True Lies
This work addresses foundational problems in formal logic and multi-agent systems, focusing on how announcements affect truth and belief, but it is incremental as it builds on existing logical frameworks.
The paper investigates the concept of 'true lies'—lies that become true when announced—within Gerbrandy's logic of believed announcements, exploring interactions between announced formulas, preconditions, and postconditions, with results on satisfiability, validity, iterated announcements, and syntactic characterizations.
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.