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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 5, Pages 1084–1090
DOI: https://doi.org/10.33048/smzh.2021.62.510 (Mi smj7616) 		 
Hybrid extensions of the minimal logic

L. L. Maksimova, V. F. Yun

Sobolev Institute of Mathematics, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/smzh.2021.62.510
Abstract: We consider some extensions of Johansson's minimal logic J. Hybrid logics extend the intersection of the intuitionistic logic Int and the negative logic Neg. We show that the perceptibility and recognizability of a hybrid logic are reduced to the analogous properties of its intuitionistic and negative counterparts. Also, the interpolation properties of a hybrid logic are reduced to those of its intuitionistic and negative counterparts. The restricted interpolation property IPR and the projective Beth property PBP are known to be equivalent in the well-composed logics. Here we give an easier proof of this fact for hybrid logics.
Keywords: minimal logic, Johansson's logic, hybrid logic, algorithmic properties, decidability, recognizable logic, perceptible formula, interpolation properties.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0002
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project 0314–2019–0002 “Formal Logical Languages, Their Semantics, and Algorithmic and Structural Properties”).
Received: 04.10.2020
Revised: 09.03.2021
Accepted: 14.04.2021
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 5, Pages 876–881
DOI: https://doi.org/10.1134/S0037446621050104
Bibliographic databases:
Document Type: Article
UDC: 510.64
MSC: 35R30
Language: Russian
Citation: L. L. Maksimova, V. F. Yun, “Hybrid extensions of the minimal logic”, Sibirsk. Mat. Zh., 62:5 (2021), 1084–1090; Siberian Math. J., 62:5 (2021), 876–881
Citation in format AMSBIB
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