Polish Notation

Taneli Huuskonen

Formalized Mathematics (2015)

  • Volume: 23, Issue: 3, page 161-176
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Taneli Huuskonen. "Polish Notation." Formalized Mathematics 23.3 (2015): 161-176. <http://eudml.org/doc/276418>.

@article{TaneliHuuskonen2015,
abstract = {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.},
author = {Taneli Huuskonen},
journal = {Formalized Mathematics},
keywords = {Polish notation; syntax; well-formed formula},
language = {eng},
number = {3},
pages = {161-176},
title = {Polish Notation},
url = {http://eudml.org/doc/276418},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Taneli Huuskonen
TI - Polish Notation
JO - Formalized Mathematics
PY - 2015
VL - 23
IS - 3
SP - 161
EP - 176
AB - 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.
LA - eng
KW - Polish notation; syntax; well-formed formula
UR - http://eudml.org/doc/276418
ER -

References

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  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. 
  2. [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
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  11. [11] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. 
  12. [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. Zbl06585187
  13. [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. Zbl1086.03024
  14. [14] Andrzej Grzegorczyk. Filozofia logiki i formalna logika niesymplifikacyjna. Zagadnienia Naukoznawstwa, XLVII(4), 2012. In Polish. 
  15. [15] Jan Łukasiewicz. Uwagi o aksjomacie Nicoda i ‘dedukcji uogólniajacej’. In Ksiega pamiatkowa Polskiego Towarzystwa Filozoficznego, Lwów, 1931. In Polish. 
  16. [16] Andrzej Nedzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990. 
  17. [17] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990. 
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  19. [19] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990. 

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