论题1-2： 什么样的推理是正确的？ Logic--The discipline that deals with the methods of reasoning majun@nju.edu.cn 2017.10.12
论题1-2： 什么样的推理是正确的？ majun@nju.edu.cn 2017.10.12 Logic--The discipline that deals with the methods of reasoning
What is Logic? 。Logic The discipline that deals with the methods of reasoning The study of the principles and criteria of valid inference and demonstration Ma hematical lo IC Philosophical logic a brana cs that the application of formal logic to grew ut of symboli logic philosophical problems
What is Logic？ • Logic • The discipline that deals with the methods of reasoning • The study of the principles and criteria of valid inference and demonstration Mathematical logic a branch of mathematics that grew out of symbolic logic Philosophical logic the application of formal logic to philosophical problems
计算机解题与数学 ·对问题的理解必须用严格的数学语言描述。 ·其前提是必须建立问题的数学模型。 ·可用的数学模型必须是计算机能对其进行操作的。 ·让计算机能理解的解题plan必须建立在严密的数学基础上 ·将plan表示为计算机能执行的“指示”的语言必须建立在严密的 数学基础上 ·分析计算机计算的结果必须使用数学方法： ·用逻辑证明结果正确： ·动用必要的数学手段分析解法的效率
计算机解题与数学 • 对问题的理解必须用严格的数学语言描述。 • 其前提是必须建立问题的数学模型。 • 可用的数学模型必须是计算机能对其进行操作的。 • 让计算机能理解的解题plan必须建立在严密的数学基础上 • 将plan表示为计算机能执行的“指示”的语言必须建立在严密的 数学基础上 • 分析计算机计算的结果必须使用数学方法： • 用逻辑证明结果正确； • 动用必要的数学手段分析解法的效率
An Example We know that Bill,Jim and Sam are from Boston,Chicago and Detroit, respectively. Each of following sentence is half right and half wrong: Bill is from Boston,and Jim is from Chicago. Sam is from Boston,and Bill is from Chicago. Jim is from Boston,and Bill is from Detroit. Tell the truth about their home town
An Example • We know that Bill, Jim and Sam are from Boston, Chicago and Detroit, respectively. • Each of following sentence is half right and half wrong: • Bill is from Boston, and Jim is from Chicago. • Sam is from Boston, and Bill is from Chicago. • Jim is from Boston, and Bill is from Detroit. • Tell the truth about their home town
How to solve it? Understanding the problem! Bill,Jim and Sam are from Boston,Chicago and Detroit,respectively Each of following sentence is half right and half wrong: Bill is from Boston,and Jim is from Chicago. Bill is from Boston,if and only if Jim is NOT from Chicago. Jim is from Chicago,if and only if Bill is NOT from Boston. Guess and Reasoning Sam is from Boston,and Bill is from Chicago. Sam is from Boston,if and only if Bill is NOT from Chicago. Bill is from Chicago,if and only if Sam is NOT from Boston. Jim is from Boston,and Bill is from Detroit. Jim is from Boston,if and only if Bill is NOT from Detroit. Bill is from Detroit,if and only if Jim is NOT from Boston
How to solve it? • Understanding the problem! • Bill, Jim and Sam are from Boston, Chicago and Detroit, respectively • Each of following sentence is half right and half wrong: • Bill is from Boston, and Jim is from Chicago. • Bill is from Boston, if and only if Jim is NOT from Chicago. • Jim is from Chicago, if and only if Bill is NOT from Boston. • Sam is from Boston, and Bill is from Chicago. • Sam is from Boston, if and only if Bill is NOT from Chicago. • Bill is from Chicago, if and only if Sam is NOT from Boston. • Jim is from Boston, and Bill is from Detroit. • Jim is from Boston, if and only if Bill is NOT from Detroit. • Bill is from Detroit, if and only if Jim is NOT from Boston. Guess and Reasoning