Reasoning about knowledge of unawareness

• 成果类型: Article
• 署名作者: Halpern, Joseph Y.; Rego, Leandro C.
• 署名单位: Universidade Federal de Pernambuco; Cornell University; Cornell University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2009.02.001
• 发表日期: 2009
• 页码: 503-525
• 关键词: Modal logic; awareness; Axiomatization; Decidability; Multi-agent system; interactive epistemology

摘要

Awareness has been shown to be a useful addition to standard epistemic logic. However, standard propositional logics for knowledge and awareness cannot express the fact that an agent knows that there are facts of which he is unaware without there being an explicit fact that the agent knows he is unaware of. We extend Fagin and Halpern's logic of general awareness to a logic that allows quantification over variables, so that there is a formula in the language that says an agent explicitly knows that there exists a fact of which he is unaware. Moreover, that formula can be true without the agent explicitly knowing that he is unaware of any particular formula. We provide a sound and complete axiomatization of the logic. Finally, we show that the validity problem for the logic is recursively enumerable, but not decidable. (C) 2009 Elsevier Inc. All Fights reserved.