离散数学（Discrete Math）

                                           - 谓词逻辑

目录

离散数学（Discrete Math）

                                           - 谓词逻辑

Defs

Predicate Logic 谓词逻辑

Universal Quantifier 全称量词

Existential Quantifier 存在量词

Universal Quantifier VS Existential Quantifier 对比

The uniqueness quantifier  唯一量词 ∃!

Binding and Free Variables (静态变量和可变变量)

交换律和结合律

Defs

Predicate Logic 谓词逻辑

The area of logic that deals with predicates and quantitfiers is called the predicate calculus.

Ex：P(x,y,z) = “x=y+z”,故P(3,2,1) = True   P(1,2,1) = False

Universal Quantifier 全称量词

The universal quantification of P(x) is the statement “P(x) for all value of x in the domain.”

∀ is called the universal quantifier.

∀x P(x) is read “for all x P(x) ” or ”for every x P(x)” or ”任取x对于P(x)……”

Key concept :

The Domain 语集/论域 .The domain of discourse , and universal of discourse.

Existential Quantifier 存在量词

The existential quantification of P(x) is the statement “ There exists an element x in the domain such that P(x).”

∃ is called the existential quantifier.

∃x P(x) is read “ There exists an element x in the domain such that P(x). ” or ” 存在x对于P(x)…… ”

The statement is false if and only if ∀x ┐P(x) , i.e., (后接内容解释上述内容，e.g.是for example的意思)

┐(∃x P(x)) ≡ ∀x ┐P(x)

Universal Quantifier VS Existential Quantifier 对比

The uniqueness quantifier  唯一量词 ∃!

∃! x P(x) is the statement “There exists exactly one x such that P(x) is true.”

优先级：∀和∃要高于之前所有的优先级。

例：∀x P(x)∨Q(x) != ∀x ( P(x)∨Q(x) )

Binding and Free Variables (静态变量和可变变量)

交换律和结合律

最后

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