一、知识学习

声明：知识学习中本文主体按照浙江大学陈华钧教授的《知识图谱》公开课讲义进行介绍，并个别地方加入了自己的注释和思考，希望大家尊重陈华钧教授的知识产权，在使用时加上出处。感谢陈华钧教授。

（一）B站《浙大知识图谱完整版》——5

学识时间：2023年5月16日15:32:30

5、知识图谱推理

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5.1什么是推理

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5.1.1 Deductive Reasoning——演绎推理

Top-down logic

（1）Modus ponens（肯定前件假言推理）
mode that affirms by affirming（通过确认来确认的模式）

推理	举例
P一> Q (conditional statement，环境设定)	If today is Tuesday, then John will go to work
P (hypothesis stated，假设设定)	Today is Tuesday
Q（conclusion deduced，结论推理）	Therefore, John will go to work

（2）Modus tollens（否定后件假言推理）
mode that denies by denying（通过否定来否定的模式）

推理	举例
P一> Q	If it is raining, then there are clouds in the sky
Q	There are no clouds in the sky.
Therefor ，we can conclude that P	Thus, it is not raining.

（3）Law of syllogism（三段论）

推理	举例
P一> Q	If Larry is sick, then he will be absent.
Q一>R	If Larry is absent, then he will miss his classwork.
Therefor , P一>R	Therefore, if Larry is sick, then he will miss his classwork

5.1.2 Inductive Reasoning——归纳推理

Bottom-up logic
The derivation of general principles from specific observations, for example, if all swans that we have observed so far are white, we may induce that the possibility that all swans are white is reasonable.
将来自特定观测值当做广泛的通用原则,例如,如果到目前为止，我们观测到的所有的天鹅都是白色的,我们很可能得出这种结论，即所有的天鹅都是白色是合理的。

（1）Inductive Generalization（归纳概括）

The proportion Q of the sample has attribute A.
Therefore:
The proportion Q of the population has attribute A.
如果样本的比例Q具有属性A，那么，所有的比例Q都具有属性A

There are 20 balls—either black or white—in an urn. To estimate their respective numbers,you draw a sample of four balls and find that three are black and one is white. A good inductive generalization would be that there are 15 black and five white balls in the urn。
一个盒子里有20个球，非黑即白。为了估计他们各自的数目，你做了一个4个球的取样，发现有3个黑的一个白的。那么比较好的归纳概括结果是，在盒子里共有15个黑的和5个白的球。

（2）Statistical syllogism（统计三段论）
A proportion Q of population P has attribute A.
An individual X is a member of P.
Therefore:
There is a probability which corresponds to Q that X has A.

如果所有的P的比例Q有属性A，且独立样本X是P的成员，那么，很可能X也有A属性。

90% of graduates from Excelsior Preparatory school go on to University.Bob is a graduate of Excelsior Preparatory school.Bob will go on to University.
从卓越预科学校毕业的学生有90%的人接着上了大学。Bob是从卓越预科学校毕业的。bob也将继续上大学。

5.1.3 Abductive Reasoning——溯因推理

Inference to the best explanation（最佳解释推理）
a form of logical inference which starts with an observation or set of observations then seeks to find the simplest and most likely explanation for the observations。
逻辑推理的一种形式，此方法从一个或一组观察结果开始，然后试图找到对此观测结果最简单、最可能的解释。
For E to be an explanation of O (Observation) according to T (Theory), it should satisfy two conditions：O follows from E and T;E is consistent with T.
对于E是根据理论T得出的针对观察O的一个解释，这需要满足两个条件：一个是观测O是跟随解释E和理论T产生的；另一个是解释E是与理论T一致的。