RE: FOL versus Rule Languages - A tutorial

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 
> about ALL Herbrand models. 

Not just about Herbrand models but about all kinds of models.
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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Received on Friday, 26 August 2005 09:35:26 UTC