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Re: SNAF, NAF, and monotonicity [was: Comments on * DRAFT * Rules...]

From: <jos.deroo@agfa.com>
Date: Fri, 26 Aug 2005 01:00:30 +0200
To: kifer@cs.sunysb.edu
Cc: Dan Connolly <connolly@w3.org>, public-rule-workshop-discuss@w3.org, public-rule-workshop-discuss-request@w3.org
Message-ID: <OFF413F521.4BF2DB22-ONC1257068.00745E53-C1257068.007E5C0F@agfa.com>

>>> Michael Kifer wrote:
>>> Dan Connolly wrote:
>>>> On Aug 24, 2005, at 8:11 PM, Michael Kifer wrote:
>>>>> [...]
>>>>> No, you got me wrong. I do believe that nonmonotonicity is
>>>>> important, but you already have it in the form of SNAF.
>>>> 
>>>> I'm having trouble understanding that. I see it shows up in
>>>> several of your recent messages, e.g.
>>>> 
>>>> "SNAF is nonmonotonic."
>>>> http://lists.w3.org/Archives/Public/public-rule-workshop-discuss/2005Aug/0029.html
>>>> 
>>>> My understanding is that SNAF is monotonic.
>>>> 
>>>> Earlier[1] we discussed this example rule...
>>>> 
>>>> { :car.auto:specification log:notIncludes {:car auto:color []}}
>>>>      => {:car auto:color auto:black}.
>>>> 
>>>> That rule is monotonic; if the antecedent is true, the
>>>> consequent remains true regardless of how many other
>>>> things are also true.
>>>
>>> Hi Dan,
>>> Welcome to the discussion! Yes, it is very important to
>>> get to the bottom of it so that everybody will start
>>> speaking the same language.
>>>
>>> No, the above rule is nonmonotonic. If you add a color
>>> specification to that car then :car.auto:specification
>>> will now include a color specification and log:notIncludes
>>> will become false. Therefore 
>>>    :car auto:color auto:black
>>> will no longer be derived.
>>
>> I'm aware of following sentence from
>> http://www.w3.org/2000/10/swap/doc/Reach
>> 
>> [[
>> Also, if we start to just loosely talk about defaults in
>> the sense of "if you don't already know a color", then
>> different agents will end up drawing different conclusions
>> from the same data, which is not a good foundation for a
>> scalable web.
>> ]]
>> 
>> and believe that
>> 
>> <uri-of-document> log:semantics ?F.
>> ?F log:notIncludes {set-of-triples}.
>> 
>> is a robust approach and is monotonic
>> (you cannot add things to ?F)
>
> Jos,
>
> Monotonicity or nonmonotonicity is a property of a logical
> language, not of a particular set of formulas. 

Okay

> Furthermore, in your example, ?F is just a variable whose
> quantification you neglected to specify.

Well, I should have said that the triples

  <uri-of-document> log:semantics ?F.
  ?F log:notIncludes {set-of-triples}.

were in the premise of a N3 rule and then ?F is a
universally quantified variable with the scope of
that rule.

> A proper thing to do here would be to write something like:
>
> <uri-of-document> log:semantics t.
> t log:notIncludes {set-of-triples}.
>
> where t is a term that represents (reifies) the set of
> formulas that are encoded in uri-of-document. Now, t is
> a term, not a formula, so your statement about "adding
> things to ?F" is irrelevant as far as monotonicity
> of the language is concerned.

Well, this is indeed where we seem to have a disconnect..
I meant that for the set triples represented by ?F (and
which are real triples in my machine) there is no way to
add triples to that set; you can of course add triples to
the document at <uri-of-document> on the web but then,
formula A in your (**) has a different interpretation.


-- 
Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/
Received on Thursday, 25 August 2005 23:00:55 GMT

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