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.
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Original Russian Text Copyright © 2017 Maksimova L.L. and Yun V.F.
The authors were partially supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh–6848.2016.1).
Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 6, pp. 1341–1353, November–December, 2017
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Maksimova, L.L., Yun, V.F. Slices and Levels of Extensions of the Minimal Logic. Sib Math J 58, 1042–1051 (2017). https://doi.org/10.1134/S0037446617060131
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DOI: https://doi.org/10.1134/S0037446617060131