命题逻辑（Propositionallogic，sententiallogic）
其形式是a declarative sentence, or part of a sentence，具有事实（facts）判断（真或假）。一些例子如：
· 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.
命题逻辑的不足：
Propositional logic not expressiveenough
Cannot deduce/compose factsautomatically
Declarative vs. Procedural
自然语言的其他形式
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
基本思路
Don’t treat propositions as “atomic”entities.
基本元素
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
函数Functions: Best_friend(),beginning_of() : Returns object(s)
连接符Connectives: ˄，˅，˺，==>，<==>.
量化，量纲？Quantifiers:
•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king很geedy，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
· Fuzzylogic，Uncertainty, contradictions
分析方法
分析句子中的对象Objects，属性property，和关系relation
例子1：Squares neighboring the wumpus are smelly。
Objects: squares, wumpus
Property: smelly
Relation: neighboring(对象之间的关系)
例子2：Evil king john rules England in 1200
Objects: jonh, England (注意John才是对象)
Property: evil, king(都是修辞对象的)
Relation：rules
形式化表达
Lucy* is aprofessor：is_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)
机器如何理解：在知识库Knowledge Base中，将谓词表示为函数。
知识工程怎么利用一阶逻辑
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
在前面的例子中，All professors are people是领域基本知识，Lucy* is a professor是具体实例描述，Is John no friend of Lucy?即是问题。问题会在基本知识和具体实例基础上做出推理。
后面就交由FOL的求解和推理了，相对而言也更为复杂，暂时不看了。
参考文献：
http://www.iep.utm.edu/prop-log/
http://www.cs.cornell.edu/courses/cs4700/2011fa/lectures/16_firstorderlogic.pdf
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