In this thesis, I develop a novel framework for quantifying the information dynamics of brain-body-environment systems, and demonstrate its application to several model agents. I begin by extending one of the core concepts of information theory--the mutual information--into a new method for decomposing informational relationships between multiple variables, called partial information decomposition. Then, using partial information decomposition as the theoretical backbone, I derive techniques for quantifying the flow of information both within and between the components of a brain-body-environment system. Finally, I apply these techniques to analyze specific examples of embodied cognitive behavior, analyzing model agents that perform a simple relational comparison task between two visually presented objects. I explore questions such as how these agents extract and store information about individual objects, and how they integrate information about different objects. Among other key findings, this analysis shows how agents utilize their bodies to actively elicit and structure information from their environments, and use their bodies as extra degrees of freedom to store and process information, illustrating some of the unique ways that embodiment can influence intelligent behavior. |