--- a/model/derivation.html	Fri Aug 05 12:49:53 2011 +0100
+++ b/model/derivation.html	Fri Aug 05 12:59:35 2011 +0100
@@ -219,24 +219,31 @@
 
 <p>A process execution independent derivation states the existence of a derivation, by any means whether direct or not, and regardless of any process executions. </p>
 
-<p>A process execution independent derivation, written isEventuallyDerivedFrom (e2, e1)</b> 
+<p>A process execution independent derivation, written <b>isEventuallyDerivedFrom (e2, e1)</b>, 
 <ul>
 <li> refers to an entity <b>e2</b>, denoting the used characterized thing;
 <li> refers to an entity <b>e1</b>, denoting the generated characterized thing;
 </ul>
 
 
-<p>If <b>e2</b> is derived from <b>e1</b>, then 
-this means that the thing represented by <b>e1</b> has an influence on the thing represented by <b>e2</b>, which is captured by a dependency between their attribute values; it also implies temporal ordering. These are specified as follows:</p>
+<p>If <b>e2</b> is derived (isEventuallyDerivedFrom) from <b>e1</b>, then 
+this means that the thing represented by <b>e1</b> has an influence on the thing represented by <b>e2</b>,
+  which at the minimum implies temporal ordering, specified as follows:</p>
 
 <p>Given two entities <b>e1</b> and <b>e2</b>, if the assertion <b>isEventuallyDerivedFrom(e2,e1)</b>
  holds, then:
-that the use
-of characterized thing denoted by <b>e1</b> precedes the generation of
+generation of the characterized thing denoted by <b>e1</b> precedes the generation of
 the characterized thing denoted by <b>e2</b>.
 </p>
 
-<div class='note'>Should we like isEventuallyDerivedFrom to attributes as we did for isDerivedFrom?  If so, this type of inference should be presented upfront, for both.</div>
+<p>Note that temporal ordering is between generations of <b>e1</b>
+and <b>e2</b>, as opposed to process execution linked derivation,
+which implied temporal ordering between the use of <b>e1</b> and
+generation of <b>e2</b>.  Indeed, in the case of
+isEventuallyDerivedFrom, nothing is known about the use of <b>e1</b>,
+since there is no associated process execution.</p>
+
+<div class='note'>Should we link isEventuallyDerivedFrom to attributes as we did for isDerivedFrom?  If so, this type of inference should be presented upfront, for both.</div>
 
 
 
@@ -248,14 +255,20 @@
 <h4>Transitivity</h4>
 
 
-<p>Show why the attributes invalidates transitivity of <b>isDerivedFrom</b>.
+<p>
+If <b>isDerivedFrom(e2,e1)</b> holds because attribute <b>a2.1</b> of <b>e2</b> is determined by attribute <b>a1.1</b> of <b>e1</b>,
+and if <b>isDerivedFrom(e3,e2)</b> holds because attribute <b>a3.1</b>of <b>e3</b> is determined by  attribute <b>a2.2</b> of <b>e1</b>, it is not necessary the case that an attribute of <b>e3</b> is determined by an attribute of <b>e1</b>, so, an asserter may not be able to assert <b>isDerivedFrom(e3,e1)</b>.  Hence, constraints on attributes invalidate transitivit in the general case.
 </p>
 
-<p>The relationship <dfn id="dfn-isDerivedFrom+">isDerivedFrom+</dfn> is the transitive closure of <b>isDerivedFrom</b> and <b>isDerivedFromInMultipleSteps</b>.</p>
+<p>However, there is sense that <b>e3</b> still depends on <b>e1</b>, since <b>e3</b> could not be generated without <b>e1</b> existing. Hence, we introduce a weaker notion of derivation, which is transitive.</p>
 
-
+<p>The relationship <dfn id="dfn-dependsOn">dependsOn</dfn> is defined as follows:
+<ul> 
+<li>If <b>isDerivedFrom(e2,e1)</b> or <b>isDerivedFrom(e2,e1,pe,r2,r1)</b> holds, then <b>dependsOn(e2,e1)</b>.</li>
+<li>If <b>isEventuallyDerivedFrom(e2,e1)</b> holds, then <b>dependsOn(e2,e1)</b>.</li>
+<li>If <b>dependsOn(e3,e2)</b> and <b>dependsOn(e2,e1)</b> hold, then <b>dependsOn(e3,e1)</b>.</li>
+</ul>
 </section>
-
 </section>