Definition:Tableau Proof/Natural Deduction

Definition
A tableau proof by natural deduction is a technique for presenting a logical argument in a straightforward, standard form.

A tableau proof is a sequence of lines specifying the order of premises, assumptions, inferences and conclusion in support of an argument.

Each line of a tableau proof has a particular format. It consists of the following parts:


 * Line: The line number of the proof. This is a simple numbering from 1 upwards.
 * Pool: The list of all the lines containing the pool of assumptions for the formula introduced on this line.
 * Formula: The formula or statement form introduced on this line.
 * Rule: The justification for introducing this line. This should be the appropriate abbreviation of the proof rule being used to derive this line, for example:
 * P (for Premise)
 * A (for Assumption)
 * $\implies \mathcal I$ (for example)
 * Depends on: The lines (if any) upon which this line directly depends. For premises and assumptions, this field will be empty.

Optionally, a comment may be added to explicitly point out possible intricacies.

If any assumptions are discharged on a certain line, for the sake of clarity it is preferred that such be mentioned explicitly in a comment.

At the end of a tableau proof, the only lines upon which the proof depends may be those which contain the premises.