Synthese 195 (10):4581-4615 (
2018)
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Abstract
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 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, and for lying as private announcements to different agents. Detailed examples illustrate our lying concepts.