无觉知结构中的隐式知识
Implicit Knowledge in Unawareness Structures
AI总结：
本文在 HMS 无觉知结构中定义与显式知识一致的隐式知识，并构造可表示主观视图的 FH 模型类别，证明两类模型等价及相应逻辑的可靠性与完备性。
摘要：
Fagin 与 Halpern（1988）（FH）的觉知结构以句法觉知对应和可达关系为特征，用于建模隐式知识。它们是灵活的无觉知模型，最适合从外部建模者的视角加以解释。Heifetz、Meier 与 Schipper（2006，2008）（HMS）的无觉知结构通过状态空间格建模觉知，并通过可能性对应建模显式知识；其中的子格可被解释为智能体的主观视图。尚未解决的问题包括：（1）如何在 HMS 结构中定义隐式知识；（2）可以通过何种方式扩展 FH 结构以建模智能体的主观视图。本文通过定义一种与 HMS 模型中的显式知识相一致的隐式知识来处理问题（1）。我们还引入了 HMS 模型的一个变体，该变体不把显式知识，而是把隐式知识和觉知作为原语。此外，我们通过引入一类 FH 模型来处理问题（2）：这些模型相对于子语言是模态等价的，并且可根据智能体的觉知被解释为其主观视图。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，基于一种同时包含隐式知识和显式知识的语言，我们获得了 HMS 模型相对于命题觉知逻辑的可靠性与完备性。
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 possibility correspondences. Sublattices thereof can be interpreted as 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 defining implicit knowledge such that it is consistent with 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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