SKOS comments: conflict in broader/broaderTransitive and transitivity?

Regarding the SKOS reference at http://www.w3.org/TR/2009/CR-skos-reference-20090317/:

Section 8.1 says:

   ... the propert[y] skos:broader ... [is] not declared as [a] transitive
   propert[y].


However, section 8.3 says:

   skos:broader is a sub-property of skos:broaderTransitive

and:

   skos:broaderTransitive ... [is an] instance[] of owl:TransitiveProperty.

Are subproperties of a transitive property necessarily transitive?  (That is,
in math or in OWL, if a property is transitive, does that imply that any
subproperty of that property is also transitive?)  (I'm more familiar with
class/subclass relationships than property/subproperty relationships.)


If the answer is yes, is there a contradiction between sections 8.3 and
8.1?


Daniel
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