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Formalized Mathematics

(a computer assisted approach)

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Volume 23, Issue 3 (Sep 2015)


Polish Notation

Taneli Huuskonen
  • Department of Mathematics and Statistics University of Helsinki Finland
Published Online: 2015-09-30 | DOI: https://doi.org/10.1515/forma-2015-0014


This article is the first in a series formalizing some results in my joint work with Prof. Joanna Golinska-Pilarek ([12] and [13]) concerning a logic proposed by Prof. Andrzej Grzegorczyk ([14]).

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 [15], eliminates the need for parentheses and is generally well suited for rigorous reasoning about syntactic properties of formulas.

Keywords: Polish notation; syntax; well-formed formula

MSC: 68R15; 03B35

MML identifier:: POLNOT 1


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  • [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.

  • [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

  • [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

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  • [6] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.

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  • [8] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

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  • [11] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

  • [12] Joanna Golinska-Pilarek and Taneli Huuskonen. Logic of descriptions. A new approach to the foundations of mathematics and science. Studies in Logic, Grammar and Rhetoric, 40(27), 2012.

  • [13] Joanna Golinska-Pilarek and Taneli Huuskonen. Grzegorczyk’s non-Fregean logics. In Rafał Urbaniak and Gillman Payette, editors, Applications of Formal Philosophy: The Road Less Travelled, Logic, Reasoning and Argumentation. Springer, 2015.

  • [14] Andrzej Grzegorczyk. Filozofia logiki i formalna logika niesymplifikacyjna. Zagadnienia Naukoznawstwa, XLVII(4), 2012. In Polish.

  • [15] Jan Łukasiewicz. Uwagi o aksjomacie Nicoda i ‘dedukcji uogólniajacej’. In Ksiega pamiatkowa Polskiego Towarzystwa Filozoficznego, Lwów, 1931. In Polish.

  • [16] Andrzej Nedzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990.

  • [17] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.

  • [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

  • [19] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.

About the article

Received: 2015-04-30

Published Online: 2015-09-30

Published in Print: 2015-09-01

Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, DOI: https://doi.org/10.1515/forma-2015-0014. Export Citation

© by Taneli Huuskonen. This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

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