zhehaoli1999 / system-L

:arrow_right:Formal logic deduction based on system-L

system-L

Descripton

it's a formal logic deduction based on system-L

symbols

~ , -> (in the script, i use > to repr it)

rules

The basic three axioms:

• L1: p->(q->p)
• L2: (p->(q->r)) -> ((p->q)->(p->r))
• L3: ~q->~p -> (p->q)

deduction

{p,p->q} |- q

you can read the professional book or click here to see more details

Idea

To prove one proposition:

• Firstly, I use deduction theorem(演绎定理) to de-level the formula and finally get a prop varible or a prop in form of ~(...). let's mark it as p or ~p
• Next, I create a set garma and fill it with some generated formulas using the three axioms(公理),some theorem and conclusions.
• Then, I search p or ~p in `garma, or further, using modus ponent(MP) to deduct p or ~p.
• Finally, if using mp can't prove it, I will use Proof by contradiction(反证法) to prove it.

Requirement

python modules

• sympy

Visual

To do

• 将证明过程对象化,便于处理,打印(英文版,中文版),
• 其他连接词的转换
• 处理简单的, 有一定模式的自然语言, 形成命题推理

Contact

• mail: [e-mail]
• QQ : 414313516

Licence

MIT