Note: AU Introspection and Symmetry under Non-Trivial Unawareness

Abstract

This note discusses the relationship between AU Introspection and Symmetry for non-trivial unawareness without Negative Introspection using a set-theoretical approach on standard state-space models. Previous studies have explored the equivalence between Negative Introspection and AU Introspection, or the equivalence between Negative Introspection and Symmetry, by assuming Necessitation of the knowledge operator. Given the two equivalences, AU Introspection will expectedly be equivalent to Symmetry. However, no studies have explored the relationship between AU Introspection and Symmetry without Negative Introspection. Therefore, we explore this issue and show that Necessitation is not necessary to prove the equivalence of AU Introspection and Symmetry on standard state-space models. Instead, we show that both AU Introspection and Symmetry hold without crashing into non-trivial unawareness.