True Lies
Thomas {\AA}gotnes, Hans van Ditmarsch, Yanjing Wang

TL;DR
This paper explores the concept of true lies within a logic of announcements, analyzing how false statements can become true upon announcement in belief and knowledge systems, with implications for iterated and private announcements.
Contribution
It provides a formal semantic and syntactic analysis of true lies and announcement interactions in belief and knowledge logics, including iterated and private announcements.
Findings
Characterization of satisfiability and validity of true lies
Analysis of iterated and arbitrarily repeated announcements
Extension to knowledge logic and private announcements
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 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…
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