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