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Siberian Mathematical Journal

, Volume 58, Issue 6, pp 1042–1051 | Cite as

Slices and Levels of Extensions of the Minimal Logic

  • L. L. Maksimova
  • V. F. Yun
Article
  • 13 Downloads

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

minimal logic Kripke frame decidability slice level recognizable logic 

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirsk State UniversityNovosibirskRussia

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