Polish Notation

• Autorzy: Taneli Huuskonen
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Polish notation; syntax; well-formed formula

Kategorie tematyczne

• 03B35: Mechanization of proofs and logical operations
• 68R15: Combinatorics on words

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2015
• Tom: 23
• Numer: 3
• Strony: 161-176

Daty

wydano

2015-09-01

otrzymano

2015-04-30

online

2015-09-30

Twórcy

autor

Taneli Huuskonen

• Department of Mathematics and Statistics University of Helsinki Finland

Bibliografia

• [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
• [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.
• [5] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
• [6] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
• [7] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
• [8] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
• [9] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
• [10] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
• [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.

Identyfikatory

DOI

10.1515/forma-2015-0014