heqin-zhu/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

• ~: negation
• ->: deduce (denoted as '>')

Axioms

The three basic axioms:

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

Deduction

{p,p->q} |- q

Read this book or click here to see more details.

Methods

To prove one proposition:

• Firstly, Use deduction theorem to de-level the formula and get a proposition variable or a proposition in form of ~(...). Let's denote it as p or ~p.
• Next, Create a set called garma and fill it with some generated formulas which is deduced from the above axioms, some theorems and conclusions.
• Then, Search p or ~p in garma, or further, using modus ponent(MP) to deduce p or ~p.
• Finally, if MP can't prove it, use Proof by contradiction instead.

Requirements

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

Licence

MIT