A. U. Frank. Spatial Cognition II (International Workshop on Maps and Diagrammatical Representations of the Environment, Hamburg, August 1999), volume 1849 of Lecture Notes in Computer Science, chapter Spatial Communication with Maps: Defining the Correctness of Maps Using a Multi-Agent Simulation, pages 80–99. Springer-Verlag, Berlin, 2000. [url]
This paper present an approach to defining the correctness of a map using two agents, one that explore a given real environment and produce a representation of it (literally a map). The second agent reads the map and try to navigate the real space using that information. The interaction between the two agents is logged and measured to track errors in communication, and evalued to proof the Correctness (the success in navigating the environment) and the effectiveness (the size of different representations to communicate the same information) of the map.
Map-maker and map-user can make mistakes in the perception and form erroneus beliefs about the environment. Simulated agents observe the environment and form a set of beliefs about it, which may be incomplete, imprecise or even wrong. The agents can produce artifacts, which represent their knowledge.
The author define then the homomorphism, as the correspondence between the agent’s beliefs and the environments, where objects and operations are set into correspondance.