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# Talk:Łukasiewicz words

I would greatly appreciate if anybody knowledgeable on this subject
would clarify, was it Łukasiewicz *himself* who published the formulation
for Łukasiewicz language and Łukasiewicz words, or was it somebody who named them
*after his honour*? -- Antti Karttunen 16:55, 22 June 2011 (UTC)

- (To be more logical, the question is actually whether
*Łukasiewicz words were invented by (and named after) Jan Łukasiewicz*or whether*Łukasiewicz words were invented by X and named after Jan Łukasiewicz*as the naming-part we know for sure...) -- Antti Karttunen 21:25, 22 June 2011 (UTC)

Stanley mentions in ^{[1]}
that

The bijection between bracketings and Łukasiewicz words is essentially the "reverse Polish notation" or "parenthesis-free notation" developed by the Polish logician Jan Łukasiewicz (1878-1956). He came upon the idea of this notation in 1924 and first published it in 1929, as explained in [18, p. 180, footnote 3]. The connection between reverse Polish notation and enumerative combinatorics appears in a pioneering paper of George Raney [22].

The reference [18] in Stanley's paper is to J. Łukasiewicz, *Selected Works* ^{[2]}. And footnote 3 on page 180, in the beginning of chapter *COMMENTS ON NICOD'S AXIOM AND ON "GENERALIZING DEDUCTION"* just says that

I came upon the idea of a parenthesis-free notation in 1924. I used that notation for the first time in my article

^{[3]}, p. 610, footnote. See also Łukasiewicz^{[4]}pp. 7 and 38, and Kotarbínski, p. 244

Now, by cursory looking at *Selected Works* and an English translation of the latter reference given by Łukasiewicz himself,
entitled *Elements of Mathematical Logic*^{[5]}, I can see many examples of the parenthesis-free "Polish notation" used, but nowhere appears
an exact definition of *Łukasiewicz words*,
although clearly, there is a just short conceptual step from the former to the latter.

Note also, that the notation used by Łukasiewicz is *prefix Polish notation* ^{[6]}, *not* its later variant, *Reverse Polish Notation*
(or **RPN**)^{[7]}.

## References

- ↑ R. Stanley, Hipparchus, Plutarch, Schröder and Hough, p. 7.
- ↑ J. Łukasiewicz,
*Selected Works*(L. Borkowski, ed.), North-Holland, Amsterdam, 1970. - ↑ Jan Łukasiewicz,
*O zaczeniu i potrzebach logiki matematycznej*(On the significance and requirements of mathematical logic).*Nauka Polska*, Vol. X, Warsaw, 1929. - ↑ Dr. Jan Łukasiewicz,
*Elementy logiki matematycznej*(Elements of mathematical logic). Authorized lecture notes prepared by M. Presburger. Publications of the Association of Students of Mathematics and Physics of the University of Warsaw. Vol. XVIII, 1929. - ↑
*Elements of Mathematical Logic*, (published jointly in 1963 by the Polish Scientific Publishers and Pergamon Press) - ↑ Polish notation—Wikipedia.org.
- ↑ Reverse Polish notation—Wikipedia.org.