Re: ACTION-91: comment regarding completeness -> axioms

Hi,

I believe the best way to reach consensus on the issues surrounding collections (except the specialization to Dictionaries, which we 
deal with separately) is to make sure that the relations are grounded in a set of axioms that we can use to reason about the meaning 
and consistency of a set of collections-related statements.

Luc proposed one such set of statements a few days ago precisely for with purpose. I have taken the liberty to draft an alternative 
set of very straightforward axioms, which hopefully are easily understandable and can be used to reason about all issues surrounding 
collections -- including, deciding to remove them if we are not happy.
please see [1]

Firstly, I would ask people to check these axioms and the examples that follow.

Secondly, I am going to use these to try and answer Tim's latest comment at the end of this thread, copied here:
>
>>
>>>
>>> So what you're doing is saying "if you ever try to talk about _my_ dictionary, you're talking about a different dictionary!"?
>> not sure I follow this?  if this is saying that provenance is relative to the observer and others have different views over "what 
>> happened" then yes, but again I think we have agreed (wisely, I should say)  not to go there.
>
>
> I was just trying to understand how one could avoid "having anything added", where they'd basically say "my Entity is the kind 
> that doesn't have any  more members, so if you find any others, those asserters made a mistake." Like, if someone added Paolo (or, 
> the next justice) to my list of :todays-us-supreme court, they'd just be wrong and mis-interpreted what my Entity (Dictionary) is.
>
> I'm not arguing, just trying to understand.
>
> -Tim
What I believe you indicate is that we should allow multiple  memberOf() statements regarding the same collection:

memberOf(todays-us-supreme-court, {<http://dbpedia.org/resource/John_Glover_Roberts,_Jr.>})   # todays-us-supreme-court  contains at 
least JGR Jr
memberOf(todays-us-supreme-court, {Paolo, Pietro})   # todays-us-supreme-court  contains at least Paolo and Pietro

If there is no "complete" flag anywhere, the axioms allow this and this solves the problem, as described in Example 3 in [1].
However, if one "closes" one of the two statements, which is our point of contention, then the axioms entail an inconsistency as 
expected, i.e.

memberOf(todays-us-supreme-court, {<http://dbpedia.org/resource/John_Glover_Roberts,_Jr.>}, true)   # todays-us-supreme-court  
contains _only_  JGR Jr
memberOf(todays-us-supreme-court, {Paolo, Pietro})   # todays-us-supreme-court  contains at least Paolo and Pietro

This is Example 4 in [1].  (I am assuming that members with different ID cannot be unified).

Ok, so if we accept the axioms, then this is provably inconsistent. One can then more subjectively argue whether this is what we 
want. Personally, I am happy with this. The conclusion is precisely what Tim suggests, namely that if another member of a "closed" 
collection is found to exist, then one of the two statements was wrong (in this case it is probably, er, the statement about Paolo 
or Pietro being a justice :-))
  So yes, a statement about a complete collection is a strong one, and it may conflict with others. It's one of those 
inconsistencies that need to be resolved at the application level. We have already made that point clear in the DM.

As a further observation, note that memberOf can no longer be defined simply in terms of derivedByInsertionFrom, because multiple 
such insertions into the same collection are problematic (see ex 5 in [1]).
Also, if we agree on this formulation, the collection constraints need some adjusting.

[1] http://dvcs.w3.org/hg/prov/raw-file/default/model/working-copy/wd6-collections-constraints.html#dictionaries-and-contents-2.

-Paolo




On 6/8/12 5:47 PM, Timothy Lebo wrote:
>
> On Jun 8, 2012, at 11:43 AM, Paolo Missier wrote:
>
>> Tim
>>
>> <snip>
>> On 6/8/12 4:26 PM, Timothy Lebo wrote:
>>>
>>> On Jun 8, 2012, at 11:19 AM, Paolo Missier wrote:
>>>
>>>>
>>>>>>
>>>>>> "The attributecomplete <http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm.html#membership.complete>is optional. It is 
>>>>>> interpreted as follows:
>>>>>> - if it is present and set to true, then c is known to include all and only the members specified in the key-entity-set.
>>>>>
>>>>>
>>>>> ^^^ This kind of "future proofing" is what raised the "completeness concerns", so I suggest toning this down.
>>>>> As I've said before, avoiding the OWA's "anything can come down the road" and instead focusing on "this is believed to be 
>>>>> true, according to the asserter" eases the completeness objections.
>>>>
>>>> no problems with that, but as I pointed out in past discussions on this, this is true in general for /all/ provenance 
>>>> assertions, not just collections... right?
>>>
>>> I guess so.
>>> Which is why we don't have a "complete" flag on Entity, right?
>> rather, on relations:
>>
>> wasDerivedFrom(e,a,...)
>>
>> is believed to be true by the asserter /and at the time of the assertion/.
>> We never really discussed what happens if tomorrow I find out that was not the case -- we barely managed to agree that your 
>> observations and mine need not be consistent, and we agreed that consistency is out of scope.
>>
>> so that's where I think the OWA discussion should be situated.
>>
>> regarding the specific "complete" flag issue,  I thought we had already concluded that, for the specific case of collection 
>> membership, the "complete" flag is nothing but syntactic sugar for insertion into an empty collection (or dictionary).
>
> So I'm not trying to prolong the argument. Yesterday's call seemed to settle it.
> I'm just trying to smooth out some potentially concerning phrasings, as  I pointed out.
> So that this kind of concern can be avoided when future readers might "appreciate" OWA, they need to be informed that "yes, but 
> that's what this is".
>
> -Tim
>
>
>>
>>>
>>> So what you're doing is saying "if you ever try to talk about _my_ dictionary, you're talking about a different dictionary!"?
>> not sure I follow this?  if this is saying that provenance is relative to the observer and others have different views over "what 
>> happened" then yes, but again I think we have agreed (wisely, I should say)  not to go there.
>
>
> I was just trying to understand how one could avoid "having anything added", where they'd basically say "my Entity is the kind 
> that doesn't have any  more members, so if you find any others, those asserters made a mistake." Like, if someone added Paolo (or, 
> the next justice) to my list of :todays-us-supreme court, they'd just be wrong and mis-interpreted what my Entity (Dictionary) is.
>
> I'm not arguing, just trying to understand.
>
> -Tim