# RE: FOL versus Rule Languages - A tutorial

From: Gerd Wagner <wagnerg@tu-cottbus.de>
Date: Fri, 26 Aug 2005 11:33:50 +0200
To: "'Dieter Fensel'" <dieter.fensel@deri.org>, <public-rule-workshop-discuss@w3.org>
Cc: "'Christian de Sainte Marie'" <csma@ilog.fr>
Message-Id: <20050826093514.6937450821F@smtp2.TU-Cottbus.De>
```
Just some supplementary explanations to Dieter's "tutorial":

> But the essence stays the same. The semantics is truly
> defined declarative in terms of a defined model and not
> in terms of an evaluation strategy of rules.

As you said before, it's not necessarily defined in terms
of a (i.e. exactly one) preferred/intended model but may
be defined in terms of a set of preferred/intended models.

> And that extension are truly monotonic in the sense that in
> the case of a restricted sublanguage the confirm with the simpler
> definition of the unique model.

Such an extension of a formalism is normally called "conservative",
not "monotonic".

> 3.1) In rule languages we restrict ourselves to a certain type
> of interpretations/models which are called Herbrand models.

Yes, but in general we may relax this and allow (suitably
defined) Herbrand-like models (e.g. for accommodating
non-unique names).

> 3.2) NOW COMES the important difference. In FOL we reason

That means even very strange/unintended models are taken into
account.

> With rule languages we select a certain Herbrand
> model as the ground of our inference.

As already said above, we do not necessarily select just
one, but possibly several, intended models.

> "Assume you have
>
>  p(a,b), p(b,c)
>  and the following two rules:
>  p(x,y) -> q(x,y)
>  p(x,y) & p(y,z) -> q(x,z)
>
>  Then under minimal model semantics q is the deductive closure

I think this is normally called "transitive closure".

>  of p, i.e., q(a,b), q(b,c), q(a,c) are true and no other q(x,y)
>  is true.

So, this example shows nicely the superiority of the intended
model semantics approach for computational specification
languages.

-Gerd

---------------------------------------------
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http://www.informatik.tu-cottbus.de/~wwwitec/
Tel: 0355-69-2397
Email: G.Wagner@tu-cottbus.de

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Received on Friday, 26 August 2005 09:35:26 UTC

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