Re: OWL DL extension question

On 11 Apr 2007, at 18:54, Conrad Bock wrote:

>
> Evren,
>
>>> Was wondering if anyone is looking into whether this fragment can
>>> be added tractably to OWL DL (1.0):
>
>>>   (forall (x y z)
>>>      (if (and (P x y)
>>>               (R x z))
>>>          (S y z)))
>>>
>>> For example, the uncles of my children include all my brothers
>>> (P=children, R=brothers, S=uncles).
>
>> You can turn the antecedent into a property chain using the
>> inverse of P
>> and then use the standard complex role inclusions of OWL 1.1 as:
>
>> SubObjectPropertyOf(SubObjectPropertyChain(InverseObjectPrope
>> rty(children)
>> brothers) uncles)
>
> Great, thanks.
>
>> provided that the restrictions described at [1] are not violated.
>
> Do you happen to know if anyone has shown these to be the maximal
> restrictions, ie, any loosening of them will cause undecidability?  In
> particular, is the regularity restriction maximal?

Yevgeny Kazakov has done some work on this. He has shown that the  
restriction is not maximal (which is pretty obvious), and I believe  
that he has devised an alternative and strictly more general  
restriction. I have a feeling that there is even an undecidability  
result related to maximality, but I might have imagined that :-).

Yevgeny can no doubt tell you more.

Regards,

Ian


>
> Conrad
>
>
> PS: I assume the first set of bullets are disjunctive, but the text
> doesn't say this explicitly.
>
>
>