Definition:Tableau Proof (Formal Systems)
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 propositional formula introduced on this line.
- Rule: The justification for introducing this line. This should be the rule of inference being used to derive this line.
- 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.
At the end of a tableau proof, the only lines upon which the proof depends may be those which contain the premises.
The length of a tableau proof is the number of lines it has.
When constructing a tableau proof, use the BeginTableau template to start it:
statementis the statement of logic that is to beproved, without the
$ ... $delimiters
proof systemis a link (optional) to page containing the specific proof system in which this proof is valid.
At the end of the proof, use the EndTableau template
- 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): $\S 4.3$: Derivable Formulae
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): $\S 1.2$: Conditionals and Negation
- 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems ... (previous) ... (next): $\S 1.2.1$: Rules for natural deduction
- 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 3.2$