Editing Polish notation (section)

== History ==

A quotation from a paper by [[Jan Łukasiewicz]] in 1931<ref name="Łukasiewicz_1931"/>{{rp|page=367, Footnote 3}}<ref name="Łukasiewicz_1970"/>{{rp|page=180, Footnote 3}} states how the notation was invented:

<blockquote>I came upon the idea of a parenthesis-free notation in 1924. I used that notation for the first time in my article Łukasiewicz (1), p. 610, footnote.</blockquote>

The reference cited by Łukasiewicz, i.e., Łukasiewicz (1),<ref name="Łukasiewicz_1929a"/> is apparently a lithographed report in [[Polish language|Polish]]. The referring paper<ref name="Łukasiewicz_1931"/> by Łukasiewicz was reviewed by [[Henry Pogorzelski|Henry A. Pogorzelski]] in the ''Journal of Symbolic Logic'' in 1965.<ref name="Pogorzelski_1965"/> [[Heinrich Behmann]], editor in 1924 of the article of [[Moses Schönfinkel]],<ref name="Mengelberg"/> already had the idea of eliminating parentheses in logic formulas. In one of his papers Łukasiewicz stated that his notation is the most compact and the first linearly written parentheses-free notation, but not the first one as [[Gottlob Frege]] proposed his parentheses-free [[Begriffsschrift]] notation in 1879 already.<ref name="Gottschall_2005"/>

[[Alonzo Church]] mentions this notation in his classic book on [[mathematical logic]] as worthy of remark in notational systems even contrasted to [[Alfred North Whitehead|Alfred Whitehead]] and [[Bertrand Russell]]'s logical notational exposition and work in [[Principia Mathematica]].<ref name="Church_1944"/>

In Łukasiewicz's 1951 book, ''Aristotle's Syllogistic from the Standpoint of Modern Formal Logic'', he mentions that the principle of his notation was to write the [[Function symbol|functor]]s before the [[Argument of a function|argument]]s to avoid brackets and that he had employed his notation in his logical papers since 1929.<ref name="Łukasiewicz_1957"/>{{rp|page=78}} He then goes on to cite, as an example, a 1930 paper he wrote with [[Alfred Tarski]] on the [[Propositional calculus|sentential calculus]].<ref name="Łukasiewicz_1930"/>

While no longer used much in logic,<ref name="Martínez_2011"/> Polish notation has since found a place in [[computer science]].