TY - JOUR

T1 - Slices and Levels of Extensions of the Minimal Logic

AU - Maksimova, L. L.

AU - Yun, V. F.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - We consider two classifications of extensions of Johansson’s minimal logic J. Logics and then calculi are divided into levels and slices with numbers from 0 to ω. We prove that the first classification is strongly decidable over J, i.e., from any finite list Rul of axiom schemes and inference rules, we can effectively compute the level number of the calculus (J + Rul). We prove the strong decidability of each slice with finite number: for each n and arbitrary finite Rul, we can effectively check whether the calculus (J + Rul) belongs to the nth slice.

AB - We consider two classifications of extensions of Johansson’s minimal logic J. Logics and then calculi are divided into levels and slices with numbers from 0 to ω. We prove that the first classification is strongly decidable over J, i.e., from any finite list Rul of axiom schemes and inference rules, we can effectively compute the level number of the calculus (J + Rul). We prove the strong decidability of each slice with finite number: for each n and arbitrary finite Rul, we can effectively check whether the calculus (J + Rul) belongs to the nth slice.

KW - decidability

KW - Kripke frame

KW - level

KW - minimal logic

KW - recognizable logic

KW - slice

KW - INTERPOLATION

UR - http://www.scopus.com/inward/record.url?scp=85042168430&partnerID=8YFLogxK

U2 - 10.1134/S0037446617060131

DO - 10.1134/S0037446617060131

M3 - Article

AN - SCOPUS:85042168430

VL - 58

SP - 1042

EP - 1051

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 6

ER -