1、谓词和量词Predicates and Quantifiers所有的人都是要死的，苏格拉底是人，所以苏格拉底是要死的。 Three tasks:1. 谓词、个体词、量词2. 谓词公式3. Translate in two ways each of these statements into logical expressions using predicates, quantifiers, and logical connectives. First, let the domain consist of the students in our class and second , let it
2、 consist of all people.a) Everyone in our class has a mobile phone.b) Somebody in our class has seen a foreign movie.c) All students in our class can solve quadratic equations.d) Some student in our class does not want to be rich.(1) 是无理数 .(2) x是有理数 .(3) 小王与小李同岁 .(4) x 与 y具有同学关系 .个体词 the subject 个体词
3、 是指所研究对象中可以独立存在的具体的或抽象的客体。将表示具体或特定的客体的个体词称作个体常项，一般用 a,b,c, 表示。将表示抽象或泛指的个体词称为个体变项，用 x,y,z 表示。Predicate 谓词 是用来刻画个体词性质及个体词之间相互关系的词。 The statement “x is greater than 3” has two parts. The first part, the variable x, is the subject of the statement. The second partthe predicate, “is greater than 3”refers
4、 to a property that the subject of the statement can have. We can denote the statement “x is greater than 3” by P(x). where P denotes the predicate “is greater than 3” and x is the variable. The statement P(x) is also said to be the value of the propositional function P at x. Once a value has been a
5、ssigned to the variable x, the statement P(x) becomes a proposition and has a truth value. Domain of discourse论域个体变项的取值范围为个体域（或称论域）。有一个特殊的个体域， 它是由宇宙间一切事物组成的，称为 全总个体域 。Many mathematical statements assert that a property is true for all values of a variable in a particular domain, called the domain of
6、 discourse (or the universe of discourse), often just referred to as the domain.Note that the domain specifies the possible values of the variable x.(1) 是无理数 .(2) x是有理数 .(3) 小王与小李同岁 .(4) x 与 y具有同学关系 .(1) 凡人都呼吸 .(2) 所有的人都长着黑头发 .(3) 兔子比乌龟跑得快 .(4) 在美国留学的学生未必都是亚洲人 .Universal Quantifier The universal qua
7、ntification of P(x) is the statement The notation xP(x) denotes the universal quantification of P(x). Here is called the universal quantifier. Note that the domain specifies the possible values of the variable x. The meaning of the universal quantification of P(x) changes when we change the domain. The domain must always be specified when a universal quantifier is used; without it, the universal quantification of a statement is not defined. the key word：所有的、一切的、每一个、任意的、 凡、都“P(x) for all values of x in the domain.”
