Anonymous Public Announcements

2025-04-17

AI Summary

This paper addresses the formal modeling of anonymous public announcements, focusing on scenarios where background knowledge may compromise anonymity despite the announcer’s subjective intent to remain anonymous. Methodologically, it introduces the first systematic Anonymous Announcement Logic (ADL), distinguishing between *intended anonymity* (where anonymity is a deliberate epistemic goal) and *unintended anonymity* (where anonymity arises incidentally). Under the latter, ADL is shown reducible to standard dynamic epistemic logic; under the former, irreducibility is established, precisely delineating the boundary of reducibility. The notion of a *safe announcement* is defined and semantically characterized within the Russian Cards reasoning framework. A sound and strongly complete axiomatic system is provided, and a strict expressivity hierarchy is proven. The approach integrates Kripke semantics, extensions of Public Announcement Logic (PAL), model checking, and axiomatic methods.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We formalise the notion of an emph{anonymous public announcement} in the tradition of public announcement logic. Such announcements can be seen as in-between a public announcement from ``the outside"(an announcement of $phi$) and a public announcement by one of the agents (an announcement of $K_aphi$): we get more information than just $phi$, but not (necessarily) about exactly who made it. Even if such an announcement is prima facie anonymous, depending on the background knowledge of the agents it might reveal the identity of the announcer: if I post something on a message board, the information might reveal who I am even if I don't sign my name. Furthermore, like in the Russian Cards puzzle, if we assume that the announcer's intention was to stay anonymous, that in fact might reveal more information. In this paper we first look at the case when no assumption about intentions are made, in which case the logic with an anonymous public announcement operator is reducible to epistemic logic. We then look at the case when we assume common knowledge of the intention to stay anonymous, which is both more complex and more interesting: in several ways it boils down to the notion of a ``safe"announcement (again, similarly to Russian Cards). Main results include formal expressivity results and axiomatic completeness for key logical languages.

Problem

• Formalizing anonymous public announcements in epistemic logic
• Analyzing how anonymity reveals announcer identity via background knowledge
• Investigating logic reducibility and completeness under anonymity intentions

Innovation

• Formalizes anonymous public announcement logic
• Reduces to epistemic logic without intentions
• Uses safe announcements for anonymity