Sure you have lots of slack.  But, then why are we producing mappings into
> > > the proposal?  Let's clean it up first.  If it doesn't clean up well enough
> > > then we won't have wasted the effort of producing the mappings.  
> > 
> > I didn't propose to do the mappings. But I believe this was an informal
> > exercise to see if this meets the requirements that the different people
> > have (and to find where it falls short).
> 
> I worry that the current state of the proposal is only adequate to
> determine whether there is a syntactic mapping.

I believe that both Gerd and I have explained this point quite adequately.


	--michael

Received on Friday, 19 May 2006 02:21:27 UTC