A Revised Version: Belief Revision and Epistemic Acts
Jonathan Zvesper

Abstract:

This thesis is about mathematical models for representing changes in
beliefs of groups of agents.

We do not offer directly an analysis of what a belief is. Instead we
take as a natural starting point that a belief is something which an
agent accepts as true. A richer view of belief than this 'binary' one
will in effect be presented, but to repeat: This can only indirectly
be read as an analysis of what a belief is.

One important theme of this thesis is the status of the triggers of
belief changes, as what have been called 'epistemic actions'; for
example actions of observation or of communication.

There is no principal question or thesis to this thesis. Different
ways to represent the richness of belief states in a multi-agent
setting are explored, and the theme of epistemic actions recurs. A
number of original technical results are presented1. Each of §3 - 7
offer, in lieu of a conclusion2, though not necessarily exclusively at
the end of each chapter, some precisely demarcated directions for
future research.

In §2, we start by introducing the domain of belief revision in the
single-agent case, and where the information involved in the revision
does not concern the agent's epistemic states. We explain the
inadequacy of this approach for the multi-agent and introspective
cases. We then summarise some logics for reasoning about knowledge
changes in groups of agents that overcome those inadequacies in the
case of knowledge change. At the end of the chapter we introduce a
basic semantic framework (of orderings over interpretations) that
enriches the binary view of belief states, and which will recur in
future sections of the thesis.

In §3, we consider one topic of multi-agent belief revision, viz. the
merging of belief states when these are considered purely from the
semantic perspective. The topic for further research is to give a full
syntactic account of such mergings. We will propose some initial
thoughts, and some quite concrete things, in that section.


Then in -b§4, we consider some logical languages that bring together the-A
various parts of the first chapter. That is, they express beliefs and
changes in beliefs amongst groups of agents. We provide a completeness
proof, in -b§5, of a new logic introduced in that chapter.-A

In -b§6 we discuss an algebraic approach to multi-agent belief-A
revision. Those algebraic structures enable us (the modelers) to model
agents revising their theories with respect to the epistemic actions
themselves, and not just with respect to the way the world is.

When reasoning about epistemic actions in the context of beliefs
rather than knowledge, even more pragmatic reasoning about those
actions might take place, and this is a useful way to start modeling
that reasoning. We discuss this issue in -b§7, where we consider how to-A
model those additional aspects to the reasoning that agents might make
about actions. That last chapter is the most diaphanous: It is rather
speculative, with no concrete results, and is included mainly as a
pointer to other things which are possible in the context of reasoning
about belief change.s

Keywords: