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.

翻译：Fagin与Halpern（1988年）（FH）提出的意识结构采用了句法意识对应关系和刻画隐式知识的可达关系。该模型作为无意识现象的一种灵活建模方式，最适宜从外部建模者的视角进行解释。Heifetz、Meier与Schipper（2006年、2008年）（HMS）提出的无意识结构则通过状态空间格和可能性对应关系分别建模个体意识与显式知识，其子格可理解为智能体的主观视角。尚待解决的开放性问题包括：（1）如何在HMS结构中定义隐式知识；（2）如何扩展FH结构以建模智能体的主观视角。本文通过定义与HMS模型中显式知识保持一致的隐式知识解决了问题（1），同时提出将隐式知识与意识作为原始概念的HMS模型变体。针对问题（2），我们构建了在子语言层面模态等价的FH模型范畴，这些模型可依据智能体的意识层级被解释为其主观视角。上述构造方法揭示了HMS模型与FH模型间的等价关系。作为推论，基于同时包含隐式知识与显式知识的语言体系，我们获得了HMS模型相对于命题意识逻辑的可靠性与完全性。