This article is cited in 6 scientific papers (total in 6 papers)
Joint consistency in extensions of the minimal logic
L. L. Maksimovaab
a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk
Analogs of Robinson's theorem on joint consistency are found which are equivalent to the weak interpolation property (WIP) in extensions of Johansson's minimal logic J. Although all propositional superintuitionistic logics possess this property, there are J-logics without WIP. It is proved that the problem of the validity of WIP in J-logics can be reduced to the same problem over the logic Gl obtained from J by adding the tertium non datur. Some algebraic criteria for validity of WIP over J and Gl are found.
minimal logic, interpolation, joint consistency.
PDF file (335 kB)
Siberian Mathematical Journal, 2010, 51:3, 479–490
L. L. Maksimova, “Joint consistency in extensions of the minimal logic”, Sibirsk. Mat. Zh., 51:3 (2010), 604–619; Siberian Math. J., 51:3 (2010), 479–490
Citation in format AMSBIB
\paper Joint consistency in extensions of the minimal logic
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
L. L. Maksimova, “Decidability of the weak interpolation property over the minimal logic”, Algebra and Logic, 50:2 (2011), 106–132
Maksimova L., “Interpolation and Definability Over the Logic Gl”, Stud. Log., 99:1-3, SI (2011), 249–267
L. L. Maksimova, “Interpolation and the projective Beth property in well-composed logics”, Algebra and Logic, 51:2 (2012), 163–184
L. L. Maksimova, “The decidability of craig's interpolation property in well-composed $\mathrm J$-logics”, Siberian Math. J., 53:5 (2012), 839–852
L. L. Maksimova, “The projective Beth property in well-composed logics”, Algebra and Logic, 52:2 (2013), 116–136
L. L. Maksimova, V. F. Yun, “Extensions of the minimal logic and the interpolation problem”, Siberian Math. J., 59:4 (2018), 681–693
|Number of views:|