A Complete Epistemic Logic for Multiple Agents

Abstract

In the field of Artificial Intelligence and Computer Science, the modal system 55 is a familiar logic to model knowledge. Although the system on the one hand models an idealized notion of knowledge (the epistemic agent is assumed to be fully introspective, for example, and 55 knowledge also suffers from the problem of logical omniscience—the agent knows all logical validities, and his knowledge is closed under logical consequence— see Wansing, 1990 for a discussion and relaxations of these properties), its nice mathematical properties, on the other hand, often motivate researchers to adopt this system in their first exploration of the field. Then, for specific purposes, such as decision-and game-theoretic applications, some or many of these idealizations concerning introspective properties or logical omniscience are given up or, sometimes, replaced by weaker assumptions about knowledge.KeywordsEquivalence RelationModal LogicCommon KnowledgeAccessibility RelationCanonical ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.