True Lies

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 lying concepts.