Knowledge, Logical Omniscience, and Resource-bounded Reasoning

Agent theories typically use modal epistemic logic for modeling knowledge of agents. Since the modal approach to epistemic logic cannot formalize resource-bounded reasoning adequately, it it not suited to describe realistic, implementable agents. We develop a framework for solving that problem. We introduce the notion of algorithmic knowledge — a concept that establishes a direct link between and agent’s available resources and his knowledge. We show that our concept of knowledge is useful for modeling resource-bounded agents. Moreover, because a resource-bounded agent is naturally not logically omniscient, all variants of the logical omniscience problem are solved intuitively within our framework.