From: Paolo Missier <Paolo.Missier@ncl.ac.uk>

Date: Thu, 15 Dec 2011 18:49:36 +0000

Message-ID: <4EEA4140.5060105@ncl.ac.uk>

To: Graham Klyne <graham.klyne@zoo.ox.ac.uk>

CC: Paolo Missier <paolo.missier@newcastle.ac.uk>, W3C provenance WG <public-prov-wg@w3.org>

Date: Thu, 15 Dec 2011 18:49:36 +0000

Message-ID: <4EEA4140.5060105@ncl.ac.uk>

To: Graham Klyne <graham.klyne@zoo.ox.ac.uk>

CC: Paolo Missier <paolo.missier@newcastle.ac.uk>, W3C provenance WG <public-prov-wg@w3.org>

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 -- ----------- ~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.MissierReceived on Thursday, 15 December 2011 18:50:00 UTC

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