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Re: viewOf / complementOf discussion in 201-12-15 telecon

From: Graham Klyne <Graham.Klyne@zoo.ox.ac.uk>
Date: Fri, 16 Dec 2011 10:44:59 +0000
Message-ID: <4EEB212B.4090902@zoo.ox.ac.uk>
To: Paolo Missier <Paolo.Missier@ncl.ac.uk>
CC: Paolo Missier <paolo.missier@newcastle.ac.uk>, W3C provenance WG <public-prov-wg@w3.org>
Paolo,

Summary:  I think we are converging here.  Your revised text is looking pretty 
good to me, modulo small details and nits.

...

Rather than respond to your email, I'll comment on your updated document:

Section 5.3.3.3

"1. e2 provides a more concrete characterization of Bob than e1 does" - I don't 
see this.  Did you mean e2 (Bob+twitter) more concrete than e3 (Bob+person)?

"foobar(B,A) is transitive: foobar(C,B) and foobar(B,A) implies foobar(C,A)."  I 
think it's only transitive if you do not require any overlap for [foobar].

"entity records may only be valid within certain events interval".  Nit: should 
this be something like "entity records may only be valid within certain a 
event's interval"?

"Let val(e) denote the validity interval of e."  Nit:  I find the choice "val(e) 
potentially confusing; too much like "value", would prefer "validity".  Also, is 
there any danger of confusion with logical validity?  (I think not, just asking.)

The main difference between your revised proposal and mine that I see is your 
appeal to the validity interval where I appeal to an instances set.  But at the 
level of abstraction stated, I think they are formally different by just a 
change of name - your "val" performs the same role as my "instances".  The 
difference is in "val"s intuitive appeal to a time interval, which I can live 
with (as in voting "-0") as I think this is the main case we'll come across in 
practice.

<aside>
I did, however finally come up with a practical example for "viewOf" that is not 
based on time intervals.  It comes from representations of workflows.

Suppose one has a workflow template that may specify some resources to be used, 
but leaves others open to specification (inputs, parameters, etc.).  Then 
suppose one derives a new workflow that uses the original but specifies some of 
the previously unspecified inputs.  (In functional programming terms, this would 
be like partial function application.)  One might claim that, for provenance 
purposes, the more specific workflow is a viewOf the original workflow.
</aside>

The remaining question, then, would be whether or not we want to formalize the 
relationship between viewOf and [foobar] as I have suggested, by defining 
[foobar] in terms of viewOf?

I think that any further formalization of viewOf (and the rest) can be dealt 
with in James' semantics document.  I think that's also what you are suggesting 
in your reference to a model theoretic interpretation?

#g
--


On 15/12/2011 18:49, Paolo Missier wrote:
> Graham,
>
> I guess while you were typing this, I was typing a new much simplified version
> of what I had in the PROV-DM internal draft, trying to capture the comments I
> heard.
> So my take is independent from yours, however I don't think they are far apart
> at all.
>
> I am basically suggesting to have two relations, viewOf and "foobar" (I am
> deliberating avoiding the term "complement"), which together attempt to capture
> intuitions that I believe reflect your (1) and (2) below.
>
> Then I am suggesting to saddle them with the properties (transitivity, symmetry)
> that we need to reflect their intended meaning -- again, I see no controversy,
> although you set (1) as non-transitive. fine by me if the others agree.
>
> Then I say that /if/ validity intervals are known, /then/ a containment
> condition is necessary in order to preserve transitivity (at least in your case
> (2)).
>
> That's it. You go further by suggesting a model-theoretical interpretation. I
> think this is a promising start but it belongs to a broader semantic model where
> the interpretation is grounded in some domain where concepts like "isAbout" are
> well-defined, as you point out.
>
> The result is here:
> http://dvcs.w3.org/hg/prov/raw-file/default/model/ProvenanceModel.html#record-complement-of
>
>
> Cheers,
> -Paolo
>
>
>
>
> On 12/15/11 6:19 PM, Graham Klyne wrote:
>> Paolo, and all,
>>
>> Re: viewOf / complementOf discussion in 201-12-15 telecon
>>
>> Prompted by discussion in today's teleconferences, and in particular by Paolo's
>> articulation of the intuition behind "complementOf" (as was), here are some
>> thoughts...
>>
>> It seems we have two competing intuitions, yet much of the contention is about
>> naming and how to formalize or otherwise define them. So I'd like to take the
>> following approach:
>>
>> 1. describe the intuitions, with examples
>>
>> 2. assign names to the intuitions
>>
>> 3. discuss the extent to which they can be formalized, and how
>>
>>
>> == Two intutiions ==
>>
>> 1. two entities that are constrained forms of the same real-world object; e.g.
>> (a) Bob as Twitter account holder
>> (b) Bob as Facebook account holder
>> or
>> (a) Luc in Boston
>> (b) Luc in Southampton
>>
>> I think this intuition is clearly symmetric and not, in general, transitive.
>>
>> The intuition has been further constrained in some discussions as requiring some
>> overlap between the two entities, so the first example might apply, but the
>> second would not.
>>
>> 2. an entity that is a constrained form of some other entity; e.g.
>> (a) Luc in his office
>> (b) Luc in Southampton
>> or
>> (a) Luc in Southampton
>> (b) Luc through his lifetime
>> or
>> (a) Luc in Boston
>> (b) Luc through his lifetime
>> or
>> (a) Bob as a Twitter account holder
>> (b) Bob as a computer user
>>
>> This intuition is transitive non-symmetric.
>>
>>
>> == Naming ==
>>
>> For me, the name "complementOf" applies reasonably to the first intuition about
>> two entities that are some facet of the same real-world entity.
>>
>> The term "viewOf" applies to the second intuition.
>>
>> I'll use these terms for the discussion that follows.
>>
>>
>> == Formalization ==
>>
>> What can we say about these?
>>
>> Notation used below:
>> ':' such that
>> '==' defined as
>> '=>' implies (logical implication)
>> '|=' entails
>>
>> === complementOf ===
>>
>> We might capture the intuition thus:
>>
>> complementOf(a, b0 == exists r : isRealWorldThing(r) and
>> isAbout(a, r) and isAbout(b, r)
>>
>> but this begs a formalization of isRealWorldThing and isAbout
>>
>> Previously, there was an appeal to attributes, but that seems somewhat
>> arbitrary, and for me not directly reflecting the original intuition.
>>
>> (I'm not sure where to go from here.)
>>
>>
>> === viewOf ===
>>
>> I start by suggesting that an entity denotes a set of instances. Thus, when we
>> talk about "Luc in Boston", we mean the set of all (instantaneous) instances of
>> Luc for which Luc is in Boston. This is presumed to be a primitive assertion
>> (rather like a primitive class in a Description Logic).
>>
>> For some entity a, let us call this set instances(a) (somewhat as RDF formal
>> semantics introduces a class extension ICext(c) to denote the members of a
>> class c)
>>
>> Then we can formalize
>> viewOf(a, b) == forall(x) : x in instances(a) => x in instances(b)
>>
>> A corollory of this would be that if a provenance assertion A[p](a) is an
>> assertion about a using some predicate p such that:
>>
>> A[p](a) == forall(x) : x in instances(a) => p(a)
>> (i.e. A[p] asserts that p is true for all instances of a, which
>> captures the original notion we discussed months ago that
>> provenance assertions are invariant with respect to an entity)
>>
>> then
>>
>> viewOf(a, b) |= A[p](a) => A[p](b)
>>
>> I think the transitivity of viewOf follows from the above.
>>
>>
>> === viewOf and complementOf ===
>>
>> Given this formalism of viewOf, I think it is now possible to propose a more
>> complete formalism of complementOf:
>>
>> complementOf(a, b) == exists(x) : viewOf(x, a) and viewOf(x, b)
>>
>> <aside>
>> Note that the existential x here replaces the need for the predicate
>> isRealWorldThing, but is not necessarily itself a real world thing, whatever
>> that may be. We might try and define isRealWorldThing thus:
>>
>> isRealWorldThing(x) == not exists(y) : isView(x, y)
>>
>> so one might say that real world things are anything that sit at the top of the
>> isView hierarchy.
>>
>> Similarly, one might also define:
>> isAbout(a, b) == viewOf(a, b)
>> </aside>
>>
>> This definition of complementOf does not capture the notion of overlap between
>> complements. But we could do that too, if needed, e.g.
>>
>> strictComplementOf(a, b) == complementOf(a, b) and
>> exists(x) : viewOf(x,a) and viewOf(x,b)
>>
>>
>> == Conclusion ==
>>
>> I believe this substantiates my previous claim that viewOf is somehow more
>> fundamental. Based on just a simple set-theoretic definition of viewOf, I have
>> been able to construct a formal definition of complementOf. But I don't believe
>> it would be as easy to construct a primitive definition of complementOf and use
>> just that to define viewOf.
>>
>>
>> #g
>
>
Received on Friday, 16 December 2011 10:46:34 UTC

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