A logic of knowledge and justified assumptions

In this paper we define the logic GK of knowledge and justified assumptions. GK is best understood as a formalization of autoepistemic reasoning processes that are more general than those in Moore's autoepistemic logic, and is formally defined via a modification of Shoham's preference semantics. We show that GK includes not only Moore's autoepistemic logic, but also Reiter's default logic. To our knowledge GK is the first complete semantic unification of the two logics. Similarly to circumscription, GK is based on the notion of logical minimization, and thus provides a bridge between circumscription and fixed-point nonmonotonic logics, an outstanding problem in nonmonotonic logics. As an application of this bridge, we propose a formalization of logic programs with negation-as-failure in circumscription.