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Minus 1a5aa4f1c08b567c9107cba729de26bc87c17ab2b2f690eb45059193a1d6f587 Using Abstract Resources to Control Reasoning
Weyhrauch, R. W. and Cadoli, M. and Talcott, C. L. - 1998

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 don’t 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, by using reification, 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 \it 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 on resources. Using principles about resources without assigning 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 ordinarily used in problem solving –such as axiom \bf K of modal logic about belief– without being forced to attribute logical omniscience to any agent. In particular we address the issue of how we can attribute knowledge to others using resource-unbounded (e.g., logically omniscient) reasoning without introducing contradictions. We do this by showing how such ideas can be introduced as a \it conservative extension\/ over resource-bounded reasoning.

Keywords: FOL context, resource limited reasoning, omniscience, attributing knowledge