logic

1. proposition是一个声明性描述，只有T或F

2. proposition通过logical connectives成为larger proposition，故而logical connectives是一个operations

 

 

although=and=but=nevertheless

3. Compound propositions复合命题的正确性取决于子命题

 

4. Vacuous truth

A → B  If A (premise) then B (conclusion)

只有premise成立但是conclusion不成立时才是False

 5. # X={}

Every x∈X is odd(True)

Every x∈X is even(True)

6. A proposition is:

a tautology if it is always true,

a contradiction if it is always false,

a contingency if it is neither a tautology or a contradiction,

satsfiable if it is not a contradiction.

7. Logical equivalence

e.g. A=¬(¬A)

8. valid

An argument is valid if the conclusions are true whenever all the premises are true. Thus: if we believe the premises, we should also believe the conclusion

9. Syntax is how things are written:

Semantics is what things mean

“Rabbit” and “Bunny” are syntactically different, but semantically the same.

10. well-formed-formulas

 

 

 

p∧¬T没有（）不符合

(p∧q∧r)三个用一个（）不符合

通俗习惯有:

a) 无歧义时省略括号，e.g. p∧q

b) ¬ binds more tightly than ∧ and ∨, which bind more tightly than → and ↔ (e.g. p∧q → r instead of ((p∧q) → r)

11. Parse trees

The structure of well-formed formulas (and other grammar-defined syntaxes) can be shown with a parse tree