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

> > 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.

> > > 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.  

> > 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?

> > > 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.

[...]

> 	--michael  

Peter F. Patel-Schneider

Received on Friday, 19 May 2006 01:39:48 UTC