Slices and Levels of Extensions of the Minimal Logic
- Authors: Maksimova L.L.1, Yun V.F.1
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Affiliations:
- Sobolev Institute of Mathematics
- Issue: Vol 58, No 6 (2017)
- Pages: 1042-1051
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171585
- DOI: https://doi.org/10.1134/S0037446617060131
- ID: 171585
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Abstract
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.
Keywords
About the authors
L. L. Maksimova
Sobolev Institute of Mathematics
Author for correspondence.
Email: lmaksi@math.nsc.ru
Russian Federation, Novosibirsk
V. F. Yun
Sobolev Institute of Mathematics
Email: lmaksi@math.nsc.ru
Russian Federation, Novosibirsk