The Dynamics of Group Knowledge and Belief

Thomas Agotnes
University of Bergen/Southwest University


ABSTRACT:
Principles of reasoning about group knowledge and belief have received attention over the past decade, in particular in the context of reasoning about the dynamics of interaction. In the talk I will review some of this work, hopefully provide some new insights, and pose some open problems. I will focus on formalisations in modal logic.

What we mean when we say that a group knows something can be radically different depending on context. Well-known notions of group knowledge that have been proposed in the literature include general knowledge (everybody-knows), distributed knowledge, common knowledge, relativised common knowledge. What group belief is, however, is murkier. Applying the same definitions to belief, group belief is not actually always belief. The existence of group belief depends on the particular properties one assumes of belief, and I will map out different possible notions of group belief under different notions of belief. I will also discuss intermediate notions of group belief between distributed and common belief.

Moving to dynamics, we first look at the consequences of adding new group knowledge operators to dynamic epistemic logics such as public announcement logic and action model logic. The relationship between distributed and common knowledge har been of special interest in the dynamic setting, an intuitive idea being that distributed knowledge is potential common knowledge. However this idea is clearly false: it is possible to have distributed knowledge of a Moore-like sentence, which can never even become individual knowledge. I will discuss a dynamic operator that exactly captures what is true after the group have shared all their information with each other; this is what we call resolving distributed knowledge. Intuitions about group knowledge, such as the one just mentioned, are often related to group ability; which states of knowledge a group can make come about. I will thus discuss group knowledge first in the context of general group ability operators such as those found in Alternating-time Temporal Logic and Coalition Logic, and then circle back to dynamic epistemic logics again and discuss cases where ability means ability to achieve some state of knowledge by using public announcements. I will have something to say about how all these different static and dynamic takes on group knowledge and belief are tied together.