Re: PROV-ISSUE-153 (complementarity): Complementarity description differs from model definition [Primer]

Hi Graham,

On 11/23/11 9:18 AM, Graham Klyne wrote:
>
>> -1 for using "contextualized" as the basis for "complementarity".
>> as Graham points out:
>>
>> A1 \subset B and A1 \subset B does not imply that A1 and A2 are not disjoint.
> Out of interest, do you have a use-case for which complementarity depends on
> there being an actual overlap of attributes, as opposed to both being
> contextualizations of some common thing?
the old "royal society" example is meant to exemplify a pattern where each observer has a partial view on some system state (state = 
complete set of attribute value pairs), but there is  no "common thing" that is given to them: nobody has the /complete/ state. 
Indeed, the idea is that the common thing emerges by taking the union of the two sets of attributes, on the basis that the 
overlapping portions are mutually consistent (i.e. a mapping can be established).
We may be saying the same thing: a "common thing" that subsumes both exists, but in this example it only becomes manifested /as a 
consequence of/ the observers agreeing that they are each looking at two projections of it.

Indeed your last comment seems to agree with this view: in an open world, there is some common entity that subsumes our views, but 
it may not have been explicated.

   The inspiration for this is the notion of "record linkage", or the process by which you "discover" such common entity, and you 
benefit from the discovery by taking all that you know from each of the individual pieces. I just would like to have this setting 
expressed as part of  PROV because it's the only place where you can make an attempt at "joining up" or reconcile different 
assertions made independently about what is in reality the "common thing".

I think what you are referring is complementary to this, namely you do have a a priori "common thing", you derive views from it, and 
you call them the complement of each other.

I see no conflicts here, I believe that both should be expressible.

Regarding terminology, either "restriction" or "projection" work relative to the common thing, but they don't work in relation to 
each other.  In any case, both are meant in their algebraic sense:

restriction:  "Any function can be restricted to asubset <http://en.wikipedia.org/wiki/Subset>of its domain. The restriction of/g/ : 
/A/ ? /B/to/S/, where/S/?/A/, is written/g/ |_/S/  : /S/? /B/."  (http://en.wikipedia.org/wiki/Function_restriction)

projection: well, this we all know :-)

--Paolo


>
> (Arguably, in an open-world environment such as the web, the fact that two
> entities contextualize some common other entity suggests very strongly that
> there does exist some attribute that is common, even if it has not been explicated.)
>
> #g
> --