--- a/model/prov-dm-constraints.html Fri Mar 30 08:52:09 2012 +0100
+++ b/model/prov-dm-constraints.html Fri Mar 30 09:51:30 2012 +0100
@@ -993,6 +993,37 @@
<section id="term-Specialization">
<h3>Specialization</h3>
+
+<p>Specialization is <em>neither reflexive nor irreflexive</em>.</p>
+
+<div class="anexample" id="anexample-specialization-not-reflexive">
+???
+</div>
+
+<div class="anexample" id="anexample-specialization-not-irrreflexive">
+???
+</div>
+
+
+<p>Specialization is <em>neither symmetric nor anti-symmetric</em>.
+</p>
+
+<div class="anexample" id="anexample-not-symmetric">
+"Alice's toyota car on fifth Avenue" is a specialization of "Alice's toyota car", but the converse does not hold.
+</div>
+
+<div class="anexample" id="anexample-specialization-not-anti-symmetric">
+anti-symmetric example???
+</div>
+
+
+<p>Specialization is <em>not transitive</em>. Indeed if <span class="name">specializationOf(e1,e2)</span> holds, then there is some common thing, say <span class="name">e1-2</span> they both refer to. Likewise, if <span class="name">specializationOf(e2,e3)</span> holds, then there is some common thing, say <span class="name">e2-3</span> they both refer to. It does not follow there is a common thing both <span class="name">e1</span> and <span class="name">e3</span> refer to.</p>
+
+<div class="anexample" id="anexample-specialization-not-transitive">
+???
+</div>
+
+
</section>
<section id="term-Alternate">
@@ -1000,19 +1031,39 @@
</section>
- <div class="note">
-In order to further convey the intended meaning, the following properties are associated to these two relations.
+<p>Alternate is <em>reflexive</em>. Indeed, <span class="name">alternate(e,e)</span> holds for any entity <span class="name">e</span> since any entity is always a specialization of another entity.</p>
- <ul>
- <li><span class="name">specializationOf(e2,e1)</span> is <strong>transitive</strong>: <span class="name">specializationOf(e3,e2)</span> and <span
-class="name">specializationOf(e2,e1)</span> implies <span class="name">specializationOf(e3,e1)</span>.
- <li><span class="name">specializationOf(e2,e1)</span> is <strong>anti-symmetric</strong>: <span class="name">specializationOf(e2,e1)</span> implies that <span
-class="name">specializationOf(e1,e2)</span> does not hold.
- <li><span class="name">alternateOf(e2,e1)</span> is <strong>symmetric</strong>: <span class="name">alternateOf(e2,e1)</span> implies <span class="name">alternateOf(e1,e2)</span>.
- </ul>
+<div class="note">
+Is it the case that any entity is always a specialization of another? If no, then this rules out reflexivity.
+</div>
-There are proposals to make alternateOf a transitive property. This is still under discussion and the default is for alternateOf <strong>not</strong> to be transitive, and this is what the current text reflects.</div>
+
+<p>Alternate is <em>symmetric</em>. Indeed, if <span class="name">alternate(e1,e2)</span> holds,
+then there exists an unspecified entity <span class="name">e</span>, such that
+both <span class="name">e1</span> and <span class="name">e2</span> are specialization of <span class="name">e</span>.
+Therefore, <span class="name">alternate(e2,e1)</span> also holds.
+</p>
+
+
+
+<p>Alternate is <em>not transitive</em>. Indeed, if <span class="name">alternate(e1,e2)</span> holds,
+then there exists an unspecified entity <span class="name">e1-2</span>, such that
+both <span class="name">e1</span> and <span class="name">e2</span> are specialization of <span class="name">e1-2</span>.
+Likewise, if <span class="name">alternate(e2,e3)</span> holds,
+then there exists an unspecified entity <span class="name">e2-3</span>, such that
+both <span class="name">e2</span> and <span class="name">e3</span> are specialization of <span class="name">e2-3</span>.
+It does not imply that there is a common entity <span class="name">e1-3</span>
+that both <span class="name">e1</span> and <span class="name">e3</span> specialize.
+</p>
+
+<div class="anexample" id="anexample-alternate-not-transitive">
+<p>
+"Bob's blue car" is an alternate of "Bob's red car" (both specialization of "Bob's car").
+"Bob's red car" is an alternate of "Alice's red car" (both specialization of the "red car in the garage").
+This does not imply that "Bob's blue car" is an alternate of "Alice's red car".
+</div>
+
<div class='issue'>A discussion on alternative definition of these relations has not reached a satisfactory conclusion yet. This is <a