  Existing semantics for answer-set program updates fall into two categories:
either they consider only strong negation in heads of rules, or they primarily
rely on default negation in heads of rules and optionally provide support for
strong negation by means of a syntactic transformation. In this paper we
pinpoint the limitations of both these approaches and argue that both types of
negation should be first-class citizens in the context of updates. We identify
principles that plausibly constrain their interaction but are not
simultaneously satisfied by any existing rule update semantics. Then we extend
one of the most advanced semantics with direct support for strong negation and
show that it satisfies the outlined principles as well as a variety of other
desirable properties.
