Using Abstract Resources to Control Reasoning

  • Authors:

  • Richard W. Weyhrauch;Marco Cadoli;Carolyn L. Talcott

  • Affiliations:

  • Ibuki Inc., P.O. Box 1627, Los Altos, CA 94022, U.S.A. (E-mail: rww@ibuki.com);Dipartimento di Informatica e Sistemistica, Università di Roma ’’La Sapienza‘‘, Via Salaria 113, I-00198 Roma, Italy (E-mail: cadoli@dis.uniroma1.it);Department of Computer Science, Stanford University, Stanford, CA 94305, U.S.A. (E-mail: clt@cs.stanford.edu)

  • Venue:
  • Journal of Logic, Language and Information
  • Year:
  • 1998

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Abstract

Many formalisms for reasoning about knowing commit an agent to belogically omniscient. Logical omniscience is an unrealistic principle for usto use to build a real-world agent, since it commits the agent to knowinginfinitely many things. A number of formalizations of knowledge have beendeveloped that do not ascribe logical omniscience to agents. With fewexceptions, 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 explicitrepresentation of notions such as problems, solutions, and problem solvingactivities, notions which are usually left implicit in the discussions ofautonomous agents. A second technique is to take explicitly into account thenotion of ’’resource‘‘ when we formalize reasoning principles. We use thenotion of resource to describe interesting principles of reasoning that areused for ascribing knowledge to agents. For us, resources are abstractobjects. We make extensive use of ordering and inaccessibility relations onresources, but we do not find it necessary to define a metric. Usingprinciples about resources without using a metric is one of the strengthsof our approach. We describe the architecture of a reasoner, built from a finite numberof components, who solves a puzzle, involving reasoning about knowing, byexplicitly using the notion of resource. Our approach allows the use ofaxioms about belief ordinarily used in problem solving – such as axiomK of modal logic – without being forced toattribute logical omniscience to any agent. In particular we address theissue 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 beintroduced as a ’’conservative extension‘‘ over resource-bounded reasoning.