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.

翻译：Fagin与Halpern（1988）提出的意识结构（FH）以语法意识对应关系和可达关系建模隐含认知，是一种灵活的无意识模型，更适合从外部建模者视角进行解释。Heifetz、Meier与Schipper（2006, 2008）提出的无意识结构（HMS）通过状态空间格和可能对应关系分别建模意识与显性认知，可解释为提供主体的主观视角。当前未解决的问题包括：(1) 如何在HMS结构中定义隐含认知；(2) 如何扩展FH结构以建模主体主观视角。本文通过展示如何在HMS模型中从显性认知推导隐含认知来解决(1)，同时引入一种以隐含认知和意识为基元（而非显性认知）的HMS变体。进一步，通过引入一类在子语言上模态等价且可依据意识状态解释为主体主观视角的FH模型范畴来解决(2)。这些建构使我们得以证明HMS模型与FH模型之间的等价性。作为推论，我们获得了HMS模型相对于命题意识逻辑（一种同时包含隐含与显性认知的语言）的可靠性与完备性。