Definition:Abbreviation of WFFs of Propositional Logic/Rules
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Rules for Abbreviation of WFFs
The following rules allow WFFs of propositional logic to be abbreviated so as to make them more readable.
- $(2): \quad$ 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).
- but not:
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.
Sources
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.4$: Main Connective