Reasoning About Knowledge of Unawareness Revisited

TL;DR

This paper revisits a logic of awareness by allowing models with different languages at each world, enabling representation of agents uncertain about their own awareness, and provides a sound and complete axiomatization.

Contribution

It introduces a new model framework with world-dependent languages to better capture agents' unawareness and uncertainty, extending previous logical systems.

Findings

Provided a sound and complete axiomatization for the new logic.

Characterized the quantifier-free fragment using existing axioms.

Extended the logic to model agents uncertain about their awareness.

Abstract

In earlier work, we proposed a logic that extends the Logic of General Awareness of Fagin and Halpern [1988] by allowing quantification over primitive propositions. This makes it possible to express the fact that an agent knows that there are some facts of which he is unaware. In that logic, it is not possible to model an agent who is uncertain about whether he is aware of all formulas. To overcome this problem, we keep the syntax of the earlier paper, but allow models where, with each world, a possibly different language is associated. We provide a sound and complete axiomatization for this logic and show that, under natural assumptions, the quantifier-free fragment of the logic is characterized by exactly the same axioms as the logic of Heifetz, Meier, and Schipper [2008].