Re: complementOf -> viewOf: proposed text: however... :-)

On 14/01/2012 15:41, Paolo Missier wrote:
> Graham
>
> the bottom line is that if we want specializationOf to be a special case (a
> sub-relation of) alternateOf, as Khalid has proposed, then (it seems to me that)
> you cannot define alternateOf in terms of specializationOf:
>
> alternativeOf(a, b) == exists (c) :
> specializationOf(a,c) and
> specializationOf(b,c)
>
> (or variations as you show below).
>
> In fact Khalid and I now have come to believe that this definition is too
> strong, in addition to leading to problems for transitivity.

Hmmm... I accept that this might be the case, but I'm not seeing why this 
definition is "too strong".  Can you elucidate a little?)

OTOH, if you prefer to go with alternativeOf and speclializationOf as 
primitives, with the appropriate intuitions asserted as constraints, I think 
that's fine too.

(Did you see my other response on this?  I'm not sure if it's relevant.  Even if 
it's not part of the published framework, knowing that there's a way to 
axiomatize the desired properties might be handy - if it works!)

#g
--

> And yes, transitivity seems quite natural for this relation. It leads not to a
> lattice of alternates for an entity, but more simply to a cluster of alternates.
> So I propose that alternateOf is a primitive relation, i.e., not defined in
> terms of any other, and on the other hand
>
> specializationOf \subset alternateOf
>
> (and I am still late in my updates to the doc, apologies)
>
> -Paolo
>
>
>
> problem is On 1/13/12 3:18 PM, Graham Klyne wrote:
>> On 13/01/2012 12:44, Paolo Missier wrote:
>>> Graham
>>>
>>> glad you agree, however meanwhile I spotted a problem in my own proposal that
>>> entities should form a lattice. It doesn't sit well with your axiom, because
>>>
>>> alternateOf(a, b) and
>>> alternateOf(c, d)
>>>
>>> it follows that a,b,c,d are /all/ alternate of each other (because their def. is
>>> now based on specialization, and specialization is transitive, and there is a
>>> Top where they all meet).
>> Oh yes. I guess you need multiple non-overlapping lattices, where each tops out
>> in its own "real world thing".
>>
>>> But this is too much :-)
>>>
>>> something has to give... let me sit on transitivity of alternate while I fix the
>>> rest of the text
>> Of course. Is the transitivity of alternativeOf actually important for anything?
>>
>> ...
>>
>> I just had a thought, but there may be errors here as my head isn't really in
>> this context right now.
>>
>> Roughly, instead of defining:
>>
>> alternativeOf(a, b) == exists (c) :
>> specializationOf(a,c) and
>> specializationOf(b,c)
>>
>> use something like:
>>
>> alternativeOf(a, b) == exists (c) :
>> specializationOf(a,c) and
>> specializationOf(b,c) and
>> not exists (d) : specializationOf(c,d) and
>>
>> I think all the other proofs using "specializationOf" still work.
>>
>> Hmmm... we still need to assert or prove uniqueness of the c above. How about
>> defining a new relation:
>>
>> specializeTop(a, b) ==
>> specializationOf(a, b) and
>> not exists (z) : specializationOf(b, z)
>>
>> Then we can assert:
>>
>> specializeTop(a, b) and specializeTop(a, c) => b = c
>>
>> (which is the lattice-like constraint) Then, if alternateOf is defined in terms
>> of specializeTop, I think its transitivity then follows. Further, I think this
>> notion of specializeTop reflects the intuition we're trying to capture (see my
>> very first comment above)
>>
>> #g
>> --
>>
>>
>>> -Paolo
>>>
>>>
>>>
>>> On 1/12/12 6:32 PM, Graham Klyne wrote:
>>>> Paolo,
>>>>
>>>> Summary: I think we are in agreement. I may need to re-check the text to make
>>>> sure it doesn't still lead me to one of the misunderstandings from my earlier
>>>> message.
>>>>
>>>> On 12/01/2012 10:06, Paolo Missier wrote:
>>>>> Graham
>>>>>
>>>>> sorry for letting this slip. To recall, the context is that I am tasked with
>>>>> fixing the alternateOf section of PROV-DM.
>>>>>
>>>>> I have a few comments to yours and Khalid's. Original text copied where
>>>>> needed.
>>>>>
>>>>> My main comment is that I like your axiomatization of the two relations,
>>>>> but it
>>>>> seems to lead to properties that are not exactly what we want. But there is a
>>>>> simple fix.
>>>> :)
>>>>
>>>>> Specifically:
>>>>>
>>>>>> In other words, what I am suggesting is that:
>>>>>> specializationOf(e1,e2) implies alternateOf(e1,e2)
>>>>> that's fine, I have no problems with that.
>>>>>
>>>>>> *BUT*, this is not what the current text allows, since specializationOf is
>>>>>> defined to be anti-symmetric, which means that it is also anti-reflexive:
>>>>>>
>>>>>> forall (a, b) : specializationOf(a,b) => not specializationOf(b,a)
>>>>>>
>>>>>> setting b = a we see that specializationOf(a,a) must be false, since its
>>>>>> truth
>>>>>> would give rise to a contradiction.
>>>>> not really. Anti-symmetry is defined differently. I hate to quote
>>>>> wikipedia, as
>>>>> I don't have the provenance of the content handy :-), but it's just
>>>>> convenient, so:
>>>>> http://en.wikipedia.org/wiki/Antisymmetric_relation
>>>>>
>>>>> basically, an anti-symmetric relation can be reflexive so that's not a
>>>>> problem.
>>>> That would be good. From memory, I wasn't going so much by a definition of
>>>> "antisymmetry" but because I though the text was suggesting something like the
>>>> implication above. But if that's not intended, we can focus on making sure the
>>>> text doesn't confuse.
>>>>
>>>>> More interestingly, about transitivity of alternateOf(): I believe we can
>>>>> still
>>>>> save your axiomatization:
>>>>>> alternativeOf(a, b) == exists (c) :
>>>>>> specializationOf(a,c) and
>>>>>> specializationOf(b,c)
>>>>> just by insisting that the set of all entities forms a lattice. In fact, we
>>>>> only
>>>>> need an upper semi-lattice.
>>>> Yes, I think that's about where I'd got to, but I wasn't sure how to axiomatize
>>>> that cleanly.
>>>>
>>>>> This does not ensure that
>>>>>> specializationOf(x, y) or specializationOf(y, x)
>>>>> but it does ensure that for each x,y, there is some z such that
>>>>>
>>>>> specializationOf(x, z) and specializationOf(y, z). alternateOf(a,c) follows.
>>>>>
>>>>> Having a top element is quite natural in class hierarchies (see owl:Thing).
>>>>> But
>>>>> this should come as no surprise as all we are doing is re-invent class
>>>>> hierarchies with a a top element.
>>>>>
>>>>> So in summary:
>>>>> - I am fine with your axiomatization, plus the easy condition that entities
>>>>> form
>>>>> an upper semi-lattice.
>>>>> - I think it belongs in PROV-SEM
>>>>> - I am inclined to keep the properties of the two relations as they are.
>>>>>
>>>>> (and yes, more specific may be better than more concrete).
>>>>>
>>>>> are we in agreement?
>>>> On the basis of what you say here, yes.
>>>>
>>>> Thanks.
>>>>
>>>> #g
>>>> --
>>>>
>>>>> On 1/6/12 4:44 PM, Graham Klyne wrote:
>>>>>> Paolo,
>>>>>>
>>>>>> I've now looked at the text and am happy with the direction, but have some
>>>>>> niggles with the details...
>>>>>>
>>>>>> First a nit: you say e1 and e2 provide a more *concrete* characterization
>>>>>> than
>>>>>> e1. I would say more *specific* rather than more *concrete*.
>>>>>>
>>>>>> For the rest, using Using Khalid's comments as a spingboard:
>>>>>>
>>>>>> On 05/01/2012 18:43, Khalid Belhajjame wrote:
>>>>>>> Hi,
>>>>>>>
>>>>>>> The new Alternate and Specialization records seem to make sense to me.
>>>>>>>
>>>>>>> - Looking at the definitions of *specializationOf* and *alternateOf*, I for
>>>>>>> few
>>>>>>> seconds was wondering if it is a good idea to define a more general
>>>>>>> relationship
>>>>>>> that simply says that two entity records are representations of the same
>>>>>>> entity,
>>>>>>> without specifying if there is difference in abstraction or context. But, I
>>>>>>> changed my mind as a result, and I now think that the general relationship
>>>>>>> that
>>>>>>> I was looking for is *alternateOf* itself. Indeed, such a relationship
>>>>>>> seems to
>>>>>>> be usable in both cases, i.e., different abstractions and/or different
>>>>>>> contexts.
>>>>>>> In other words, what I am suggesting is that:
>>>>>>> specializationOf(e1,e2) implies alternateOf(e1,e2)
>>>>>>>
>>>>>>> Does that make sense?
>>>>>>>
>>>>>> I think this depends on how the definitions are set up.
>>>>>>
>>>>>> I see specializationOf as a primnitive using which alternativeOf can be
>>>>>> defined:
>>>>>>
>>>>>> alternativeOf(a, b) == exists (c) :
>>>>>> specializationOf(a,c) and
>>>>>> specializationOf(b,c)
>>>>>>
>>>>>> My preference is for specializationOf to be reflexive; i.e.
>>>>>>
>>>>>> forall (a) : specializationOf(a, a)
>>>>>>
>>>>>> your result follows from this:
>>>>>>
>>>>>> given:
>>>>>> specializationOf(e1,e2) [per premise]
>>>>>> specializationOf(e2,e2) [per reflexivity]
>>>>>>
>>>>>> we set a=e1, b=e2, c=e2 to satisfy the RHS of alternativeOf definition, hence
>>>>>> have alternativeOf(e1, e2) as you suggest.
>>>>>>
>>>>>>
>>>>>> *BUT*, this is not what the current text allows, since specializationOf is
>>>>>> defined to be anti-symmetric, which means that it is also anti-reflexive:
>>>>>>
>>>>>> forall (a, b) : specializationOf(a,b) => not specializationOf(b,a)
>>>>>>
>>>>>> setting b = a we see that specializationOf(a,a) must be false, since its
>>>>>> truth
>>>>>> would give rise to a contradiction.
>>>>>>
>>>>>> Which in turn means that the above proof of your suggested inference does not
>>>>>> hold.
>>>>>>
>>>>>> ...
>>>>>>
>>>>>> So my question is this: is there any particular reason to require
>>>>>> anti-symmetry
>>>>>> of specializationOf?
>>>>>>
>>>>>> (An alternative would be to modify the definition of alternativeOf, thus:
>>>>>>
>>>>>> alternativeOf(a, b) == exists (c) :
>>>>>> (specializationOf(a,c) or a = c) and
>>>>>> (specializationOf(b,c) or b = c)
>>>>>>
>>>>>> Absent and particular reason to do otherwise, I'd rather go with the simpler
>>>>>> definitions.)
>>>>>>
>>>>>>
>>>>>>> - *alternateOf* is transitive.
>>>>>> I think it should be, but let's see how this plays:
>>>>>>
>>>>>> alternativeOf(a, b) == exists (x) :
>>>>>> specializationOf(a,x) and
>>>>>> specializationOf(b,x)
>>>>>>
>>>>>> alternativeOf(b, c) == exists (y) :
>>>>>> specializationOf(b,y) and
>>>>>> specializationOf(c,y)
>>>>>>
>>>>>> If we can show specializationOf(x, y) or specializationOf(y, x) then the
>>>>>> result
>>>>>> can be derived using transitivity of specializationOf and the definition of
>>>>>> alternativeOf.
>>>>>>
>>>>>> We have:
>>>>>> specializationOf(b,x) and
>>>>>> specializationOf(b,y)
>>>>>>
>>>>>> Intuitively a specializationOf relation holds between x and y as their is a
>>>>>> single non-branching path from b to the "top" of the specialization tree.
>>>>>> But I
>>>>>> think we need more stated constraints to derive this.
>>>>>>
>>>>>> Right now, I'm not sure how best to capture this, and am thinking that simply
>>>>>> asserting the required relation would be easiest; i.e.
>>>>>>
>>>>>> specializationOf(b,x) and
>>>>>> specializationOf(b,y)
>>>>>> |=
>>>>>> specializationOf(x,y) or specializationOf(y,x)
>>>>>>
>>>>>> (If specialization is anti-reflexive, we need to add "or x = y" to the above
>>>>>> constraint.)
>>>>>>
>>>>>> Or maybe:
>>>>>>
>>>>>> specializationOf(b,x) and
>>>>>> specializationOf(b,y)
>>>>>> |=
>>>>>> exists (z) : specializationOf(x,z) and specializationOf(y,z)
>>>>>>
>>>>>> An alternative would be to not care about this, in which case
>>>>>> alternativeOf is
>>>>>> not inferrable from specializationOf. Does this actually matter?
>>>>>>
>>>>>> #g
>>>>>> --
>>>>>>
>>>>>>> On 15/12/2011 15:25, Paolo Missier wrote:
>>>>>>>> Hi,
>>>>>>>>
>>>>>>>> in response to the comments about complementarity on the wiki and on the
>>>>>>>> list,
>>>>>>>> we have prepared a revised version of the section,
>>>>>>>> where "complementarity" disappears in favour of "viewOf", and the
>>>>>>>> definition
>>>>>>>> is hopefully simplified and more in line with the
>>>>>>>> expectations:
>>>>>>>> http://dvcs.w3.org/hg/prov/raw-file/default/model/ProvenanceModel.html#record-complement-of
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> (the anchor name hasn't changed :-))
>>>>>>>>
>>>>>>>> this is for feedback as per today's agenda
>>>>>>>>
>>>>>>>> atb -Paolo
>>>>>>>>
>>>>>>>>
>>>
>
>

Received on Monday, 16 January 2012 08:44:53 UTC