A Logical Account of Causal and Topological Maps

Abstract

We consider the problem of how an agent creates a discrete spatial representation from its continuous interactions with the environment. Such representation will be the minimal one that explains the experiences of the agent in the environment. In this paper we take the Spatial Semantic Hierarchy as the agent’s target spatial representation, and use a circumscriptive theory to specify the minimal models associated with this representation. We provide a logic program to calculate the models of the proposed theory. We also illustrate how the different levels of the representation assume different spatial properties about both the environment and the actions performed by the agent. These spatial properties play the role of “filters” the agent applies in order to distinguish the different environment states it has visited.