Implicit Knowledge in Unawareness Structures -- Extended Abstract

TL;DR

This paper explores the relationship between implicit and explicit knowledge in unawareness models, establishing formal connections and equivalences between FH and HMS structures, and advancing the logical understanding of subjective awareness.

Contribution

It introduces methods to derive implicit knowledge from explicit knowledge in HMS models and extends FH models to incorporate agents' subjective views, establishing their equivalence.

Findings

Derived implicit knowledge from explicit knowledge in HMS models.

Introduced a variant of HMS models with implicit knowledge and awareness as primitives.

Proved equivalence between HMS and FH models and established soundness and completeness results.

Abstract

Awareness structures by Fagin and Halpern (1988) (FH) feature a syntactic awareness correspondence and accessibility relations modeling implicit knowledge. They are a flexible model of unawareness, and best interpreted from a outside modeler's perspective. Unawareness structures by Heifetz, Meier, and Schipper (2006, 2008) (HMS) model awareness by a lattice of state-spaces and explicit knowledge via a possibility correspondence. They can be interpreted as providing the subjective views of agents. Open questions include (1) how implicit knowledge can be defined in HMS structures, and (2) in which way FH structures can be extended to model the agents' subjective views. In this paper, we address (1) by showing how to derive implicit knowledge from explicit knowledge in HMS models. We also introduce a variant of HMS models that instead of explicit knowledge, takes implicit knowledge and awareness as primitives. Further, we address (2) by introducing a category of FH models that are modally equivalent relative to sublanguages and can be interpreted as agents' subjective views depending on their awareness. These constructions allow us to show an equivalence between HMS and FH models. As a corollary, we obtain soundness and completeness of HMS models with respect to the Logic of Propositional Awareness, based on a language featuring both implicit and explicit knowledge.