命题逻辑和谓词逻辑之间的区别

逻辑推理构成了计算机科学和数学领域的基础。它们有助于建立有效或无效的数学论证。

1.命题逻辑：
命题基本上是具有真实价值的陈述性句子。真值可以是true或false，但是需要为其分配两个值中的任何一个，并且不要含糊不清。使用命题逻辑的目的是单独或组合分析陈述。

例如 ：
以下语句：

1. 如果x是实数，则x ² > 0
2. 你叫什么名字?
3. (a + b) ² = 100
4. 这句话是错误的。
5. 这句话是真的。

不是命题，因为它们没有真理的价值。他们是模棱两可的。

但是以下语句：

1. (a + b) ² = a ² + 2ab + b ²
2. 如果x是实数，则x ² > = 0
3. 如果x是实数，则x ² <0
4. 太阳从东边升起。
5. 太阳从西边出来。

是所有命题，因为它们具有特定的真值(是非)。

命题逻辑的分支是命题逻辑。

2.谓词逻辑：
谓词是属性，可以用来更好地表达句子主题的其他信息。定量谓词是一个命题，也就是说，当您为带有变量的谓词分配值时，它可以成为一个命题。

例如 ：

在P(x)中：x> 5，x是主题或变量，而’> 5’是谓词。

P(7)：7> 5是一个命题，其中我们为变量x赋值，并且它有一个真值，即True。

谓词变量可以采用的一组值称为“ Universe”或“ Domain of Discourse”或“ Predicate Domain”。

命题逻辑与谓词逻辑的区别：

	Propositional Logic	Predicate Logic
1	Propositional logic is the logic that deals with a collection of declarative statements which have a truth value, true or false.	Predicate logic is an expression consisting of variables with a specified domain. It consists of objects, relations and functions between the objects.
2	It is the basic and most widely used logic. Also known as Boolean logic.	It is an extension of propositional logic covering predicates and quantification.
3	A proposition has a specific truth value, either true or false.	A predicate’s truth value depends on the variables’ value.
4	Scope analysis is not done in propositional logic.	Predicate logic helps analyze the scope of the subject over the predicate. There are three quantifiers : Universal Quantifier (∀) depicts for all, Existential Quantifier (∃) depicting there exists some and Uniqueness Quantifier (∃!) depicting exactly one.
5	Propositions are combined with Logical Operators or Logical Connectives like Negation(¬), Disjunction(∧), Conjunction(∨), Exclusive OR(⊕), Implication(⇒), Bi-Conditional or Double Implication(⇔).	Predicate Logic adds by introducing quantifiers to the existing proposition.
6	It is a more generalized representation.	It is a more specialized representation.
7	It cannot deal with sets of entities.	It can deal with set of entities with the help of quantifiers.