  Weak ontic necessity is the ontic necessity expressed by ``should'' or
``ought to'' in English. An example of it is ``I should be dead by now''. A
feature of this necessity is whether it holds does not have anything to do with
whether its prejacent holds. In this paper, we present a logical theory for
conditional weak ontic necessity based on context update. A context is a set of
ordered defaults, determining expected possible states of the present world.
Sentences are evaluated with respect to contexts. When evaluating the
conditional weak ontic necessity with respect to a context, we first update the
context with the antecedent, then check whether the consequent holds with
respect to the updated context. The logic is complete. Our theory combines
premise semantics and update semantics for conditionals.
