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Re: Survey on titles for OWL2 Semantics documents

From: Bijan Parsia <bparsia@cs.man.ac.uk>
Date: Mon, 22 Sep 2008 15:08:23 +0100
Message-Id: <7654E5A8-B5D2-4C63-96D9-21ACA3837FBC@cs.man.ac.uk>
Cc: Sandro Hawke <sandro@w3.org>, Ivan Herman <ivan@w3.org>, public-owl-wg@w3.org
To: Uli Sattler <sattler@cs.man.ac.uk>

Let me take it a bit further.

On 22 Sep 2008, at 14:10, Uli Sattler wrote:

> On 22 Sep 2008, at 12:58, Sandro Hawke wrote:
>
>>> On 19 Sep 2008, at 16:29, Ivan Herman wrote:
>>>
>>>> Ah! So the remark could be translated as 'there is nothing DL  
>>>> specific
>>>> in it'. Right? This makes sense...
>>>>
>>>
>>> indeed, this is what I tried to say, cheers, Uli
>>
>> I'm baffled by this.
>>
>> I'm pretty sure they are not the semantics of full first-order logic.
>
> no, but the basic idea and structure is the same.

Consider the following three sorts of semantics:

1) We have constants interpreted as and variables ranging over  
individuals while classes are interpreted as sets of individuals.
2) We have constants interpreted as and variables ranging over  
individuals while classes are interpreted as individuals which have a  
relation to a set of individuals.
3) We have constants interpeted as and variables ranging over  
individuals *and* sets of individuals and classes interpreted as sets  
of individuals.

1 is what I would call "standard first order semantics" regardless of  
other details of the presentation. The second is (more or less) rdf  
semantics, or hilog semantics, or  henkin semantics. It's really  
quite a different beast. 3 is standard second order semantics.

Another way of seeing it is, when giving a semantics by translation,  
1 involves a *transliteration* into FOL; 2 involves a more complex  
axiomitzation (including introducing an "isa" predicate); 3 cannot be  
reduced to FOL at all.

>> And they are the semantics of OWL DL, which I understand is a
>> description logic (DL) language.  (As the W3C Recommendation on the
>> subject says, "OWL DL is so named due to its correspondence with
>> description logics".)
>>
>> So that makes them very DL specific.
[snip]

Not in the sense we're talking. The standard model theoretic  
semantics of a description logic are in the standard first order  
logic family. Compare with the standard semantics for propositional  
modal logics which *can* be seen as being in the standard first order  
logic style, but generally are given a much different presentation  
(e.g., in terms of Kripke structures).

I know people coming from a first order background who generally read  
too much into the "DL" when people say "DL Semantics". Indeed, I've  
(and many others) have wasted a lot of time trying to get people to  
believe that the semantics of a DL is just normal first order semantics.

Cheers,
Bijan.
Received on Monday, 22 September 2008 14:05:48 UTC

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