A logic of normality and exception

It has been well recognized that common-sense reasoning is nonmonotonic. Nonmonotonic reasoning is prototypically described by the reasoning about normality and exception. In this paper, we firstly propose a modal logic about normality and exception. We then present a nonmonotonic modal logic which formalizes the intuitions of nonmonotonic reasoning directly, rather than go around to indirect criterion. The results can be seen by comparing our logic with major nonmonotonic logics in recent literature. In particular, we provide a first-order extension of default logic and autoepistemic logic, and the capability of circumscription to infer universal statement. As a result, the relations among various existing nonmonotonic logics coincide in our logic.>