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.
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Funding
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”).
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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 5, pp. 1084–1090. https://doi.org/10.33048/smzh.2021.62.510
To Sergey Savost’yanovich Goncharov on His Anniversary.
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Maksimova, L.L., Yun, V.F. Hybrid Extensions of the Minimal Logic. Sib Math J 62, 876–881 (2021). https://doi.org/10.1134/S0037446621050104
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DOI: https://doi.org/10.1134/S0037446621050104
Keywords
- minimal logic
- Johansson’s logic
- hybrid logic
- algorithmic properties
- decidability
- recognizable logic
- perceptible formula
- interpolation properties