Definition:Łukasiewicz's Polish Notation

Definition

Łukasiewicz's Polish notation is a system of prefix notation for propositional logic.

Statements are represented by lowercase letters, as the conventional notation.

Logical connectives are represented by uppercase letters as follows:

Connective	Conventional symbology	Łukasiewicz's Polish notation
Negation	$\lnot p$	$\operatorname N p$
Conjunction	$p \land q$	$\operatorname K p q$
Implication	$p \implies q$	$\operatorname C p q$
Disjunction	$p \lor q$	$\operatorname A p q$
Biconditional	$p \iff q$	$\operatorname E p q$

Examples

Arbitrary Example

The compound statement expresssed in infix notation as:

$\paren {p \land \lnot q} \implies \paren {p \lor \lnot r}$

would be expressed in Łukasiewicz's Polish notation as:

$\operatorname C \operatorname K p \operatorname N q \operatorname A p \operatorname N r$

Also see

• Results about Łukasiewicz's Polish notation can be found here.

Source of Name

This entry was named for Jan Łukasiewicz.

Historical Note

Łukasiewicz's Polish notation was introduced by Jan Łukasiewicz in $1920$ as a parenthesis-free notation for propositional logic.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): prefix notation (Polish notation)