In this paper, a kind of tree method is proposed to investigate Roos extensions about the reasoning by cases in default logic, discuss deeply the computation of Roos extensions and analyze the relationship between Roos extensions and Reiter s extensions.

The Research on the Application of Plausible Reasoning in Middle School Mathematics Teaching;

The functions of plausible reasoning in advanced mathematics,analyzing and solving problems are discussed from the following aspects: understanding mathematical concepts,mastering theorems,solving problems.

But the greatest change is from the logical reasoning to the balance between logical reasoning and sensible reasoning.

An elementary study of reasonable inference in the new mathematics course in the middle school in China;

Since long ago, our country mathematics educator pays great attention to the use "the formalization" the way develops student s deductive inference ability, neglected the student to gather the reasonable inference ability the raise.

It is just because our traditional mathematical teaching that emphasizes the rigour of inference, our using the way of "formalization" to improve the students ability of deductive inference and emphasizing the rigour of deductive inference that divide the inference into two incompatible parts, ignoring the function of the reasonable inference and ot.

The paper discusses the component, structure and the hierarchy of the moral reasoning, and points out that the moral pluralists can use the axiomatic method to these ethic systems nontraditional-ly, but in order to resolve the impact of ethical values, all the axiomatic systems of ethics must contain the consistency axiom and the situational inference.