TY - JOUR

T1 - Recognizability in pre-Heyting and well-composed logics

AU - Maksimova, Larisa L.vovna

AU - Yun, Veta Fedorovna

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this paper the problems of recognizability and strong recognizavility, perceptibility and strong perceptibility in extensions of the minimal Johansson logic J [1] are studied. These concepts were introduced in [2, 3, 4]. Although the intuitionistic logic Int is recognizable over J [2], the problem of its strong recognizability over J is not solved. Here we prove that Int is strong recognizable and strong perceptible over the minimal pre-Heyting logic Od and the minimal well-composed logic JX. In addition, we prove the perceptibility of the formula F over JX. It is unknown whether the logic J+F is recognizable over J.

AB - In this paper the problems of recognizability and strong recognizavility, perceptibility and strong perceptibility in extensions of the minimal Johansson logic J [1] are studied. These concepts were introduced in [2, 3, 4]. Although the intuitionistic logic Int is recognizable over J [2], the problem of its strong recognizability over J is not solved. Here we prove that Int is strong recognizable and strong perceptible over the minimal pre-Heyting logic Od and the minimal well-composed logic JX. In addition, we prove the perceptibility of the formula F over JX. It is unknown whether the logic J+F is recognizable over J.

KW - Calculus

KW - Heyting algebra

KW - Johansson algebra

KW - Minimal logic

KW - Pre- Heyting logic

KW - Recognizability

KW - Strong recognizability

KW - Superintuitionistic logic

UR - http://www.scopus.com/inward/record.url?scp=85071154488&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=42735070

U2 - 10.33048/semi.2019.16.024

DO - 10.33048/semi.2019.16.024

M3 - Article

AN - SCOPUS:85071154488

VL - 16

SP - 427

EP - 434

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -