Reason to Believe
Chenwei Shi

Abstract:
We are confronted with new information all the time. The information
we face and on which our beliefs are based, is often chaotic,
disordered, and even contradictory. Yet at the same time, our belief
is expected to be consistent. At least, we strive for consistent
beliefs. Is it possible for us to achieve and maintain consistency in
our beliefs? If yes, how do we manage to extract consistent belief
from inconsistent information?  We attempt to answer these questions
from a logician's perspective, borrowing ideas and techniques from
other fields, for example, topology, formal argumentation theory,
non-monotonic reasoning and Markov chain theory.

The dissertation is structured around two topics -- single-agent
belief and group belief. For both a single agent and a group of
agents, we take belief formation as a process of resolving the
inconsistency in its basis.  The difference is that in the case of a
single agent, evidence is taken as the basis of her belief and in the
case of a group of agents, each group member's belief is taken as the
basis of the group's belief.

For a single agent, we understand the process of resolving conflicts
between different pieces of evidence to be the agent's reasoning. Two
forms of reasoning are investigated -- argumentational reasoning and
default reasoning. The problem thus becomes how the agent coordinates
her default reasoning and argumentational reasoning to achieve full
consistency in her beliefs. We employ the topological semantics for
evidence, formal argumentation theory and non-monotonic reasoning to
tackle the problem and study the logic of the resulting notions of
belief and their relationship with evidence.

For group belief, we investigate two ways of resolving conflicts
between the different group members' beliefs. One is based on
argumentation, and the other is opinion diffusion by social influence.
We model these two forms of "group reasoning" by combining the Kripke
semantics with formal argumentation theory and Markov chain theory
respectively, which paves the way for our logical analysis of the
notions of group belief based on them.

Throughout the whole dissertation, the recurrent theme is a tension
between believing more and believing more consistently. We demonstrate
that in the case of a single agent, it is possible to strike a balance
in a meaningful way.  For group belief, nonetheless, besides its
amount of content and consistency, we also need to consider whether
the aggregation of the group members' beliefs is democratic enough.
So, the tension is between believing more, believing more
consistently, and believing more democratically. Our proposals
exemplify possible ways of relieving this tension.