Grzegorczyk’s Logics. Part I

Taneli Huuskonen

Formalized Mathematics (2015)

  • Volume: 23, Issue: 3, page 177-187
  • ISSN: 1426-2630

Abstract

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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].

How to cite

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Taneli Huuskonen. "Grzegorczyk’s Logics. Part I." Formalized Mathematics 23.3 (2015): 177-187. <http://eudml.org/doc/276430>.

@article{TaneliHuuskonen2015,
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].},
author = {Taneli Huuskonen},
journal = {Formalized Mathematics},
keywords = {non-Fregean logic; logic of descriptions; non-classical propositional logic; equimeaning connective},
language = {eng},
number = {3},
pages = {177-187},
title = {Grzegorczyk’s Logics. Part I},
url = {http://eudml.org/doc/276430},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Taneli Huuskonen
TI - Grzegorczyk’s Logics. Part I
JO - Formalized Mathematics
PY - 2015
VL - 23
IS - 3
SP - 177
EP - 187
AB - 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].
LA - eng
KW - non-Fregean logic; logic of descriptions; non-classical propositional logic; equimeaning connective
UR - http://eudml.org/doc/276430
ER -

References

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  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
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  9. [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. Zbl06585187
  10. [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. Zbl1086.03024
  11. [11] Andrzej Grzegorczyk. Filozofia logiki i formalna logika niesymplifikacyjna. Zagadnienia Naukoznawstwa, XLVII(4), 2012. In Polish. 
  12. [12] Taneli Huuskonen. Polish notation. Formalized Mathematics, 23(3):161-176, 2015. doi:1 0.1515/forma-2015-0014. 
  13. [13] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990. 
  14. [14] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990. 
  15. [15] Roman Suszko. Non-Fregean logic and theories. Analele Universitatii Bucuresti. Acta Logica, 9:105-125, 1968. Zbl0233.02010
  16. [16] Roman Suszko. Semantics for the sentential calculus with identity. Studia Logica, 28: 77-81, 1971. Zbl0243.02016
  17. [17] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990. 
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  21. [21] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990. 

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