Definition:Abbreviation of WFFs of Propositional Logic/Rules

Rules for Abbreviation of WFFs

The following rules allow WFFs of propositional logic to be abbreviated so as to make them more readable.

$(1): \quad$ The outermost brackets of a WFF need not be written.

$(2): \quad$ Brackets can be removed around parts of nested WFFs if the inner WFF has a higher binding priority than the outer one.

$(3): \quad$ In the case of repeated $\land$ or $\lor$ connectives, we can replace:

$\paren {\paren {\mathbf A \land \mathbf B} \land \mathbf C}$ with $\paren {\mathbf A \land \mathbf B \land \mathbf C}$

but not:

$\paren {\mathbf A \land \paren {\mathbf B \land \mathbf C} }$ with $\paren {\mathbf A \land \mathbf B \land \mathbf C}$

(there is a reason for this).

Any string obtained from a WFF $\mathbf A$ by applying any of the above rules is called an abbreviation of $\mathbf A$.

The resulting strings are not actually WFFs as such, but can be translated back uniquely into full WFFs.