无意识结构中的隐式知识——扩展摘要
Implicit Knowledge in Unawareness Structures -- Extended Abstract
AI总结：
本文研究无意识结构中隐式知识的定义与主观视角建模，通过从 HMS 模型显式知识推导隐式知识、引入以隐式知识和意识为原始概念的 HMS 变体，并构造模态等价的 FH 模型，证明了 HMS 与 FH 模型的等价性及 HMS 模型相对命题意识逻辑的可靠性与完全性。
摘要：
Fagin 和 Halpern（1988）（FH）提出的意识结构以句法意识对应关系和刻画隐式知识的可及关系为特征。它们是一种灵活的无意识模型，最适合从外部建模者的视角加以解释。Heifetz、Meier 和 Schipper（2006, 2008）（HMS）提出的无意识结构通过状态空间格来刻画意识，并通过可能性对应关系刻画显式知识。它们可以被解释为提供智能体的主观视角。未解决的问题包括：（1）如何在 HMS 结构中定义隐式知识，以及（2）可以通过何种方式扩展 FH 结构以刻画智能体的主观视角。在本文中，我们通过展示如何从 HMS 模型中的显式知识推导出隐式知识来解决问题（1）。我们还引入 HMS 模型的一种变体，该变体不再以显式知识为原始概念，而是以隐式知识和意识为原始概念。此外，我们通过引入一类 FH 模型来解决问题（2），这类模型相对于子语言是模态等价的，并且可以根据智能体的意识被解释为其主观视角。这些构造使我们能够证明 HMS 模型与 FH 模型之间的等价性。作为推论，我们基于一种同时包含隐式知识和显式知识的语言，得到了 HMS 模型相对于命题意识逻辑的可靠性和完全性。
英文摘要：
Awareness structures by Fagin and Halpern (1988) (FH) feature a syntactic awareness correspondence and accessibility relations modeling implicit knowledge. They are a flexible model of unawareness, and best interpreted from a outside modeler's perspective. Unawareness structures by Heifetz, Meier, and Schipper (2006, 2008) (HMS) model awareness by a lattice of state-spaces and explicit knowledge via a possibility correspondence. They can be interpreted as providing the subjective views of agents. Open questions include (1) how implicit knowledge can be defined in HMS structures, and (2) in which way FH structures can be extended to model the agents' subjective views. In this paper, we address (1) by showing how to derive implicit knowledge from explicit knowledge in HMS models. We also introduce a variant of HMS models that instead of explicit knowledge, takes implicit knowledge and awareness as primitives. Further, we address (2) by introducing a category of FH models that are modally equivalent relative to sublanguages and can be interpreted as agents' subjective views depending on their awareness. These constructions allow us to show an equivalence between HMS and FH models. As a corollary, we obtain soundness and completeness of HMS models with respect to the Logic of Propositional Awareness, based on a language featuring both implicit and explicit knowledge.
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