RE: PROV-ISSUE-45: isDerivedFrom and IVPof are transitive. [Conceptual Model]

Paolo,

 

The "holds over the temporal intersection" clause is already there in
the definition of IVPof.  I am questioning the transitivity of the
relation even with this clause.  I think that inference of IVPof using
transitivity from two IVPof assertions is only valid if all three bobs
involved have mutually overlapping intervals (i.e. X must overlap Z in
my example), and it is this condition which is not captured.   

 

Stephen Cresswell

Tel:  +44 (0) 01603 69 6926

Web:  www.tso.co.uk <http://www.tso.co.uk/> 

 

________________________________

From: Paolo Missier [mailto:Paolo.Missier@ncl.ac.uk] 
Sent: 28 July 2011 14:29
To: Cresswell, Stephen
Cc: public-prov-wg@w3.org
Subject: Re: PROV-ISSUE-45: isDerivedFrom and IVPof are transitive.
[Conceptual Model]

 

Stephen,

your observation is correct, of course, and it does make the IVP-of
relation look not well-behaved, but that's because the temporal interval
that defines Bobs validity explicitly, has remained  "hidden" in the
def. of IVP-of relation, while it should have been made explicit there,
as well.
 So if you add your sentence "B IPVof A is defined to only hold over the
temporal intersection of A and B" to the def. of IVP-of (as we should
have done as it makes no sense to establish a relation between two Bobs,
one of which is out of scope), then over this restricted interval the
relation /is/ transitive, right?
What I mean is that the problem is not that IVP-of is not transitive,
but that in the def. we omitted to qualify the scope within which the
relation itself holds. 

Regarding better-behaved relations, personally (and bear in mind this is
not /my/ def.) I rather like the general case in which 
- the set of attributes overlap (with no strict set containment
requirement)
- the temporal scopes overlap (with no strict interval containment
requirement)
as these conditions lead, within a possibly restricted scope, to an
equivalence relation.  That said, whether this is still practically
useful is a separate issue...  

-Paolo

On 7/28/11 1:13 PM, Cresswell, Stephen wrote: 

 

Paolo,

 

I don't see how IVPof can be usefully considered transitive in its
current definition, as I think it would be possible for some
transitively-derived IVPof relations to be valid only over empty time
intervals.  This is because B IPVof A is defined to only hold over the
temporal intersection of A and B, but the relation of having non-empty
temporal intersection is itself not transitive.  

 

For example, we can have three time intervals X, Y, Z such that X
overlaps Y, Y overlaps Z, but X is disjoint from Z.

Then if we have bobs Bx, By, Bz which hold over the respective time
intervals, and we asserted 

Bx IVPof By

By IVPof Bz

... then transitivity would allow us to derive 

Bx IVPof Bz

... but that is dubious because it would hold only over the temporal
intersection of X and Z, which is empty.

 

I was hoping that the definition of B IVPof A would turn out to require
that the time interval of B was contained in the time interval of A.  I
think that would be a simpler and better-behaved relation, which should
be glorified with a name, even it's not "IVPof".

 

Stephen Cresswell

Tel:  +44 (0) 01603 69 6926

Web:  www.tso.co.uk <http://www.tso.co.uk/> 

 

________________________________

From: public-prov-wg-request@w3.org
[mailto:public-prov-wg-request@w3.org] On Behalf Of Paolo Missier
Sent: 25 July 2011 12:30
To: public-prov-wg@w3.org
Subject: Re: PROV-ISSUE-45: isDerivedFrom and IVPof are transitive.
[Conceptual Model]

 

Khalid

I don't think we have ever agreed on that, but I should really check the
voting history. The latest definition of IVP-of (or complement-of) is
sufficiently precise (i.e., algorithmic) that transitivity follows, but
derivation is purely asserted and as such there is no ground to say that
it is transitive -- unless we say axiomatically that it should be.

-Paolo





 
 
PROV-ISSUE-45: isDerivedFrom and IVPof are transitive. [Conceptual
Model]
 
http://www.w3.org/2011/prov/track/issues/45
<http://www.w3.org/2011/prov/track/issues/45> 
 
Raised by: Khalid Belhajjame
On product: Conceptual Model
 
 
If we agree that "isDerivedFrom" and "IVPof" are transitive, then I
would suggest that this should be specified in the model working draft.
 
khalid



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-- 
-----------  ~oo~  --------------
Paolo Missier - Paolo.Missier@newcastle.ac.uk, pmissier@acm.org 
School of Computing Science, Newcastle University,  UK
http://www.cs.ncl.ac.uk/people/Paolo.Missier


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