  Over the years, nonmonotonic rules have proven to be a very expressive and
useful knowledge representation paradigm. They have recently been used to
complement the expressive power of Description Logics (DLs), leading to the
study of integrative formal frameworks, generally referred to as hybrid
knowledge bases, where both DL axioms and rules can be used to represent
knowledge. The need to use these hybrid knowledge bases in dynamic domains has
called for the development of update operators, which, given the substantially
different way Description Logics and rules are usually updated, has turned out
to be an extremely difficult task.
  In [SL10], a first step towards addressing this problem was taken, and an
update operator for hybrid knowledge bases was proposed. Despite its
significance -- not only for being the first update operator for hybrid
knowledge bases in the literature, but also because it has some applications -
this operator was defined for a restricted class of problems where only the
ABox was allowed to change, which considerably diminished its applicability.
Many applications that use hybrid knowledge bases in dynamic scenarios require
both DL axioms and rules to be updated.
  In this paper, motivated by real world applications, we introduce an update
operator for a large class of hybrid knowledge bases where both the DL
component as well as the rule component are allowed to dynamically change. We
introduce splitting sequences and splitting theorem for hybrid knowledge bases,
use them to define a modular update semantics, investigate its basic
properties, and illustrate its use on a realistic example about cargo imports.
