# Polish notation

## English

### Etymology

After the nationality of the logician Jan Łukasiewicz

### Noun

1. () A notation for arithmetic (and logical) formulae in which operations (respectively, quantifiers and operands) are written immediately before their operands, used to avoid the need for parentheses; for example, 3 * (4 + 7) is written as * 3 + 4 7 and A AND B is written as AND A B.
• 2009, Brandon C. Look, “Symbolic Logic II, Lecture 6”, in www.uky.edu/~look[1], retrieved 2012-11-22:
In Polish Notation, the connectives are placed before the wffs. The virtue of this sentence is that its grammar is simpler, for it has no need for parentheses. Sider’s examples: (P ∧ Q) → R and P ∧ (Q → R) become → ∧PQR and ∧P → QR.
If you actually look at a text in this tradition, you’ll find something slightly different. “C” stands for “consequence”, i.e., implication (→) and “N” for negation (∼).
So,consider the following from Tarski and Łukasiewicz’s Investigations into the Sentential Calculus. The claim there is that there are three axioms:
‘CCpqCCqrCpr’
‘CCNppp’
‘CpCNpq’