Nonmonotonic Reasoning And Its Applications

The inferential form of classical logic is deductive and monotonic, and it is generally named monotonic reasoning. In solving the issues of basic theories it is accurate and strict, but there are some limitations when it is used to solve the problems of daily complex reasoning. In contrast, nonmonotonic reasoning has certain flexibility and its reasoning conclusion is temporary. When new conditions appear, the conclusions will be corrected in order to comply with the fact. The difference between monotonic reasoning and nonmonotonic reasoning is similar to the comparison proposed by Frege---the comparison between microscope and eyes on the function. Namely, microscope is characteristic of its accuracy and it is helpful to study the micro world but doesn't have the flexibility of eyes in daily life. However, eyes couldn't directly observe the microscopic world which could be observed only through a microscope.The concept non-monotonic reasoning was put forward in 1970s. After years of study, nonmonotonic logic has been gradually formed which is different from classical monotonic logic. The most obvious different is nonmonotonic theorem increases, with the increasing of the prerequisite of the set. Specifically, in daily context, people could draw new conclusions on the premise of existing knowledge and newly-added knowledge. Usually, new conclusions will face two kinds of situations: they are either in contradiction with existing knowledge or not. The first situation accords with the characteristic of monontonic logic and its second accords with nonmonotonic logic. For the second situation, if we could ensure that new conclusion accords with general facts. Then, we have to make changes to the existing knowledge, thus to develop new knowledge. This process of modifying existing knowledge and developing new knowledge accords with the general rule of knowing the world. On the one hand, nonmonotonic reasoning has important enlightening significance to understand the way to know the world; on the other hand, as a useful reasoning method, it could be applied to the study of other scientific fields. So it is of a great importance to study nonmonotonic reasoning.To study nonmonotonic reasoning, we must firstly study nonmonotonic logical systems. From the point of logic, through the study of consistency and completeness of nonmonotonic logical systems, we could prove that nonmonotonic reasoning can satisfy the legitimacy in daily reasoning. So far, the most often discussed systems are modal nonmonotonic logic and default logic. Through discussing the two logical systems, we could deeply understand the modal nonmonotonic reasoning and default reasoning. In the context, first of all, we should have a whole view about the nonmonotonic reasoning through the discussion of two of its systems--modal nonmonotonic logic and default logic. And then, we should have a clear understanding about the relation and distinction between monotonic reasoning and nonmonotonic reasoning. On this basis, we explore its utility in common sense reasoning and its theoretical value in other subjects.