[DL] Horn clauses and DLs

[Rodrigo de Salvo Braz]

On Tue, 5 Oct 2004, Mathieu Roger wrote:

> Hello, I suggest a point to this debate :
>
> Horn clause are well knowned to be "negation"-less (how can negative
> facts expressed ?), whereas most DLs are complete under negation...

(...)

> I consider any language that is bias on positive facts to be not enought
> general, and if I choose to be in a restricted language, I prefer not to
> give up negation. That is only my opinion.

Thanks. Indeed negation is an important issue. As you pointed out, the
closed-world assumption can alleviate things a bit.

I would just like to mention that it seems to me that Horn clauses are
more disjunction-less than negation-less. In certain cases I can derive
negative facts from a Horn clause. For example if we have
p => not q
then a system could derive not q from p. The above is not a Prolog
statement but it is a Horn clause. Also,
not p, r, s => not q
is a Horn clause and it both concludes and uses negative information.

The problem with some clauses using negation, like
not p => q,
which is not Horn, is that really it is a disjunction: p or q.
That seems to be the source of complexity, not negation per se.
Or am I mistaken in this?

Thanks,

Rodrigo