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I've just completed a relatively careful terminology pass over the
concepts file, paying close attention to superclass, direct superclass
etc. The term I really miss having and which makes for a lot of wording
headaches, is ``superclass or equal,'' a parallel to ``less than or
equal.''  This is Moon's superclass^n, n non-negative.  I believe the
proper term in lattice theory is ``filter.'' That is, the class itself and
all its superclasses form a filter over the set consisting of that
singleton class.  This is not very intuitive (plus, I might be wrong).

The reason that ``superclass'' is not a misnomer as ``component''
might be is that it is abstract, meaning exactly that is it a
class that is the direct ancestor of the class, or the direct
ancestor of the direct ancestor, etc. That is, it is too abstract to
have an intuitive meaning outside of the hierarchy (sic).