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I'm studying Propositional and First Order Logic and I have to practice with the Tableaux Method in order to check satisfiability of a formula.

I create new nodes of the tree by using the Completion Rules in a straightforward way, but I have a doubt about it.

Everytime I have a new node, I repeat some of the previous node's formulas. I make an example:

I have this block:

Tableaux with branches

Is it legit to repeat the two "or" formulas again in the two new branches?

I rewrite them because in this way I don't forget to use them, it is only for my comfort.

Thanks in advance.

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    One advantage of your method is that it makes the connection to other styles of proof easier to see. – 2017-01-20
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    @FabioSomenzi That's an excellent point, though I suppose it does depend on exactly which method. E.g. for a Fitch-style proof where I use subproofs, the connection is of course between branches and subproofs, but I typically don't copy (reiterate) statements from outside the subproofs into the subproofs. – 2017-01-20

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You have two options:

  1. Either you do what you do, which is to copy all of the remaining statements into the branches below. The disadvantage of this is that you have to copy all those statements (i.e. it will be more work)

  2. You don't copy the statements, but when you apply a tree rule on any of the remaining statements, you have to make sure to put the result in all of the branches under it. The disadvantage of this is that you have to be a bit more careful in making sure that indeed you do this.

So yes, what you do is fine, but not necessary, as long as you are careful!

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    Thank you Bram28, so if it is fine to mantain them, I will continue to use the first option you wrote :) Thanks again – 2017-01-22
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    @SimoneC. yes, that's fine, whichever you are more comfortable with! Personally, I hate doing more work than I have to, so I typically use the second option :) – 2017-01-22