Modal Logic via Global Consequence

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