Polish notation

After the nationality of the logician Jan Łukasiewicz

Polish notation (uncountable)

1. (arithmetic, logic) 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, 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’

• prefix notation

• infix notation
• postfix notation
• reverse Polish notation