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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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Volume 23, Issue 3 (Sep 2015)

Issues

Grzegorczyk’s Logics. Part I

Taneli Huuskonen
  • Department of Mathematics and Statistics University of Helsinki Finland
Published Online: 2015-09-30 | DOI: https://doi.org/10.1515/forma-2015-0015

Abstract

This article is the second in a series formalizing some results in my joint work with Prof. Joanna Golinska-Pilarek ([9] and [10]) concerning a logic proposed by Prof. Andrzej Grzegorczyk ([11]).

This part presents the syntax and axioms of Grzegorczyk’s Logic of Descriptions (LD) as originally proposed by him, as well as some theorems not depending on any semantic constructions. There are both some clear similarities and fundamental differences between LD and the non-Fregean logics introduced by Roman Suszko in [15]. In particular, we were inspired by Suszko’s semantics for his non-Fregean logic SCI, presented in [16].

Keywords: non-Fregean logic; logic of descriptions; non-classical propositional logic; equimeaning connective

MSC: 03B60; 03B35

MML identifier:: GRZLOG 1

References

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

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

  • [3] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.

  • [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.

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

  • [6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

  • [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

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

  • [9] 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.

  • [10] 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.

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

  • [12] Taneli Huuskonen. Polish notation. Formalized Mathematics, 23(3):161-176, 2015. doi:1 0.1515/forma-2015-0014.

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

  • [14] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.

  • [15] Roman Suszko. Non-Fregean logic and theories. Analele Universitatii Bucuresti. Acta Logica, 9:105-125, 1968.

  • [16] Roman Suszko. Semantics for the sentential calculus with identity. Studia Logica, 28: 77-81, 1971.

  • [17] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 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.

  • [20] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

  • [21] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 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-2015-0015. 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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