Hierarchy in Cognitive Maps and the Simplicity Principle

The aim of this paper is to relate the research on cognitive maps, mental representations of the external world, which are thought to be organized hierarchically, with the simplicity principle, a formal version of Occam’s Razor inductive bias, which states that short hypotheses are to be preferred over longer ones. First, I will describe some important properties of hierarchical structures and define what is meant by simplicity. Next, I will review some results supporting the view that cognitive maps are structured hierarchically, not following Euclidean metrics, and that some cognitive functions seem to prefer simpler representations over complex ones. This hints at the possibility that the hierarchical organization of cognitive maps may also follow the simplicity principle. Finally, I will suggest an experiment in which such hypothesis could be tested and discuss the implications and limitations of integrating both approaches. 1 What are hierarchies and why are they important? Hierarchies are ordered structures of objects arranged over several distinct levels. Individuals at the same level share common properties and are related to each other through a partial ordering relation. Ob∗Master of Logic, n.: 0127019 jects at higher levels are more abstract than objects at lower levels, which are more detailed. Hierarchical organizations seem to fit naturally spatial representations, such as Geographic Information Systems (Timpf, 1998). But it can also appear in non-spatial contexts, such as systems theory (Pattee, 1973) and biology (Braitenberg, 1984). An important assumption in Hierarchy Theory is that the behavior of the whole system can be determined by the sum of the individual behaviors of smaller subsystems. Grouping objects in a hierarchical fashion presents some advantages. It allows decomposing a complex task into many independent subtasks, reducing the combinatorial costs of designing large abstract plans from primitive operators (Russell and Norvig, 1995). Suppose that the problem at hand is to build a house. In this case, the abstract plan Buildthe-House could be decomposed into less abstract subtasks including, for instance, Build-the-Roof and Build-the-Floor. The only requirements for this abstract plan are consistency and completeness. Such an abstraction, however, does not entail the actual building of the house, since the agents responsible for the primitive operations cannot act directly on abstract operators. To do so, the task must be gradually decomposed until it produces primitive operators like Hammer(nail). By breaking down tasks into manageable bits, hierarchical decomposition enhances the potential for parallel processing. In other words, systems organized hierarchically may simulate features of parallel distributed architectures. This property of hierarchical organizations already hints