Re: PROV-ISSUE-29 (mutual-iVP-of): can two bobs be mutually "IVP of" each other [Conceptual Model]

On 30/03/12 10:01, Luc Moreau wrote:
>
> Dear all,
>
> I am getting conflicting messages on this topic!
>
> James has listed some properties derived from the semantics
> http://lists.w3.org/Archives/Public/public-prov-wg/2012Mar/0470.html
> But not all of them seem to be aligned with what we are reading on 
> this thread.
>
> So, I started drafting a section in prov-dm part II listing the 
> properties of these relations [1].
>
> I am proposing to justify each property either by reasoning based on 
> its definition,
> or by a counter-example.
>
> *Your suggestions are needed to help us complete this section. *
>
> James, unless my reasoning is incorrect, I do not have transitivity 
> for specializationOf.

Hi Luc,

Your reasoning (quoting from [1])  is:

> Specialization is /not transitive/. Indeed if specializationOf(e1,e2) 
> holds, then there is some common thing, say e1-2 they both refer to. 
> Likewise, if specializationOf(e2,e3) holds, then there is some common 
> thing, say e2-3 they both refer to. It does not follow there is a 
> common thing both e1 and e3 refer to.

In the WD3 formal semantics [2], I modeled entities-referring-to-things 
as a function thingOf : Entity -> Thing.

Thus, if thingOf(e1) = e1-2 = thingOf(e2) and thingOf(e2) = e2-3 = 
thingOf(e3) then (by transitivity of equality) e1-2 = e2-3 and all three 
entities refer to the same thing, e1-2.

Of course, it is an assumption I made that an entity "refers to" exactly 
one thing.  If we want to allow entities to refer to multiple things, 
then the reasoning I give above fails, and specializationOf is not 
necessarily transitive.

--James

[1] 
http://dvcs.w3.org/hg/prov/raw-file/default/model/prov-dm-constraints.html#component4
[2] http://www.w3.org/2011/prov/wiki/FormalSemanticsWD3