Logics of Communication and Knowledge
Floor Sietsma
Abstract:
The goal of this dissertation is to give a logical representation of the
knowledge dynamics that takes place during communication. I present a
number of different logical frameworks for a number of different scenarios,
ranging from an email conversation where all information that is sent is
considered to be true, to a game of Liar~s Dice where lying is expected of
the players.
In Chapter 3, I present a framework for modeling the knowledge of agents
who exchange messages, using Dynamic Epistemic Logic. This framework uses
Kripke models to represent the agents~ knowledge in a static situation, and
action models to update these Kripke models when the situation changes.
Because the models are supposed to be finite, and all messages are
represented explicitly in the model, the messages that are considered
possible by the agents are limited to a finite set. This framework is
useful in a situation in which there is a number of rounds in each of which
a finite set of new messages becomes available to the agents. These
messages can gradually be added to the model.
The framework presented in Chapter 4 is of a more general nature. It models
a setting where agents communicate with messages over a specific network in
accordance to a certain protocol. This framework is very flexible because
the nature of communicative events and the observational power of the
agents can be adapted to the situation at hand. It combines properties of
the Dynamic Epistemic Logic approach with the perspective of Interpreted
Systems.
In Chapter 5 and 6 I focus on email communication specifically. I first
study the existence of common knowledge in a group of agents who
communicate via emails. Unlike the approach presented in Chapter 3, all
possible emails are represented in the model, which is therefore of
infinite size. I prove a number of properties of finite states in this
infinite model, and show that common knowledge of an email with BCC
recipients is rare.
Apart from common knowledge, I consider two new kinds of knowledge:
potential and definitive knowledge. These two types of knowledge make a
distinction between the assumption that every agent immediately reads every
email he receives, or that every agent has only read the emails he replied
to or forwarded. I also present a method to do model checking, even though
the model is of infinite size.
Chapter 7 is a study of the properties of action models, which are used to
model communicative events. I define a notion of action emulation that
signifies when two canonical action models are equivalent. Because every
action model has an equivalent canonical action model which can be
computed, this gives a general method to determine action model equivalence.
In Chapter 8 I move from knowledge to belief. I use the same Kripke models
as for knowledge, only without the assumption that all relations are
equivalence relations. I propose a different assumption, namely that the
relations are linked. I also give a number of updates of these models that
preserve this property, representing communicative events.
Finally, Chapter 9 gives different perspectives on the issue of lying. It
includes a complete logic of manipulative updating, which can be used to
represent the effects of lying in a group of agents. I also analyze a game
of Liar~s Dice and implement this scenario in the model checker DEMO.
Furthermore, I show that in a game where lying is considered normal, a lie
is no longer a lie: because the agents who hear the lie do not believe it,
no false belief is created.