Editing Method of analytic tableaux (section)

===Uniform notation===

When writing tableaux expansion rules, formulae are often denoted using a convention, so that for example {{mvar|&alpha;}} is always considered to be <math>\alpha_1 \land \alpha_2</math>. The following table provides the notation for formulae in propositional, first-order, and modal logic.

{|class="wikitable"
|+
! Notation 
! colspan="3" | Formulae
|-
| {{mvar|&alpha;}}
| <math>\alpha_1 \land \alpha_2</math>
| <math>\neg (\overline{\alpha_1} \lor \overline{\alpha_2})</math>
| <math>\neg (\alpha_1 \to \overline{\alpha_2})</math>
|-
| {{mvar|&beta;}}
| <math>\beta_1 \lor \beta_2</math>
| <math>\overline{\beta_1} \to \beta_2</math>
| <math>\neg (\overline{\beta_1} \land \overline{\beta_2})</math>
|-
| {{mvar|&gamma;}}
| <math>\forall x \gamma_1(x)</math>
| <math>\neg\exists x \overline{\gamma_1(x)}</math>
|-
| {{mvar|&delta;}}
| <math>\exists x \delta_1(x)</math>
| <math>\neg\forall x \overline{\delta_1(x)}</math>
|-
| {{mvar|&pi;}}
| <math>\Diamond \pi_1</math>
| <math>\neg\Box \overline{\pi_1}</math>
|-
| {{mvar|&nu;}}
| <math>\Box \nu_1</math>
| <math>\neg\Diamond \overline{\nu_1}</math>
|}

Each label in the first column is taken to be either formula in the other columns. An overlined formula such as <math>\overline{\alpha_1}</math> indicates that <math>\alpha_1</math> is the negation of whatever formula appears in its place, so that for example in formula <math>\neg (a \lor b)</math> the subformula <math>\alpha_1</math> is the negation of {{mvar|a}}.

Since every label indicates many equivalent formulae, this notation allows writing a single rule for all these equivalent formulae. For example, the conjunction expansion rule is formulated as:

:<math>(\alpha) \frac{\alpha}{\begin{array}{c}\alpha_1\\ \alpha_2\end{array}}</math>