# Re: SNAF, NAF, and monotonicity [was: Comments on * DRAFT * Rules...]

From: Michael Kifer <kifer@cs.sunysb.edu>
Date: Thu, 01 Sep 2005 11:01:12 -0400
To: Christian de Sainte Marie <csma@ilog.fr>

Message-Id: <20050901150112.DA979CB5D3@kiferserv.kiferhome.com>
```

> Michael Kifer wrote:
> >
> > Inference rule is a useful way to think of it at an intuitive level.
> > However, the only version of CWA that is defined as an inference rule that
> > I know of is NAF. Not what is being called NAF in this discussion thread,
> > but the real NAF, as in Prolog.
> >
> > All the other popular versions of CWA (well-founded, stable,
> > circumscription) use model-theoretic definitions or axiomatic.
>
> I stand corrected: I had Clark's NAF in mind.

But Clark's NAF is not a good thing to use. It has several undesirable
properties and is considered not suitable for knowledge representation
where semantics is important. (Clark's NAF doesn't have model-theoretic
semantics and thus can't be incorporated into languages that have.)

>
> > Then you are checking whether S3 still entails F, and sure enough it does.
> > So, you conclude it is monotonic.
>
> Point taken: I tried so hard to hide the assert that I did not notice it
> myself!
>
> > But here you have "monotonicity" for
> > formulas of a certain kind (the same problem as Dan had), not for all
> > formulas. As far as I recall, according to so called Gabbay's postulates,
> > *every* *non*monotonic logic also has the property that if S |= F then
> > S+F+something |= F.
> > In any case, the most popular CWA flavors (the well-founded and stable
> > models) do have the above property.
> > So, your argument in the use case doesn't establish anything as far as
> > monotonicity goes.
>
> I fear that it had more to do with the ostrich's postulate than
> Gabbay's. Something like: S |= F, but S + B |\= F? No problem: just
> ignore B! (What do you tell me, S |= F is non-monotonic nonetheless?)

What is nonmonotonic is not "S|=F", but |=. And it, indeed, is nonmonotonic
according to what you are describing. (There is no sense in which one could
say that a particular "S|=F" is nonmonotonic.)

> What? Me? Foolish?
>
> > What we should do is to remove the clause that NAF is out of scope and
> > remove the reference to monotonicity. Then let the WG deal with it.
>
> I could leave with that, but for the fear of that being Pandora's box...

What kind of creatures do you expect to crawl out of it?

--michael
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Received on Thursday, 1 September 2005 15:01:20 UTC

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