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

Date: Thu, 15 Dec 2011 18:19:15 +0000

Message-ID: <4EEA3A23.8040304@zoo.ox.ac.uk>

To: Paolo Missier <Paolo.Missier@ncl.ac.uk>, W3C provenance WG <public-prov-wg@w3.org>

Date: Thu, 15 Dec 2011 18:19:15 +0000

Message-ID: <4EEA3A23.8040304@zoo.ox.ac.uk>

To: Paolo Missier <Paolo.Missier@ncl.ac.uk>, W3C provenance WG <public-prov-wg@w3.org>

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. #gReceived on Thursday, 15 December 2011 18:23:30 UTC

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