Verifying one hundred prisoners and a lightbulb

This is a case-study in knowledge representation and dynamic epistemic protocol verification. We analyze the `one hundred prisoners and a lightbulb' puzzle. In this puzzle it is relevant what the agents (prisoners) {\em know}, how their knowledge {\em changes} due to {\em observations}, and how they affect the state of the world by {\em changing facts}, i.e., by their actions. These actions depend on the history of previous actions and observations. Part of its interest is that all actions are {\em local}, i.e.\ not publicly observable, and part of the problem is therefore how to disseminate local results to other agents, and make them {\em global}. The various solutions to the puzzle are presented as protocols (iterated functions from agent's local states, and histories of actions, to actions

One Hundred Prisoners and a Lightbulb --- Logic and Computation

This is a case-study in knowledge representation. We analyze the `one hundred prisoners and a lightbulb' puzzle. In this puzzle it is relevant what the agents (prisoners) {\em know}, how their knowledge {\em changes} due to {\em observations}, and how they affect the state of the world by {\em changing facts}, i.e., by their actions. These actions depend on the history of previous actions and observations. Part of its interest is that all actions are {\em local}, i.e.\ not publicly observable, and part of the problem is therefore how to disseminate local results to other agents, and make them {\em global}. The various solutions to the puzzle are presented as protocols (iterated functions from agent's local states, and histories of actions, to actions). The computational aspect is about average runtime termination under conditions of random (`fair') scheduling

On the Logic of Lying

We model lying as a communicative act changing the beliefs of the agents in a multi-agent system. With Augustine, we see lying as an utterance believed to be false by the speaker and uttered with the intent to deceive the addressee. The deceit is successful if the lie is believed after the utterance by the addressee. This is our perspective. Also, as common in dynamic epistemic logics, we model the agents addressed by the lie, but we do not (necessarily) model the speaker as one of those agents. This further simplifies the picture: we do not need to model the intention of the speaker, nor do we need to distinguish between knowledge and belief of the speaker: he is the observer of the system and his beliefs are taken to be the truth by the listeners. We provide a sketch of what goes on logically when a lie is communicated. We present a complete logic of manipulative updating, to analyse the effects of lying in public discourse. Next, we turn to the study of lying in games. First, a game-theoretical analysis is used to explain how the possibility of lying makes games such as Liar's Dice interesting, and how lying is put to use in optimal strategies for playing the game. This is the opposite of the logical manipulative update: instead of always believing the utterance, now, it is never believed. We also give a matching logical analysis for the games perspective, and implement that in the model checker DEMO. Our running example of lying in games is the game of Liar's Dice

Neighbourhood contingency bisimulation

We introduce a notion of bisimulation for contingency logic interpreted on neighbourhood structures, characterise this logic as bisimulation-invariant fragment of modal logic and of first-order logic, and compare it with existing notions in the literature

Reachability of Five Gossip Protocols

Gossip protocols use point-to-point communication to spread information within a network until every agent knows everything. Each agent starts with her own piece of information (‘secret’) and in each call two agents will exchange all secrets they currently know. Depending on the protocol, this leads to different distributions of secrets among the agents during its execution. We investigate which distributions of secrets are reachable when using several distributed epistemic gossip protocols from the literature. Surprisingly, a protocol may reach the distribution where all agents know all secrets, but not all other distributions. The five protocols we consider are called 햠햭햸, 햫햭햲, 햢햮, 햳햮햪, and 햲햯햨. We find that 햳햮햪 and 햠햭햸 reach the same distributions but all other protocols reach different sets of distributions, with some inclusions. Additionally, we show that all distributions are subreachable with all five protocols: any distribution can be reached, if there are enough additional agents

On the Logic of Lying

We look at lying as an act of communication, where (i) the proposition that is communicated is not true, (ii) the utterer of the lie knows (or believes) that what she communicates is not true, and (iii) the utterer of the lie intends the lie to be taken as truth. Rather than dwell on the moral issues, we provide a sketch of what goes on logically when a lie is communicated. We present a complete logic of manipulative updating, to analyse the effects of lying in public discourse. Next, we turn to the study of lying in games. First, a game-theoretical analysis is used to explain how the possibility of lying makes such games interesting, and how lying is put to use in optimal strategies for playing the game. Finally, we give a matching logical analysis. Our running example of lying in games is liar's dice

Epistemic protocols for dynamic gossip

A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. In each call between a pair of connected agents, the two agents share all the secrets they have learnt. In dynamic gossip problems, dynamic connection graphs are enabled by permitting agents to spread as well the telephone numbers of other agents they know. This paper characterizes different distributed epistemic protocols in terms of the (largest) class of graphs where each protocol is successful, i.e. where the protocol necessarily ends up with all agents knowing all secrets