重言式

Studies on the tautologies in some lattice valued logic systems and formula computation by means of neural net works.(1) Tautologies play a significant role in logic applications.

二、一类格值逻辑系统中的重言式和逻辑公式的神经网络计算 1、重言式在逻辑系统的应用中起着重要的作用。

WT9.BZ: Theory of generalized tautology in logic system , W and W k is generalized and applied to Lukasiewicz logic system. The main results are as follows: congruence about on set of logic formulas F has been obtained in the system; it is proved that in this system, for any irrational number α, there does not exist accessible α-tautology; and for any real number α, there does not exist accessible α+-tautology; and the relation theorems have been given between categori...

将逻辑系统 W ，W ，Wk 中的广义重言式理论进行推广并应用到Lukasiewicz逻辑系统中，主要结果是：得到了逻辑公式集F在该系统中关于﹁同余的分划；证明了在该逻辑系统中对每个无理数α而言，不存在可达α重言式，且对每个实数α而言，不存在可达α+重言式；给出了广义重言式、广义矛盾式各类之间的关系定理。

The concept of relative Γ-tautology degree of formulas in four important propositional logics, Lukasiewicz logic, L(superscript *) logic, Gdel logic and product logic, has been proposed, and basic properties of it are obtained.

基于广义重言式理论，在四种重要的命题逻辑系统Lukasiewicz系统，L系统，Gdel系统和Ⅱ系统中，引入了公式的相对Γ-重言度概念，给出了相对Γ-重言度的若干性质。

Every tautology itself shows that it is a tautology.

每个重言式本身表明它是一个重言式。

And in fact only tautologies follow from a tautology.

当然，这种指明逻辑命题是重言式的方法，对于逻辑是完全不重要的，因为作为证明的出发点的那些命题，必定无须任何证明就表明自己是重言式。

Tautologies and F-Tautologies in some lattice valued logic systems whose truth-value lattice are products of lattice implication algebra are discussed. As examples,α-Tautologies and F-Tautologies in lattice valued logic systems L〓P and L〓P are discussed in detail.

本文分析讨论了基于格蕴涵代数直积的格值逻辑系统中的α-重言式和F-重言式，作为两个实例，详细讨论了两个格值逻辑系统L〓P和L〓P中的重言式和F-重言式的结构。

The main results are:In logic system ,G,tautologies can not be get by using upgrade algorithm to non tautologies within finite many times;In logic system G n,tautologies can be get by using upgrade algorithm to an arbitrary formula of F at most n times; Congruence partitions about on F have been given in logi...

主要结果是：在逻辑系统 G，G中，重言式不可能由对非重言式进行有限次升级算法得到；在逻辑系统 Gn 中，对任一公式最多进行 n次升级算法即可得到重言式；利用可达广义重言式概念和α-矛盾式概念分别在 G，G，Gn 中给出了 F的一个关于同余的分划。

The main results are:In logic system r,G r, tautologies can not be get by using upgrade algorithm to non tautologies within finite many times; In logic system S n , tautologies can be get by using upgrade algorithm to an arbitrary formula of F at most n times; Congruence partitions about ...

主要结果是：在逻辑系统 Gr，Gr 中，重言式不可能由对非重言式进行有限次升级算法得到；在逻辑系统Sn 中，对任一公式最多进行n次升级算法即可得到重言式；利用可达广义重言式概念和α矛盾式概念分别在 Gr，Gr，Sn 中给出了F的一个关于同余的分划。

The proof of logical propositions consists in the following process: we produce them out of other logical propositions by successively applying certain operations that always generate further tautologies out of the initial ones.

而且，事实上从一个重言式只能得出重言式来。

There is no tautology in the three-valued logic whose boolean connectives are Kleene implication and the negation in open-world.

但是，Kleene的蕴含词&→&和开放世界假定的否定词&&构成的三值命题逻辑系统没有重言式，通过选定特定的重言式作为推理的出发点进行推理行不通了。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。