For any argument form in the language of propositional logic, the tree for that argument ...
- always closes after a finite number of steps
- can always be completed after a finite number of steps
- can sometimes be closed only after an infinite number of steps
- can sometimes be completed only after an infinite number of steps
Which of the option is true? 1, 2, 3 or 4? My attempt:
My logic instructor told me infinite set of formulas are not allowed. He also told me infinite length formulas are not allowed.
Therefore, I can only deal with finite sets of finite length formulas.
There is no way to get an infinite step tree with a finite set of finite length formulas. (Not exactly sure about this)
Therefore every tree must be able to be completed in a finite number of steps.
Option 2 is my answer.
Could someone check the reasoning for my argument?