Awareness-Based Indistinguishability Logic (henceforth, AIL) is an extension of Epistemic Logic by introducing the notion of awareness, distinguishing explicit knowledge from implicit knowledge. In this framework, each of these notions is represented by a modal operator. On the other hand, HMS models, developed in the economics literature, also provide a formalization of those notions. Nevertheless, the behavior of the epistemic operators in AIL within HMS models has yet to be explored. In this paper, we define a transformation of an AIL model into an HMS model and then prove that a translation between the fragments of the language of AIL preserves truth under this transformation. As a result, we clarify the semantic role of an epistemic operator in AIL, which is induced by awareness and is essential to defining explicit knowledge, within HMS models. Furthermore, we demonstrate the differences in the implicit knowledge captured by AIL and HMS models. This work lays the groundwork for a comparative analysis between the model classes.

翻译：基于意识的不可区分性逻辑（简称AIL）是通过引入意识概念对认知逻辑的扩展，从而区分显性知识与隐性知识。在此框架下，这些概念分别由模态算子表示。另一方面，经济学文献中发展的HMS模型同样为这些概念提供了形式化表述。然而，AIL中的认知算子在HMS模型中的行为尚未得到充分探讨。本文定义了从AIL模型到HMS模型的转换方法，并证明在此转换下，AIL语言片段之间的翻译保持真值不变。由此，我们阐明了AIL中由意识诱导且对定义显性知识至关重要的认知算子在HMS模型中的语义作用。此外，我们揭示了AIL与HMS模型在捕捉隐性知识方面的差异。本研究为两类模型之间的比较分析奠定了基础。