Definition:Polish Notation/Formal Definition

Definition

Let $\AA$ be an alphabet.

Let each $s \in \AA$ be assigned a natural number called its arity.

The formal grammar for Polish notation is given by the single bottom-up rule:

If $s$ has arity $n$ and $\phi_1, \ldots, \phi_n$ are well-formed formulas, then:

$s \phi_1 \cdots \phi_n$

is also a well-formed formula.

Notably, in the case where $s$ has arity $0$, this is a vacuous truth, so any such $s$ constitutes a well-formed formula.

Sources

• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.14$: Exercise $32$
• 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\mathrm{II}.4$ Polish Notation: Definition $\mathrm{II}.4.1$