Decision Problems in Autoepistemic Logic

In this paper we will prove the complexity of three main problems in the context of autoepistemic logic. The first problem is the question if a set of premise sum has a stable expansion. The second is if a given formula exists in at least one stable expansion, this problem is also known as brave reasoning. The third is if a given formula exists in every stable expansion, also known as cautious reasoning. we will explain the basics for these problems and induct you into the notation.