知识图谱学习笔记——（五）知识图谱推理
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
5.1什么是推理
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。
It is a known rule that if it rains the grass is wet; so, to explain the fact that the grass is wet; one abduces that it has rained。
正如我们所知，天下雨草会湿；于是，去解释草是湿的这个事实，一个推理原因就是天上下过雨。
5.1.4 Analogical Reasoning——类比推理
Inference via Analogy（通过类比的推理）
In a narrower sense, analogy is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction, in which at least one of the premises, or the conclusion, is general rather than particular in nature
从狭义上讲，类比是一种从一个特定到另一个特定的推论或论证，与演绎、归纳和溯因法相对，其中至少有一个前提或结论是一般的，而不是特殊的。
Analogical Reasoning：
P and Q are similar in respect to properties a, b, and c.Object P has been observed to have further property x,Therefore, Q probably has property x also。
P和Q在属性a、b和c方面是相似的。如果对象P被观察到有新增的属性x，于是，Q可能也有属性x。
Smile is to mouth, as wink is to eye。
suppose Fred wants to prepare blueberry pancakes. Being a novice cook, the most relevant experience he can recall is one in which he successfully made plain pancakes。
Reasoning in Description Logic 描述逻辑中的推理
5.2 知识图谱推理简介
•Machine reasoning is a difficult task,（机器推理是一项很难的任务）
•Reasoning with KG simplifies the problem to fact prediction or relational reasoning.（用知识图谱进行推理可以将问题简化为事实预测或者关系推理）
•Many real life problems (link prediction, causal reasoning, KG-based question answering, recommendation, etc… )
can be formulated as knowledge graph reasoning or reasoning over a graph（许多实际的生活问题（如链接预测、因果推理、基于知识图谱的问答、推荐等）可以被公式化为知识图推理或者基于图的推理）
5.2.1 常见知识图谱推理方法分类
5.1.2 基于符号表示的推理
Deductive Reasoning with Ontological Axioms（基于本体公理的演绎推理）
Tbox语言：
- 定义：引入概念以及关系的名称
例如：Mother，Person， has_child - 包含: 声明包含关系的公理
例如：
Abox语言： - 概念断言：表示一个对象是否属于某个概念
例如，Mother(Alice)，Person(Bob) - 关系断言：表示两个对象是否满足特定关系
例如，has_child(Alice, Bob)
Simple logic deduction with ontological axioms (rules) performed mostly over TBox or Schema of KGs
基于本体公理（规则）的简单的逻辑演绎，大多在知识图谱的TBOX或者图表上进行。
演绎推理不存在可解释性的问题
Deductive reasoning with ontology can be very complex when considering more ontological axioms (can be reformulated as rules) or Datalog-like rules.
基于本体的演绎推理当考虑更多的本体公理（可以重新表示为规则）或数据逻辑一类的规则时将会非常的复杂。
Inductive reasoning is typically performed over ABox or the instance-level of KGs.
归纳推理通常在ABOX或者实例级的知识图谱上执行。
Reasoning with graph structure (path as rules), taking PRA or AMIE as examples
- Rule-based reasoning is precise and can provide insightful explanation for inference results.
基于规则的推理是精确的，能够为推理结果提供有深度的解释。 - Efficiency Problem: The main difficulty for rule learning is the huge search space when determining possible rule structures and searching for support triples to decide their truth values.
效率问题：规则学习的主要困难在于决定可能的规则结构和搜索支持三元组以确定他们的真实值时出现的巨大的搜索空间。 - Structure Sparsity Problem: It depends on the graph structure or paths to extract features.
结构稀疏性问题：依赖于图结构或图路径去提取特征
显式的路径特征或规则可直接用于对推理结果进行解释
Reasoning with KG Embedding, taking DistMult as an example.
基于嵌入知识图谱推理技术，例如使用距离乘积：
-
Embedding-based reasoning is more efficient when there are a large number of relations or triples to reason over.
-
Interpretability Problem: We know the prediction result, but do not know why.
-
Triple Sparsity Problem: One of the main difficulties for embeddinglearning is the poor capability of encoding sparse entities withinsufficient training triples
5.3基于符号逻辑的知识图谱推理
5.3.1 基于Ontology的推理
5.3.2 规则的推理
5.4基于表示学习的知识图谱推理
5.4.1基于嵌入学习的知识图谱推理
5.4.2基于规则学习的知识图谱推理
5.4.3Ontology Embedding—本体概念层推理
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6、知识图谱融合
6.1知识图谱融合概述
6.2概念层融合——本体匹配
6.3实例层的融合——实体对齐
6.4知识融合技术前沿
7、知识图谱问答
7.1 智能问答系统概述
7.2基于查询模版的知识图谱问答
7.3基于语义解析的知识图谱问答
7.4基于检索排序的知识图谱问答
7.5基于深度学习的知识图谱问答
8、图算法与图数据分析
8.1图的基本知识
8.2基础图算法
8.3图神经网络与图表示学习
8.4图神经网络与知识图谱
9、知识图谱技术发展
9.1 多模态知识图谱
9.2 知识图谱与语言预训练
9.3 事理知识图谱
