命题逻辑

Frege's second-order predicate calculus was based on the 'function-argument' analysis of propositions and it freed logicians from the limitations of the 'subject-predicate' analysis of Aristotelian logic.

弗雷格第二阶谓词微积分是基于'功能参数的分析命题，它摆脱了限制逻辑学家的'主谓'亚里士多德逻辑分析。

1265 It is always possible to construe logic in such a way that every proposition is its own proof.

6.1265 对逻辑始终可以这样来理解：每个逻辑命题都是它自身的证明。

The characteristics and contribution in this period primarily consist in: the logic merges into an integral whole, making progress from simple analogy to strict deduce, connotate-logic conversing denote-logic, Hetuvidyā handling the question of main phrase broken, its investigative point and dogmata background having variety with Hetuvidyā development.

这时期的特点及贡献主要在于：逻辑学与认知理论融为一体；从简单的类比进展到严格的演绎；内涵性逻辑转化为外延性逻辑；能够处理主词不存在的命题；其研究的侧重点和教理背景随因明理论的进展而有所变化。

We call it many-valued logic in that this kind of logic studies logic theory that handles relations of propositions in which propositions have three truth values or more, even infinite, and do not limit in two truth values.

之所以称之为多值逻辑，关键原因在于其所研究的是具有三个或三个以上乃至无穷个真值的命题之间关系的逻辑理论，而不是仅仅限于真假二值。

The paper is concerned with the ambiguity of the formalization of reasoning and the origin of the paradox of material implication.

所谓逻辑的形式化就是对概念、命题、推理给以数学化，它是构建现代逻辑系统普遍采用的方法。

Material implication is an extremely important concept of modern logic,but we encountered a lot of problems as we attempted to analyze and explain the hypothetical proposition of natural language with material implication,this situation obstructs the aim of logic norm and people's correct thinking.

实质蕴涵是现代逻辑的一个极其重要的概念，但是用实质蕴涵理论来分析和说明自然语言中的假言命题却出现了许多解释不通的问题。这种状况有悖于逻辑规范和引导人们进行正确思维及表达的宗旨。

Two intuitionistic systems of firstorder sentential calculus, Hilbert s type and natural deduction t ype, were introduced.

介绍了一阶命题演算的两个直觉主义系统：希尔伯特型及自然演绎型，并证明了这两个系统的等价性，揭示了直觉主义逻辑的内涵及与其他非经典逻辑的关

From the person gas arrives make money among have a lot of uncared-for logistic link, a little logistic link may go at all be illogical, this is paradox, it is bogus proposition.

从人气到赚钱中间有很多被忽略的逻辑环节，有些逻辑环节可能根本就走不通，这就是悖论，是伪命题。

Secondly, the realization of dialectical logic mathematics research planning" Research outline of universal logics" put forward by the authors is introduced briefly, and the main point of" the standard proposition universal logics" set up under the guidance of the outline is also introduced.

其次，简单介绍了作者提出的实现辩证逻辑数学化的规划《泛逻辑学研究纲要》，及在纲要指导下建立的《标准命题泛逻辑学》要点，指出该逻辑系统在包容各种辩证矛盾的同时，有效地排除了逻辑矛盾。

12 The fact that the propositions of logic are tautologies shows the formal--logical--properties of language and the world.

6.12 逻辑命题是重言式，这显示语言和世界的形式的——逻辑的——属性。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。