Definition:Language of Propositional Logic/Formal Grammar/WFF

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Let $\mathbf A$ be approved of by the formal grammar of propositional logic.

Then $\mathbf A$ is called a well-formed formula of propositional logic.

Often, one abbreviates "well-formed formula", speaking of a WFF of propositional logic instead.

More informally, a WFF of propositional logic is any sequence of symbols containing statement variables, such that when statements are substituted for the statement variables (the same statement for any given statement variable throughout), the result is a statement.

Also known as

There are many ways this concept is addressed in the literature, for instance:

  • propositional formula
  • statement form
  • logical formula

However, on $\mathsf{Pr} \infty \mathsf{fWiki}$, logical formula is a term used to refer to any kind of expression used in symbolic logic, whereas statement form is used in this way in some sources.

Hence on $\mathsf{Pr} \infty \mathsf{fWiki}$ WFF of propositional logic and propositional formula are the terms of choice for this concept.

Also see