Fuzzy cognitive maps over possible worlds

Generally we represent the knowledge of an intelligent agent (expert, robot, controller, and others) through graphs, fuzzy cognitive maps, knowledge maps, belief networks, probabilistic influence diagrams, and others. However, when we have a group of robots or a set of experts, in other words, a collection of intelligents agents, where each has a graph, fuzzy cognitive map, ..., there are no formal techniques to specify different levels of knowledge. The purpose of this paper is to introduce a formal technique to represent different types of knowledge in a group of agents. An appropriate causal learning law for inductively inferring fuzzy cognitive maps (FCM) from data is differential Hebbian law, which modifies causal connections by correlating time derivatives of FCM node outputs. An FCM describes causal relations between concepts, and are a form of knowledge representation far better than standard decision trees with graph search usually used in expert systems. In this article FCMs model the possible-worlds as a collection of classes and causal relations between classes. Our objective is to introduce a, novel form of knowledge acquisition using operators of modal logic of knowledge and belief and fuzzy cognitive maps