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I'm using the open logic natural deduction tool (https://proofs.openlogicproject.org/) as it makes writing proofs very clear and clean but I can't seem to apply the reduction to absurdity rule correctly.

Construct a proof for the argument: ¬Q, R → P ∴ (P → Q) → ¬R
        
1   ¬Q      
2   R → P                   
3       P → Q                       
4           R       
5           P           →E 2, 4 
6           Q           →E 3, 5 
7           ¬Q          R 1 
8           Q ∧ ¬Q      ∧I 6, 7 
9       ¬R              ¬I 4–8

I think I'm using the rule as stated in the corresponding section of the tool but I get an error message saying "Line 9: Is not a proper application of the rule ¬I (for the line(s) cited)." What am I doing wrong?

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  • 1
    Your line 8 can be simply changed to ⊥ (¬E 6, 7), line 9 then changed to ¬R (¬I 4–8), then in line 10 you can arrive at your conclusion (P → Q) → ¬R (→I 3–9) which can be verified quickly in your referenced open logic online tool... Feb 4, 2022 at 3:14
  • Thanks! It worked :)
    – daniel
    Feb 4, 2022 at 3:22
  • Now we must listen.
    – Hudjefa
    Mar 4, 2023 at 14:37

1 Answer 1

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Open Logic is an admirable project indeed.

For all those interested, I would like to recommend also Stanford Introduction to Logic and the tools therein. As a sample, I present one with the implementation of modus tollens:

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