The literature on awareness modeling includes both syntax-free and syntax-based frameworks. Heifetz, Meier \& Schipper (HMS) propose a lattice model of awareness that is syntax-free. While their lattice approach is elegant and intuitive, it precludes the simple option of relying on formal language to induce lattices, and does not explicitly distinguish uncertainty from unawareness. Contra this, the most prominent syntax-based solution, the Fagin-Halpern (FH) model, accounts for this distinction and offers a simple representation of awareness, but lacks the intuitiveness of the lattice structure. Here, we combine these two approaches by providing a lattice of Kripke models, induced by atom subset inclusion, in which uncertainty and unawareness are separate. We show our model equivalent to both HMS and FH models by defining transformations between them which preserve satisfaction of formulas of a language for explicit knowledge, and obtain completeness through our and HMS' results. Lastly, we prove that the Kripke lattice model can be shown equivalent to the FH model (when awareness is propositionally determined) also with respect to the language of the Logic of General Awareness, for which the FH model where originally proposed.

翻译：有关意识建模的文献包括不问税和基于语法的框架。 Heifetz, Meier {Schipper (HMS) 提议了一个不问税的透明意识模型。 虽然它们的平滑方法是优雅和直观的,但它排除了依赖正式语言来诱导拖车的简单选择,也没有明确区分不确定性和无知。 与此相比, 最突出的基于语法的解决方案Fagin- Halpern (FH) 模式(Fagin- Halpern) 模式(FH), 说明了这种差异, 提供了简单的认知表现, 但却缺乏拉蒂斯结构的直观性。 在这里, 我们结合了这两种方法, 提供了Kripke 模型的平坦直观和直观, 由原子子集成, 其不确定性和不知情性是分开的。 我们展示了与 HMS 和 FH 模式相等的模型的模型, 通过我们和 HMS 的结果, 我们证明 Kripke 模式的lattice 模式可以证明最初对FH 的认识, 也就是对LO 的理解。