命题逻辑

1. 命题(propositions)与 命题变元 与 命题公式 的关系

   

2. atomic propositions (原子命题)：不能再拆
3. conjunction (合取) “$\wedge$” disjunction (析取) “$\vee$”
4. exclusive or (异或)
5. 半加器

6. ($(P\rightarrow P)\rightarrow R)$

7. 指派：

   

8. A compound proposition formula is said to be
   • a tautology（重言式）if it is true under any assignment;
   • satisfiable（可满足的）if it is true under some assignment;
   • a contradiction（矛盾式）if it is false under any assignment.

9. Let a and B be two compound proposition formulas over variables $P_1,…,P_n$. If the truth values of $\alpha$ and $\beta$ are the same under any assignment,then a and B are said to be logical equivalent(等值/逻辑等价)，denoted by $\alpha\Leftrightarrow \beta$ or $\alpha=\beta$.

10. logical equivalence theorem (等值定理)

11. 德摩根律：

    

12. 

1. (tautological implication)重言蕴含

1. 证明法：

2. Example: Proof by Rules of Inferences （正常的证明）

3. Proof by Resolutions 归结法 examples