笔记 逻辑学导论 Week1

课程地址 https://class.coursera.org/intrologic-003/class/index

1逻辑概述

逻辑研究的是要能够逻辑语句的形式进行编码的信息

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

人们日常生活中都在使用逻辑

  • Language of Logic
  • Logical Reasoning
计算机使用逻辑,在人机之间采用
  • Email Reader的过滤器
  • 电子商务:
  • 软件工程:PROLOG 逻辑编程

2 逻辑的元素Elements of Logic

逻辑语言 Logical Language
  •    Logical expressions
  •    Meaning of those expressions
逻辑蕴含 Logcial Entailment
  • 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
符号操作 Symbolic Manipulation
  •    Rules for syntactically manipulating expressions
  •    to derive those conclusions
possible world
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.
演绎法(deduction)是唯一一种能够确保结论正确的推理模式

3 Formalization 形式化

用一个foamlized语言将消除歧义。
formal logic 形式逻辑的特点
  • simple syntax
  • clear semantics
  • precise rules of inference

formalization

formal logic calculation

4 Automation

使用形式化的表达方式来将问题的前提编码成计算机的数据结构,然后编程,使得计算机能够利用规则来系统性地推理。
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
应用:
数学、硬件工程、Deductive数据库系统、商业

5 Study Guide

学习逻辑所需要的数学基础知识Mathematical Background
  • Sets集合
  • Functions and Relations函数和关系

逻辑的种类

  • 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.

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