Polish Notation

Abstract

This article is the first in a series formalizing some results in my joint work with Prof. Joanna Golinska-Pilarek concerning a logic proposed by Prof. Andrzej Grzegorczyk. We present some mathematical folklore about representing formulas in "Polish notation", that is, with operators of fixed arity prepended to their arguments. This notation, which was published by Jan Łukasiewicz in, eliminates the need for parentheses and is generally well suited for rigorous reasoning about syntactic properties of formulas.