User:Lord Farin/Tableau Proof Rules

= General form of Tableau proof =

The tableau proofs work with tables and general lines like this:



= Axioms =

Throughout, $i, j \ldots$ denote arbitrary line numbers in a tableau proof.

Capital letters $I, J \ldots$ denote arbitrary sets of line numbers.

Excluded Middle
= Abbreviations for Derived results =

Many results are too common to derive every time, and therefore have been assigned an abbreviation for use in tableau proofs.

A listing is below; here is a template for a tableau proof row:

It is understood that all abbreviation links below are to be put in the fourth column of such a row.

Abbreviations and links

 * Absorption Laws (Logic): $\mathrm {AL}$;  $\mathrm {AL}$ 
 * Constructive Dilemma: $\mathrm {CD}$;  $\mathrm {CD}$ 
 * De Morgan's Laws (Logic): $\mathrm {DM}$;  $\mathrm {DM}$ 
 * Destructive Dilemma: $\mathrm {DD}$;  $\mathrm {DD}$ 
 * Double Negation Elimination: $\neg \neg \mathcal E$;  $\neg \neg \mathcal E$ 
 * Double Negation Introduction: $\neg \neg \mathcal I$;  $\neg \neg \mathcal I$ 
 * Hypothetical Syllogism: $\mathrm {HS}$;  $\mathrm {HS}$ 
 * Modus Ponendo Tollens: $\mathrm {MPT}$;  $\mathrm {MPT}$ </tt>
 * Modus Tollendo Ponens: $\mathrm {MTP}$;  $\mathrm {MTP}$ </tt>
 * Modus Tollendo Tollens: $\mathrm {MTT}$;  $\mathrm {MTT}$ </tt>
 * Praeclarum Theorema: $\mathrm {PT}$;  $\mathrm {PT}$ </tt>
 * Proof by Cases: $\mathrm {PBC}$;  $\mathrm {PBC}$ </tt>
 * Reductio ad Absurdum: $\mathrm {RAA}$;  $\mathrm {RAA}$ </tt>
 * Rule of Association: $\mathrm {Assoc}$;  $\mathrm {Assoc}$ </tt>
 * Rule of Commutation: $\mathrm {Comm}$;  $\mathrm {Comm}$ </tt>
 * Rule of Distribution: $\mathrm {Dist}$;  $\mathrm {Dist}$ </tt>
 * Rule of Idempotence: $\mathrm {Idemp}$;  $\mathrm {Idemp}$ </tt>
 * Rule of Transposition: $\mathrm {TP}$;  $\mathrm {TP}$ </tt>

For any other theorem to be cited, use:


 * Rule of Theorem Introduction: $\mathrm {TI}$;  $\mathrm {TI}$ </tt>

It is required to give a reference to the origin of your result (in the optional sixth Notes column). If it is not on ProofWiki, make a page for it, even if you don't know the proof.