--- a/model/ProvenanceModel.html	Thu Jul 21 12:00:17 2011 +0100
+++ b/model/ProvenanceModel.html	Thu Jul 21 14:39:45 2011 +0100
@@ -560,13 +560,27 @@
 </section>
 
 
-<section id="concept-IVPOf">
+<section id="concept-complementOf">
 
-<h3>IVP of</h3>
+<h3>Complement of</h3>
 
-<p><dfn id="dfn-IVPof">IVP of</dfn> is a relationship between two characterized entities asserted to have compatible characterization over some continuous time interval. Compatibility is based upon a partial mapping amongst attributes used in the BOBs used to represent the characterization (the identity mapping is a special case whereby the Bobs share some of the attributes). 
+<div class="note">This intends to replace the relation previously known as "IPV of"</div>
 
+<p><dfn id="dfn-complementOf">Complement of</dfn> is a relationship between two characterized entities asserted to have compatible characterization over some continuous time interval.
+
+The rationale for introducing this relationship is that in general, at any given time there will be multiple representations of a characterized entity, which are reflected in assertions possibly made by different asserters. In the example that follows, suppose entity "Royal Society" is represented by two asserters, each using a different set of attributes. If the asserters agree that both representations refer to "The  Royal Society", the question of whether any correspondence can be established between the two representations arises naturally. This is particularly relevant when (a) the sets of properties used by the two representations overlap partially, or (b) when one set is subsumed by the other. In both these cases, we have a situation where each of the two asserters has a partial view of "The  Royal Society", and establishing a correspondence between them on the shared properties is beneficial, as in case (a) each of the two representation <em>complements</em> the other, and in case (b) one of the two (that with the additional properties) complements the other.
+
+This intuition is made more precise by considering the BOBs that embody the representation of a characterised entity at a certain point in time. A BOB, as defined above, exists only as long as all of its attributes do not change their value. As soon as one attribute, say X changes value, say from v1 to v2, the BOB no longer exists and is replaced by a new one in which X=v2. Thus, if we overlap the timelines (or, more generally, the sequences of value-changing events) for the two characterised entities, we can hope two establish correspondences amongst the BOBs that represent them at various points along that events line. Fig. TBD-fig3. illustrates this intuition.
+
+Relation <em>complement-of</em> between two BOBs is intended to capture these correspondences, as follows. Suppose BOBs A and B share a set P of properties, and each of them has other properties in addition to P. If the values assigned to each property in P are <em>compatible</em> between A and B, then we say that <em>A is-complement-of B</em>, and <em>B is-complement-of A</em>, in a symmetrical fashion. In the particular case where the set P of properties of B is a struct superset of A's properties, then we say that <em>B is-complement-of A</em>, but in this case the opposite does not hold. In this case, the relation is not symmetric.  (as a special case, A and B may not share any attributes at all, and yet the asserters may still stipulate that they are representing the same entity "Royal Society". The symmetric relation may hold trivially in this case).
+
+The term <em>compatible</em> used above means that a mapping can be established amongst the values of attributes in P and found in the two BOBs. This is generalizes to the case where attribute sets P1 and P2 of A, and B, respectively, are not identical but they can be mapped to one another. The simplest case is the identity mapping, in which A and B share attribute set P, and furthermore the values assigned to attributes in P match exactly.
+
+It is important to note that the relation holds only as long as the BOBs involved are valid. As soon as one attribute changes value in one of them, new correspondences need to be found amongst the new BOBs. Thus, the relation has a validity span that can be expressed in terms of the event lines of the entity.
+
+<!--
 The "IVP of" relationship is designed to represent pairs of BOBs that correspond to each other. By their own nature, a BOB remains valid only as long as all of its attributes do not change their value. It follows that the correspondence "B IVP of A" is only valid within the time interval during which such invariance property holds for both A and B. When any of the property values change in either A or B, those BOBs are replaced by new ones, and a new correspondence may be established. Thus, "IVP of" is defined relative to the intersection of the temporal intervals for which A and B are valid.
+-->
 </p>