A study of nonmonotonic reasoning

This thesis contains several essays on nonmonotonic reasoning, which touch on a number of key issues in that area. It begins with the introduction of the logic GK of Grounded Knowledge as a uniform semantic basis for fixed-point nonmonotonic logics. These logics include Reiter's default logic and Moore's autoepistemic logic, and to our knowledge GK is the first semantic unification of the two. 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. Together with the unique names assumption, the formalization provides a concise representation for the facts that are true in every answer set of a logic program. We then introduce the notion of argument systems as a proof theory for nonmonotonic reasoning. By reformulating some major existing nonmonotonic logics as argument systems, we show that most nonmonotonic reasoning can be captured with the aid of a generalized negation-as-failure rule. We describe an implemented system for default logic based on this idea. Finally, we apply nonmonotonic logic to the formalization of inheritance and of theories of action, the two areas that have to a large degree motivated research in nonmonotonic reasoning. We show that various intuitions about nonmonotonic inheritance hierarchies can be conveniently formalized in logic programs with negation-as-failure. For reasoning about action, we first propose a formal yet intuitive criterion by which to evaluate the adequacy of theories of action. We then formulate a class of monotonic theories that satisfy the criterion by using explicit frame axioms. Finally for a significant subclass of the monotonic theories, we provide provably-correct nonmonotonic counterparts which avoid explicit frame axioms.