Awareness Logic: A Kripke-based Rendition of the Heifetz-Meier-Schipper Model
This work provides a more structured and separable framework for modeling awareness and uncertainty for researchers in epistemic logic and game theory, offering an incremental improvement to existing models.
The paper introduces a Kripke-based model of awareness that separates uncertainty and unawareness, addressing limitations of the syntax-free Heifetz-Meier-Schipper (HMS) lattice model. It demonstrates the equivalence of the two models by defining transformations that preserve formula satisfaction, and achieves completeness by leveraging results from both models.
Heifetz, Meier and Schipper (HMS) present a lattice model of awareness. The HMS model is syntax-free, which precludes the simple option to rely on formal language to induce lattices, and represents uncertainty and unawareness with one entangled construct, making it difficult to assess the properties of either. Here, we present a model based on a lattice of Kripke models, induced by atom subset inclusion, in which uncertainty and unawareness are separate. We show the models to be equivalent by defining transformations between them which preserve formula satisfaction, and obtain completeness through our and HMS' results.