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A bilateral Hilbert-style investigation of 2-intuitionistic logic. / Drobyshevich, Sergey.

In: Journal of logic and computation, Vol. 29, No. 5, 01.09.2019, p. 665-692.

Research output: Contribution to journal › Article › peer-review

Harvard

Drobyshevich, S 2019, 'A bilateral Hilbert-style investigation of 2-intuitionistic logic', Journal of logic and computation, vol. 29, no. 5, pp. 665-692. https://doi.org/10.1093/logcom/exz010

APA

Drobyshevich, S. (2019). A bilateral Hilbert-style investigation of 2-intuitionistic logic. Journal of logic and computation, 29(5), 665-692. https://doi.org/10.1093/logcom/exz010

Vancouver

Drobyshevich S. A bilateral Hilbert-style investigation of 2-intuitionistic logic. Journal of logic and computation. 2019 Sept 1;29(5):665-692. doi: 10.1093/logcom/exz010

Author

Drobyshevich, Sergey. / A bilateral Hilbert-style investigation of 2-intuitionistic logic. In: Journal of logic and computation. 2019 ; Vol. 29, No. 5. pp. 665-692.

BibTeX

@article{f81c05e12ea747619a47e511567a171b,
title = "A bilateral Hilbert-style investigation of 2-intuitionistic logic",
abstract = "We develop a bilateral Hilbert-style calculus for 2-intuitionistic logic of Heinrich Wansing. This calculus is defined over signed formulas of two types: formulas signed with plus correspond to assertions, while formulas signed with minus correspond to rejections. In this way, the provided system is a Hilbert-style calculus, which does take rejection seriously by considering it a primitive notion on par with assertion. We show that this presentation is not trivial and provide two equivalent axiomatizations obtained by extending intuitionistic and dual intuitionistic logics, respectively. Finally, we show that 2-intuitionistic logic is in some sense definitionally equivalent to a variant of Nelson's logic with constructible falsity.",
keywords = "2-intuitionistic logic, Hilbert-style calculi, rejection, bilateralism, definitional equivalence, NEGATION",
author = "Sergey Drobyshevich",
year = "2019",
month = sep,
day = "1",
doi = "10.1093/logcom/exz010",
language = "English",
volume = "29",
pages = "665--692",
journal = "Journal of logic and computation",
issn = "0955-792X",
publisher = "OXFORD UNIV PRESS",
number = "5",

}

RIS

TY - JOUR

T1 - A bilateral Hilbert-style investigation of 2-intuitionistic logic

AU - Drobyshevich, Sergey

PY - 2019/9/1

Y1 - 2019/9/1

N2 - We develop a bilateral Hilbert-style calculus for 2-intuitionistic logic of Heinrich Wansing. This calculus is defined over signed formulas of two types: formulas signed with plus correspond to assertions, while formulas signed with minus correspond to rejections. In this way, the provided system is a Hilbert-style calculus, which does take rejection seriously by considering it a primitive notion on par with assertion. We show that this presentation is not trivial and provide two equivalent axiomatizations obtained by extending intuitionistic and dual intuitionistic logics, respectively. Finally, we show that 2-intuitionistic logic is in some sense definitionally equivalent to a variant of Nelson's logic with constructible falsity.

AB - We develop a bilateral Hilbert-style calculus for 2-intuitionistic logic of Heinrich Wansing. This calculus is defined over signed formulas of two types: formulas signed with plus correspond to assertions, while formulas signed with minus correspond to rejections. In this way, the provided system is a Hilbert-style calculus, which does take rejection seriously by considering it a primitive notion on par with assertion. We show that this presentation is not trivial and provide two equivalent axiomatizations obtained by extending intuitionistic and dual intuitionistic logics, respectively. Finally, we show that 2-intuitionistic logic is in some sense definitionally equivalent to a variant of Nelson's logic with constructible falsity.

KW - 2-intuitionistic logic

KW - Hilbert-style calculi

KW - rejection

KW - bilateralism

KW - definitional equivalence

KW - NEGATION

UR - http://www.scopus.com/inward/record.url?scp=85084116673&partnerID=8YFLogxK

U2 - 10.1093/logcom/exz010

DO - 10.1093/logcom/exz010

M3 - Article

VL - 29

SP - 665

EP - 692

JO - Journal of logic and computation

JF - Journal of logic and computation

SN - 0955-792X

IS - 5

ER -

ID: 23290027