propositional logic
时间: 2023-04-25 13:02:32 浏览: 85
命题逻辑是一种逻辑系统,用于研究命题之间的关系和推理。它使用符号表示命题,例如“P”和“Q”,并使用逻辑运算符,例如“与”、“或”和“非”,来构建复合命题。命题逻辑的应用包括计算机科学、哲学、数学和语言学等领域。
相关问题
重写 “命题投影时序逻辑(Propositional Projection Temporal Logic,PPTL)[21]是 PTL 的一个可判定子集,PPTL 中的每个公式 均是原子命题,具有完全正则表达能力且是可判定的”
PPTL是命题投影时序逻辑(Propositional Projection Temporal Logic)的缩写,是时序逻辑 PTL 的可判定子集。PPTL中的每个公式都由原子命题组成,具有完全正则表达能力,并且可以被判定。
A new operator, ,or exclusive-or, may be defined by the following truth table Create a propositional calculus expression using only ꓥ, ꓦ and ¬that is equivalent to P Q. Prove this equivalence using truth tables.
The truth table for the exclusive-or operator is:
| P | Q | P ꓥ Q |
|---|---|-------|
| F | F | F |
| F | T | T |
| T | F | T |
| T | T | F |
To create a propositional calculus expression using only ꓥ, ꓦ, and ¬ that is equivalent to P ꓥ Q, we can use the following expression:
(P ꓦ Q) ∧ ¬(P ꓥ Q)
To prove the equivalence using truth tables, we can create a truth table for both expressions and show that they have the same values for all possible truth value combinations of P and Q.
| P | Q | P ꓥ Q | P ꓦ Q | ¬(P ꓥ Q) | (P ꓦ Q) ∧ ¬(P ꓥ Q) |
|---|---|-------|-------|----------|---------------------|
| F | F | F | F | T | F |
| F | T | T | T | F | F |
| T | F | T | T | F | F |
| T | T | F | T | T | F |
As we can see, both expressions have the same values for all possible truth value combinations of P and Q, indicating that they are equivalent.
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