Many formalisms for reasoning about knowing commit an agent to be logically omniscient. Logical omniscience is an unrealistic principle for us to use to build a real-world agent, since it commits the agent to knowing infinitely many things. A number of formalizations of knowledge have been developed that do not ascribe logical omniscience to agents. With few exceptions, these approaches are modifications of the possible-worlds semantics. In this paper we use a combination of several general techniques for building non-omniscient reasoners. (...) First we provide for the explicit representation of notions such as problems, solutions, and problem solving activities, notions which are usually left implicit in the discussions of autonomous agents. A second technique is to take explicitly into account the notion of resource when we formalize reasoning principles. We use the notion of resource to describe interesting principles of reasoning that are used for ascribing knowledge to agents. For us, resources are abstract objects. We make extensive use of ordering and inaccessibility relations on resources, but we do not find it necessary to define a metric. Using principles about resources without using a metric is one of the strengths of our approach.We describe the architecture of a reasoner, built from a finite number of components, who solves a puzzle, involving reasoning about knowing, by explicitly using the notion of resource. Our approach allows the use of axioms about belief ordinarily used in problem solving – such as axiom K of modal logic – without being forced to attribute logical omniscience to any agent. In particular we address the issue of how we can use resource-unbounded (e.g., logically omniscient) reasoning to attribute knowledge to others without introducing contradictions. We do this by showing how omniscient reasoning can be introduced as a conservative extension over resource-bounded reasoning. (shrink)