[DL] Campactness

Franz Baader baader at tcs.inf.tu-dresden.de
Tue Jan 23 09:15:01 CET 2007

There are probably two reasons why you don't find anything
on compactness of DLs in the literature:
- usually, one considers only finite knowledge bases in DL, and
  thus compactness is not relevant
- most DLs are fragments of first-order predicate logic, and thus
  inherit compactness from there

If you want to find DLs that are not compact, you could look at the ones
that are extensions of PDL (propositional dynamic logic) or ones that
allow for cyclic TBoxes with fixpoint semantics. For example, if the DL
can express that there cannot be an infinite role chain, and additionally
allows for nested existential restrictions, then it is obviously not compact.
Maybe you can find something about compactness in extensions of PDL
or the propositional mu-calculus in the literature.

Best regards,

-Franz Baader

On 1/19/07, Marcio Moretto Ribeiro <marcio.mr at gmail.com> wrote:
> I would like to ask about the compactness of the description logics. Which
> dls are compact?  Or what characteristic makes a dl compact? Is every dl
> compact?
> I have searched the literature and the web, but I haven't found any work
> mentioning the compatness of the description logics.
> Thank you.
> Márcio
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