We can reason about theories, as well as in them.  Many natural
  phenomena can be captured by theories, often by introducing a
  modality, true just of the theory.  Rather than treat these
  phenomena as the sentences true in this modality, we can treat the
  entire theory or modality as an object.  This point of view was
  proposed by McCarthy, who proposed calling these reified modalities
  contexts.
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<P>
  Contexts, viewed as theories or modalities, have structural
  properties, and associated natural structural operations, such as
  union and intersection.  These structural properties are most
  naturally captured by an algebra, a set of operations that can be
  applied to contexts to form new contexts.
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<P>
  We introduce an algebra, reminiscent of relation or dynamic algebra,
  but which acts on modalities, not relations.  This algebra allows us
  to construct new modalities from simpler modalities.  We use the
  natural correspondence between a modality and the underlying
  accessibility relation.  The operations on modalities are induced by
  operations on the underlying relations.
</P>
<P>
  Thus we have a larger space of modalities than just those that are
  explicitly named.  We add quantifiers that range over modalities, so
  that we can state propositions like, ``no context with the property
  <I>P</I> exists'', or ``all contexts obey <I>Q</I>''.  We give an
  axiomatization of these quantifiers which we show is complete with
  respect to a natural semantics.