  In modal logic, semantic consequence is usually defined locally by truth
preservation at all worlds in all models (with respect to a class of frames).
It can also be defined globally by truth preservation in all models (with
respect to a class of frames). The latter is called global consequence, which
is much less studied than the standard local one. In this paper we first study
the relationship between local and global consequence. Then we give some
correspondence results for global consequence. Finally, we illustrate two
applications of global consequence, connecting it with informational
consequence and update consequence proposed in formal semantics. Some results
in the paper are already known, which are collected in the paper for the sake
of completeness. The others appear to be new. We suggest that global
consequence is not only interesting theoretically, but also useful for
application.
