Epistemic Issues and Group Knowledge
Rachel Boddy

Abstract:
Formal models for group knowledge can help philosophers gain
additional insight into the ramifications of the philosophical
concepts that they propose by clarifying the abstract properties of
these concepts and their relationship to alternative proposals.  To
date, however, formal treatments of group knowledge have remained
largely disjointed from the related philosophical discussions and are
therefore of minimal interest to philosophers. In this thesis, I
attempt to bridge this gap by proposing a formal definition of group
knowledge that I call collective knowledge. Collective knowledge is
distributed knowledge about common questions and typically lies
between common knowledge and full distributed knowledge. It includes
two epistemic properties that make it more aligned with philosophical
concepts of group knowledge, and that are not modeled by the standard
notions from formal epistemology. The first property is that all
knowledge is in terms of questions, interpreted as distinctions that
define an agent's conceptual framework. The second property is that
group knowledge implies an epistemic group, which is a group of agents
tied together through mutual interest in each other's knowledge and
questions. To model epistemic groups and collective knowledge, I
introduce new Kripke models that I refer to as epistemic group
models. I then present an axiomatic system for the logic of collective
knowledge and prove that it is sound and complete with respect to
these new models. As such, I hope to have provided a good first step
towards a formal definition of group knowledge that can help advance
the philosophical discussion on group knowledge.