  A true lie is a lie that becomes true when announced. In a logic of
announcements, where the announcing agent is not modelled, a true lie is a
formula (that is false and) that becomes true when announced. We investigate
true lies and other types of interaction between announced formulas, their
preconditions and their postconditions, in the setting of Gerbrandy's logic of
believed announcements, wherein agents may have or obtain incorrect beliefs.
Our results are on the satisfiability and validity of instantiations of these
semantically defined categories, on iterated announcements, including
arbitrarily often iterated announcements, and on syntactic characterization. We
close with results for iterated announcements in the logic of knowledge
(instead of belief), and for lying as private announcements (instead of public
announcements) to different agents. Detailed examples illustrate our lying
concepts.
