非逻辑公理

On the base of Frege's study, Russell put forward the theory of types to settle Russell's paradox. On the base of non-set, Russell brought forward axiom of infinity and axiom of option as the premises and built a system. He tried to defined the non-negative integer in logic terms and derive the theorems of arithmetic from the laws of logic by deductive method.

罗素在弗雷格研究的基础上，提出逻辑类型论来解决罗素悖论，以非集合论理论为基础，以无穷公理和选择公理为前提，利用逻辑概念定义数学概念，并构造系统，通过逻辑演绎法从逻辑公理推导数学定理。

As we all known, with the founding of Euclidean geometry in ancient Greece, with the development of analytic geometry and other kinds of geometries, with F.Kline" s Erlanger program in 1872 and the new developments of geometry in 20th century such as topology and so on, man has developed their understand of geometry. On the other hand, Euclid formed geometry as a deductive system by using axiomatic theory for the first time. The content and method of geometry have dramatically changed, but the geometry curriculum has not changed correspondingly until the first strike from Kline and Perry" s appealing.

纵观几何学发展的历史，可以称得上波澜壮阔：一方面，从古希腊时代的欧氏综合几何，到近代解析几何等多种几何的发展，以及用变换的方法处理几何的埃尔朗根纲领，到20世纪拓扑学、高维空间理论等几何学的新发展，这一切都在不断丰富人们对几何学的认识；另一方面，从欧几里得第一次使用公理化方法把几何学组织成一个逻辑演绎体系，到罗巴切夫斯基非欧几何的发现，以及希尔伯特形式公理体系的建立，极大地发展了公理化思想方法，不管是几何学的内容还是方法都发生了质的飞跃。

From the viewpoint of axial symmetry or centrosymmetry between t and t in logic, this paper makes a minute analysis about the negation operation under different conditions in 1-order uncertainty, puts forward negation operation axiom, and does a systematic research on the definition, properties, and generation of negation operation.

从t与t在逻辑上具有轴对称性或中心对称性出发，详细分析了1阶不确定性中不同条件下的非运算，提出了"非"运算公理，系统研究了"非"运算的定义、性质和构造。

Based on the eight Chinese traditional yin and yang contradiction categories to analyze among the open and close areas in mathematics to achieve the triple unity of opposite composing relation of identical,resemble,diversity and contrary,the four basic types of logical inference.

用中华传统8大阴阳矛盾范畴分析数学中的开闭区间，得出相同、相似、相异、相反这4大逻辑推理基础类型间存在着三极对立统一的组成关系，进而提出涉及此组成关系的逻辑推理基础类型的互蕴公理及其描述内涵的反演算和逻辑外延的非演算。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。