# 笔记 逻辑学导论 Week1

### 1逻辑概述

Logic is the study of infomation encoded in the form of logical sentences.

• Language of Logic
• Logical Reasoning

• 电子商务：
• 软件工程：PROLOG 逻辑编程

### 2 逻辑的元素Elements of Logic

•    Logical expressions
•    Meaning of those expressions

• 给定一些我们已经知道为真的语句，回答还有什么语句有可能是真的问题
Given sentences we know to be true，what other sentences must also be true?
• A set of premises logically entails a conclusion if and only if every world that satisfies the premises satisfies the conclusion.
一系列的前提能够在逻辑上蕴含一个结论，当且仅当满足前提的每一个世界都满足结论

•    Rules for syntactically manipulating expressions
•    to derive those conclusions
Rules of Inference: 推理的规则
• 规则推理是一个推理的模式，包含一些前提和一些结论
A rule of inference is a reasoning pattern consisting of some premises and some conclusions.
• 如果我们相信所有的前提，那么根据一个推理的规则，我们可以知道我们应该相信哪些结论是真的
If we believe the premises, a rule of inference tell us that we should also believe the conclusions.

### 3 Formalization 形式化

formal logic 形式逻辑的特点
• simple syntax
• clear semantics
• precise rules of inference

### 4 Automation

Logic Technology
Language:
• Knowledge Interchange Format (KIF)-ANSI
• Common Logic W3C
Automated Reasoning System
• Otter/Snark/Vampire
• PTTP/Epilog
Knowledge Bases
• Definitions
• Physical Laws
• Laws

### 5 Study Guide

• Sets集合
• Functions and Relations函数和关系

• Propositional Logic命题逻辑
If it is raining, the ground is wet
• Relational Logic关系逻辑
If x is a parent of y, then y is a child of x
• Epistemic Logic认知逻辑
John believes that all men are mortal.