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Re: Question on DL negation

From: Matt Williams <matthew.williams@cancer.org.uk>
Date: Mon, 05 Mar 2007 15:13:36 +0000
Message-ID: <45EC33A0.3050807@cancer.org.uk>
To: Bijan Parsia <bparsia@cs.man.ac.uk>
CC: Semantic Web <semantic-web@w3.org>

Dear Bijan,

Thanks a lot - very helpful, as usual.

The approach with nominals is interesting - I'll have a play and see 
what happens.

I guess what I missed from my first question is that if:

\exists hasRole.\top

is a valid class expression (which I think it is) then:

(\exists hasRole.\top)

should be valid. But since adding \top to the formula doesn't seem to 
add anything, could one write (\exists hasRole) as a shorthand? I think 
the answer is no, but I'm not clear why.

Thanks,

Matt

Bijan Parsia wrote:
> 
> On 5 Mar 2007, at 10:45, Matt Williams wrote:
> 
>>
>> Dear All,
>>
>> As I understand, most DL's do not allow for the negation of roles.
>>
>> However, given a formula of the form R(x,y) (where R is some role), 
>> since this is equivalent to (R(x,y) & \top(y))
> 
> That's not a class expression. The standard negation constructor, e.g., 
> in OWL, applies only to class expresession (i.e., to formulae with at 
> most one free variable).
> 
>> which could be negated as ( R(x,y) & \top(y)),
> 
> Only if you had negation of arbitrary formulae, which you generally 
> don't. And if you did, you could just say ~R(x, y) :)
> 
>> is it possible to effectively relax this constraint in some cases 
>> without affecting the logic?
> 
> So, there are at least two forms of role negation you might consider: 
> negation of *ground* roles and negation of *arbitrary* roles. The former 
> allows you to so say that, e.g., bob does *not* love mary, where as the 
> latter allows you to say that love and hate are disjoint.
> 
> In OWL, given nominals, you can encode the former, e.g., bob: 
> complementOf(hasValue.love({mary}). In this way, it's clear that 
> nominals are more expressive than aboxes alone. In OWL 1.1, you can 
> express the former directly and you can express the latter at least in 
> the form of disjointness of properties.
> 
>> I'm interested in rules that have a single role as the head, and 
>> negation of such heads would be useful...
> 
> Hope this helps.
> 
> Cheers,
> Bijan.

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Received on Monday, 5 March 2007 15:14:27 UTC

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