# First Order Logic 一阶逻辑

·       George W. Bush is the 43rd President of the United States.

·       Paris is the capital of France.

·       Everyone born on Monday has purple hair.

Sometimes,a statement can contain one or more other statements as parts. Consider for example, the following statement:

·       Either Ganymede is a moon of Jupiter or Ganymede is a moon ofSaturn.

While the above compound sentence is itself a statement, because it is true, the twoparts, "Ganymede is a moon of Jupiter" and "Ganymede is a moonof Saturn", are themselves statements, because the first is true and thesecond is false.

Propositional logic not expressiveenough

Cannot deduce/compose factsautomatically

Declarative vs. Procedural

NL不一定全是用于表现，也可以用于communication，例子：“Look!”

First-Order Logic一阶逻辑

Don’t treat propositions as “atomic”entities.

对象（Objects）：cs4701, fred, ph219, emptylist …

关系/ Predicates（谓词）：is_Man(fred), Located(cs4701, ph219),is_kind_of(apple, fruit)…    Note: Relations typically correspondto verbs

Universal:"x: ( is_Man(x) ) is_Mortal(x) )

Existential: $y: ( is_Father(y, fred) ) 谓词Predicates 在传统语法中，谓词是句子两大主要部分之一，另一个是主语（subject），被谓词所修辞。 例子：•"John is yellow" John actsas the subject, and is yellow acts as the predicate. 谓词有些类似于动词词组（verb phrase）。在语言学语义中，谓词是对于true of something的表述。 formal mathematical logic形式逻辑类型 · Propositional logic，陈述了真或假，判断新陈述 · First order logic，需要有predicates, quantifiers and variables E.g.Philosopher(a) –> Scholar(a)$x, King(x) ˄ Greedy (x) ==> Evil (x)，如果kinggeedy，那么他将成为一个恶魔。

·        Secondorder logic，在谓词和变量集基础上的Quantify

·        Temporal logic，真假与关系依赖于时间

分析句子中的对象Objects，属性property，和关系relation

例子1Squares neighboring the wumpus are smelly

Objects: squares, wumpus

Property: smelly

Relation: neighboring(对象之间的关系)

Objects: jonh, England (注意John才是对象)

Property: evil, king(都是修辞对象的)

Relationrules

Lucy* is aprofessoris_prof(Lucy)

Allprofessors are people:  "x: (is_prof (x) ) is_person(x) )

John is thedean: is_dean(John)

Deans areprofessors: "x: (is_ dean (x) ) is_ prof (x) )

Everyone is a friend of someone: " x ( \$ y (is-friend-of (y, x) ) )

Is John nofriend of Lucy?: ˺ is_friend_of(John, Lucy)

1.识别任务

2.组合相关知识

3.确定谓词集，函数和常量

4.编码领域基本知识（general knowledge

5.编码具体实例的描述。

6.提出问题，推理，得到答案

7.调试知识库

http://www.iep.utm.edu/prop-log/

http://www.cs.cornell.edu/courses/cs4700/2011fa/lectures/16_firstorderlogic.pdf

https://blog.sciencenet.cn/blog-563898-937932.html

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