Quantifying information in structural representations

The goal of this paper is to show that the information carried by a structural representation can be decomposed into the information carried by its component parts. In particular, the relations between the components of a structural representation carry quantifiable information about the relations between components of their signifieds. It follows that the information carried by cognitive structural representations, including cognitive maps, can in principle be quantified and decomposed. This is perhaps surprising given that the formal tools of communication theory have typically only been applied to simpler representation-like states without significant structure, such as detectors or indicators. In the final section I consider using computational complexity theory to capture the processing advantages afforded by structural representation.