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和Halpern（1988）（FH）提出的意识结构具有句法意识对应关系和建模隐含知识的可达性关系。它们是灵活的无意识模型，最佳解释来自外部建模者的视角。Heifetz、Meier和Schipper（2006, 2008）（HMS）提出的无意识结构通过状态空间格和可能性对应关系分别建模意识和显性知识。其子格可解释为代理人的主观视角。未解决的问题包括：（1）如何在HMS结构中定义隐含知识，以及（2）如何扩展FH结构以建模代理人的主观视角。本文通过定义与HMS模型中显性知识一致的隐含知识来解决（1），并引入一种以隐含知识和意识为原始概念而非显性知识的HMS模型变体。此外，我们通过引入一类相对于子语言模态等价的FH模型范畴来解决（2），这些模型可根据代理人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，我们基于同时包含隐含知识和显性知识的语言，获得了命题意识逻辑下HMS模型的可靠性与完备性。