On Translating Epistemic Operators in a Logic of Awareness
This work provides a foundational comparison between AIL and HMS models for researchers in logic and economics, but it is incremental as it builds on existing frameworks.
The paper tackles the problem of translating epistemic operators from Awareness-Based Indistinguishability Logic (AIL) into HMS models, proving that a language translation preserves truth and clarifying the semantic role of these operators in HMS models.
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.