意识逻辑:作为句法和语义模型中间地带的克里普克格(CS)

关于感知建模的文献包括无语法框架和基于语法的框架。hefetz, Meier \& Schipper (HMS)提出了一种无语法的感知格模型。虽然他们的格的方法是优雅和直观的，但它排除了依赖形式语言来归纳格的简单选择，并且没有明确区分不确定性和无意识。相反，最突出的基于语法的解决方案，费金-哈尔彭(FH)模型，解释了这一区别，并提供了意识的简单表示，但缺乏晶格结构的直观性。在这里，我们将这两种方法结合起来，通过提供一个由原子子集包含诱导的Kripke模型晶格，其中不确定性和无意识是分开的。我们通过定义两种模型之间的转换来证明我们的模型等价于HMS和FH模型，这些转换保持了显式知识语言公式的满足性，并通过我们和HMS的结果获得了完备性。最后，我们证明了Kripke格模型也可以等价于跳频模型(当意识被命题决定时)，这也适用于跳频模型最初提出的《一般意识逻辑》的语言。

原文题目：Awareness Logic: Kripke Lattices as a Middle Ground between Syntactic and Semantic Models

原文：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.