Separating disbeliefs from beliefs in autoepistemic reasoning

Abstract

This paper investigates separated autoepistemic logic which is a generalization of Moore’s autoepistemic logic with separate modalities for belief and disbelief. Along the separation of beliefs and disbeliefs, the relationship between autoepistemic logic and default logic becomes very intuitive. Straightforward ways of translating default theories into separated autoepistemic theories and back are presented. These translations are shown to preserve a variety of semantics of default theories such as those based on default extensions, weak extensions and stationary extensions. These classes of extensions are captured by their analogs in separated autoepistemic logic, and vice versa. A particular novelty of the approach is that a reasonable notion of separated stationary expansions can be established.