A The Complexity of Reasoning for Fragments of Autoepistemic Logic

Non-monotonic logics are among the most important calculi in the area of knowledge representation and reasoning. Autoepistemic logic, introduced 1985 by Moore [Moore 1985], is one of the most prominent non-monotonic logics. It was originally created to overcome difficulties present in the non-monotonic modal logics proposed by McDermott and Doyle [McDermott and Doyle 1980], but was also shown to offer a unified approach to other models of non-monotonic reasoning: it is known to embed McCarthy’s circumscription [McCarthy 1980] and Reiter’s default logic [Reiter 1980] under a certain types of translation, and can be used to define the semantics of logic programs; see, e.g., [Marek and Truszczynski 1991; Lifschitz and Schwarz 1993]. Autoepistemic logic extends classical logic with a unary modal operator L expressing the beliefs of an ideally rational agent. The sentence Lφ means that the agent can derive φ based on its knowledge. To formally capture the set of beliefs of an agent, the