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Talk:Łukasiewicz words

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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].


  1. R. Stanley, Hipparchus, Plutarch, Schröder and Hough, p. 7.
  2. J. Łukasiewicz, Selected Works (L. Borkowski, ed.), North-Holland, Amsterdam, 1970.
  3. Jan Łukasiewicz, O zaczeniu i potrzebach logiki matematycznej (On the significance and requirements of mathematical logic). Nauka Polska, Vol. X, Warsaw, 1929.
  4. 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.
  5. Elements of Mathematical Logic, (published jointly in 1963 by the Polish Scientific Publishers and Pergamon Press)
  6. Polish
  7. Reverse Polish